2015-2016 Seminars
All seminars take place on Wednesdays at 1pm, in room 54/10031 (10C, first term) or 54/10037 (10B, second term), unless otherwise indicated.
Please scroll down the page to read the abstracts.
29/09/15 [Tue 2pm in 54/8031 (8C)] - Ramy Brustein (Ben Gurion U) - Quantum state of the black hole
07/10/15 - Mike Blake (Cambridge) - Momentum Relaxation from the Fluid/Gravity Correspondence
14/10/15 - Francesco Aprile (Southampton) - Geometry and Entanglement in Type IIB Holography
21/10/15 - Gianluca Inverso (Nikhef) - Electric-magnetic deformations and gauged supergravities
28/10/15 - Christopher Eling (Oxford) - Turbulence and Random Geometry
03/11/15 [Tue 2pm in 54/8031 (8C)] - Francesco Sannino (CP3, Denmark) - Rethinking Fundamental Interactions: From Asymptotic freedom to Asymptotic Safety in QFT
11/11/15 - Tomas Andrade (Oxford) - Holographic momentum relaxation in the large D limit
18/11/15 - Hadi Godazgar (Cambridge) - Quantum corrections to Hawking radiation
25/11/15 - Christopher Rosen (Imperial) - Monopole Operators, RG Flows, and Fermi Surfaces in ABJM Theory
02/12/15 - Pablo Bueno (KU Leuven) - Universal entanglement of singular surfaces
09/12/15 - Francesco Benini (Imperial) - Black hole microstates in AdS from gauge theory
- Christmas break -
12/01/16 [Tue 2pm in 54/8031 (8C)] - Georgios Papathanasiou (SLAC) - The symmetry and integrability of amplitudes in N=4 super Yang-Mills theory
27/01/16 - Saso Grozdanov (Leiden) - From holographic transport at finite coupling to bounds on conductivities at strong disorder
03/02/16 - Hendrik Ulbricht (Southampton) - Prospects to use levitated optomechanics to test quantum mechanics and gravity
10/02/16 - Alejandra Castro (Amsterdam) - Higher Spin Black Holes
17/02/16 - Paul Heslop (Durham) - Correlation functions of half BPS operators in N=4 SYM
24/02/16 - Jorge Casalderrey Solana (Oxford) - Holographic Three-Jet Events in Strongly Coupled N=4 Yang-Mills Plasma
02/03/16 - Timothy Hollowood (Swansea) - Quantum Mechanics, Born Again
09/03/16 - Jorge Rocha (Barcelona) - Dynamics of confined double-shells systems, critical behavior and chaos
16/03/16 - Philip Szepietowski (Utrecht) - Computing black hole one-loop determinants from quasi-normal modes
21/03/16 - [Mon 3pm in 54/5025 (5B)] - Andrei Parnachev (Trinity College Dublin) - Constraints from unitarity in conformal field theories
- Easter break -
20/04/16 - Zachary Kenton (Queen Mary) - Soft Limits in Multi-Field Inflation
27/04/16 - Matthew Buican (Queen Mary) - Conformal Manifolds in Four Dimensions and Chiral Algebras
04/05/16 [Seminar at 1pm] Jay Armas (ULB Brussels) - Effective theories for bubbles, branes and black holes
11/05/16 - Markus Kunesch (DAMTP) - Black hole instabilities and weak cosmic censorship in higher dimensions
17/05/16 [Tue 9:30am in 54/10031 (10C)] - Jorge Russo (Barcelona) - D-branes in background fluxes and Nielsen-Olesen instabilities
18/05/16 [in 06 / 1081 (L/R B)]- Aalok Mishra (Indian Institute of Technology) - Holographic Thermal QCD at Finite Gauge Coupling('MQGP' Limit) and G-structures
25/05/16 - Mario Martone (Cincinnati) - Cancelled!
15/06/16 [in 46/2005]- Chrysostomos Kalousios (ICTP-SAIFR, Sao Paulo) - Towards expressing amplitudes in a compact form
Abstracts
Quantum state of the black hole
Ramy Brustein (Ben Gurion U)
Hawking has discovered more than 40 years ago that black holes (BH’s) evaporate. Ever since, ideas about how they evaporate have been a source of constant interest and controversy. In recent years we are witnessing a paradigm shift: from asking whether BH’s evaporation respects the laws of quantum mechanics to finding what is the quantum state of the BH and what are its physical properties. I will propose that the quantum state of BH interior is a highly quantum bound state and present a model for this maximally entropic state. The proposal relies on the observation that the state of the radiation emitted from a finite mass BH is highly quantum.
Momentum Relaxation from the Fluid/Gravity Correspondence
Mike Blake (Cambridge)
In this talk I will explain how to use the Fluid/Gravity correspondence to provide a hydrodynamical description of a holographic theory with broken translation invariance. Beyond leading order in the strength of momentum relaxation, the results differ from a model previously proposed by Hartnoll et al. As an application of these techniques, I will derive the low frequency thermoelectric transport coefficients of the holographic theory from the linearised hydrodynamics. Finally, I will discuss the DC limit of our hydrodynamics in detail, and show that our approach is equivalent to the `horizon-fluid' of Donos and Gauntlett.
Geometry and Entanglement in Type IIB Holography
Francesco Aprile (Southampton)
I will discuss the holographic entanglement entropy in BPS multi-centered p-brane solutions and bubbling geometries. Focusing on the p-brane geometries, these backgrounds provides examples of large-N RG flows in which UV degrees of freedom rearrange across spacetime and field theory space. The codimension-2 Ryu-Takayanagi surface gives a sharp characterization of such RG flows. In particular, through the formation of a separatrix, it detects topology changes of the internal space. This separatrix defines at each energy scale the common boundary between different pieces of geometry, it is a dynamical object and "mediates" interactions. I will show how this entangling structure is understood in the dual field theory, and how it can be used to refine the notion of separability/connectivity of an RG flow. Bubbling geometries can be analyzed with the same geometric tools.
Electric-magnetic deformations and gauged supergravities
Gianluca Inverso (Nikhef)
The analysis and classification of gaugings of supergravity theories is a crucial task required to differentiate models with distinct physical properties and construct new solutions of interest, for instance, for flux compactifications and/or holography. I will discuss general methods to classify solutions and gaugings of D=4 supergravity theories, rigorously identifying their duality orbits and their deformations, providing several new interesting examples and discussing their physics.
Turbulence and Random Geometry
Christopher Eling (Oxford)
Understanding fluid turbulence is a major challenge of physics. Despite much research, we still lack a theoretical model that can yield an analytical description of fluid flows in the highly non-linear regime. In 1941 Kolmogorov proposed that the statistics of turbulent flows in the inertial range of scales is scale invariant. However, experiments and numerical simulations indicate clearly that this is incorrect in direct cascades. Inspired by the link between fluids and black holes, we propose that turbulent statistics in any number of space dimensions can be described by a scale invariant statistics coupled to a type of random geometry. Our analytical formula for the turbulent structure function exponents has one free parameter. It satisfies the theoretical constraints and shows excellent agreement with experimental and numerical data in 3 and 4 space dimensions.
Rethinking Fundamental Interactions: From Asymptotic freedom to Asymptotic Safety in QFT
Francesco Sannino (CP3, Denmark)
I will discuss new exact results in four-dimensional quantum field theory that led to the discovery to asymptotically safe theories in four dimensions without supersymmetry. I will also discuss supersymmetric extensions and present new exact results that make use of a number of non-perturbative exact tools ranging from the unitary of the conformal operators to the a-theorem and maximisation. The results have far reaching consequences for the construction of novel extensions of the standard model of particle interactions.
Holographic momentum relaxation in the large D limit
Tomas Andrade (Oxford)
In the context of the gauge/gravity duality, momentum relaxation can be incorporated in a simple way by considering bulk matter fields that enjoy a global symmetry. In some cases, we can write down the relevant black hole solutions in an arbitrary dimension which makes it possible to study the limit in which the number of dimensions goes to infinity. We will consider a simple example of this kind and obtain certain physical properties analytically in an expansion of inverse powers of the number of space-time dimensions.
Quantum corrections to Hawking radiation
Hadi Godazgar (Cambridge)
Black holes are one of the few available laboratories for testing theoretical ideas in fundamental physics. Since Hawking's result that they radiate a thermal spectrum, black holes have been regarded as thermodynamic objects with associated temperature, entropy, etc. While this is an extremely beautiful picture it has also lead to numerous puzzles. In this talk I will describe the two-loop correction to scalar correlation functions due to \phi^4 interactions and explain why this might have implications for our current view of semi-classical black holes.
Monopole Operators, RG Flows, and Fermi Surfaces in ABJM Theory
Christopher Rosen (Imperial)
In 2+1 dimensional field theories, a well known "particle-vortex" duality rephrases a system with a gauged U(1) in terms of "magnetic" variables that can be more convenient for performing calculations. These magnetic variables have historically proven useful for understanding the possible phases available to interacting matter at finite density, which is a problem of great interest across many fields of physics.
By virtue of the AdS/CFT correspondence, the ABJM theory provides an excellent testing ground for the physics of strongly interacting matter at finite density in three dimensions. There too operators carrying magnetic flux arise, and it is natural to wonder how this "composite" matter behaves when placed at finite density. Holographically, we investigate this question by studying the fermion spectral function for composite fermions in the ABJM theory by solving the Dirac equation for linearized fermionic fluctuations around particular solutions of N=8 maximal gauged supergravity in four dimensions. The backgrounds of interest correspond to zero temperature phases in which the monopole number density has been broken, and are examples of holographic RG flows. We find that these candidate ground states appear to support Fermi surfaces of composite fermions, and that the low energy fermionic fluctuations around these Fermi surfaces are perfectly stable within a particular kinematic window. In addition to an explicit identification of the participating field theory operators, the model's top-down pedigree also allows for some basic information about the stability of these states at low temperatures.
Universal entanglement of singular surfaces
Pablo Bueno (KU Leuven)
The entanglement entropy in three-dimensional conformal field theories (CFTs) receives a logarithmic contribution characterized by a regulator-independent function a(θ) when the entangling surface contains a sharp corner with opening angle θ. In the smooth-surface limit, (θ → π), this corner contribution vanishes as a(θ) = σ(θ−π)^2. I will review our recent conjecture that for any three-dimensional CFT, this corner coefficient σ is determined by C_T, the coefficient appearing in the two-point function of the stress tensor through the relation σ/CT = π^2/24. I will also describe the extension of this conjecture to general Rényi entropies and higher-dimensional CFTs, and comment on the implications of our findings.
Black hole microstates in AdS from gauge theory
Francesco Benini (Imperial College)
One of the great successes of string theory, as a theory of quantum gravity, is the explanation of the entropy of asymptotically-flat black holes. I will present, instead, a counting of the microstates of certain black holes in AdS4. The black holes have an holographic description as RG flows from a 3D CFT to superconformal quantum mechanics, and the counting of microstates proceeds via supersymmetric localization. Along the way, we will define and compute an index for topologically twisted theories, and propose an extremization principle to determine the superconformal R-symmetry in quantum mechanics.
The symmetry and integrability of amplitudes in N=4 super Yang-Mills theory
Georgios Papathanasiou (SLAC)
N=4 super Yang-Mills theory stands out as an interacting 4-dimensional gauge theory which may be exactly solvable in the planar limit. In this talk, I report on recent progress in exploiting the symmetry and integrability of the theory, for the computation of its scattering amplitudes. For the 6-particle MHV amplitude, integrability leads to explicit expressions up to 5 loops in near-collinear kinematics, from which we may also produce all logarithmic terms in the multi-Regge limit; and for 7 particles, the symmetry of the kinematic space, supplemented by a limited set of reasonable assumptions, uniquely fix the symbol of the amplitude in general kinematics up to 3 loops.
From holographic transport at finite coupling to bounds on conductivities at strong disorder
Sašo Grozdanov (Leiden University)
Holography is a tool that can be most readily applied to studies of transport properties in gauge theories with infinitely strong interactions. Coupling constant corrections can then be incorporated through higher-derivative (alpha-prime) corrections to the supergravity action in the bulk. In the first part of this talk, I will discuss the dependence of higher-order hydrodynamic transport (beyond Navier-Stokes) and the higher-frequency (quasi-normal) spectrum on the coupling constant in duals of Type IIB supergravity and curvature-squared theories. In relation to the membrane paradigm, I will then present higher-order generalisations of the universal "eta over s" relation and universal anomalous conductivities at finite coupling. Recently, studies of holographic transport in the presence of broken translational symmetry and disorder have received much attention. In particular, it has been shown how thermo-electric conductivities can be computed by using the membrane paradigm. Through the power of the membrane paradigm and with a view towards future models of many-body localisation without hydrodynamic transport, in the second part of this talk, I will discuss the proofs of the lower bounds on thermal and electrical conductivities in a large family of holographic theories with arbitrarily strong disorder.
Prospects to use levitated optomechanics to test quantum mechanics and gravity
Hendrik Ulbricht (Southampton)
We will discuss ideas to experimentally test collapse models [1] by both matter-wave interferometry [2] and non-interferometric methods [3]. Testing collapse models intrinsically also means to test the quantum superposition principle. Collapse models predict a heating effect, which results in a Brownian-like random motion of any isolated particle in space. We will emphasise levitated optomechanical systems and discuss the possibility to test the heating effect by detecting the motion of the particle in position space [4], as well as in the frequency domain where the collapse heating effect is theoretical treated as noise in a Langevin type approach and predicted to manifest itself as an increase of the area of the related power spectral density [3]. We shall also explain if gravitation decoherence has strong prospects to be tested with levitated optomechanical systems.
We will further discuss some recent ideas to probe the interplay between quantum mechanics and gravitation. One idea is to try to directly test if gravity is quantum or classical [5], while a second is to test an effect which is predicted for semi-classical gravity (Schro ̈dinger-Newton equation)[6], which would allow to experimentally test whether that semi-classical approach is valid or not.
We shall also give an update on trapping and cooling experiments of levitated optomechanics at Southampton in order to explore the experimental feasibility of tests of quantum mechanics and gravitation. The overarching goal of our attempts is to build a complete toolbox to generate and manipulate Gaussian but also non-Gaussian states, such as a spatial superposition state, of the motion of nano- and micro-particles in order to realise all possible states of the motional dynamics in phase space. This to be done for massive nanoparticles and the systematic investigation of noises will further the prospects for sensing applications of levitated optomechanics too.
References:
[1] Bassi, A., K. Lochan, S. Satin, T.P. Singh, and H. Ulbricht, Models of Wave-function Collapse, Underlying Theories, and Experimental Tests, Rev. Mod. Phys. 85, 471 - 527 (2013),
[2] Bateman, J., S. Nimmrichter, K. Hornberger, and H. Ulbricht, Near-field interferometry of a free-falling nanoparticle from a point-like source, Nat. Com. 5, 4788 (2014), Wan, C.,et al.. Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions, arXiv:1511.02738 (2015).
[3] Bahrami, M., M. Paternostro, A. Bassi, and H. Ulbricht, Non-interferometric Test of Collapse Models in Optomechanical Systems, Phys. Rev. Lett. 112, 210404 (2014).
[4] Bera, S., B. Motwani, T.P. Singh, and H. Ulbricht, A proposal for the experimental detection of CSL induced random walk, Sci. Rep. 5, 7664 (2015).
[5] Bahrami, M., A. Bassi, S. McMillen, M. Paternostro, and H. Ulbricht, Is Gravity Quantum?, arXiv:1507.05733 (2015).
[6] Grossardt, A., J. Bateman, H. Ulbricht, and A. Bassi, Optomechanical test of the Schrödinger-Newton equation, arXiv:1510.01696 (2015).
Higher Spin Black Holes
Alejandra Castro (Amsterdam)
I'll overview recent progress on non-perturbative aspects of higher spin theories in three dimensions with emphasis on black holes. The two main results I will discuss are: 1) novel properties of extremal and BPS solutions, and 2) how to interpret a higher spin bh as a thermo-field state.
Correlation functions of half BPS operators in N=4 SYM
Paul Heslop (Durham)
Correlation functions of half BPS operators in planar N=4 SYM are dual (at strong coupling, via AdS/CFT) to supergravity in AdS_5xS^5. At weak coupling in the limit where the operators are consecutively lightlike separated, they yield scattering amplitudes. At four-points they contain within them information about an infinite number of 3-point functions involving more complicated operators, which have been the subject of a recent remarkable conjecture using integrability. In this talk, I will review the progress over the last few years in computing these correlation functions perturbatively, culminating in the recent eight loop result for the 4-pnt stress-energy correlator and the result for all half-BPS 4-pnt correlators at 3 loops.
Holographic Three-Jet Events in Strongly Coupled N=4 Yang-Mills Plasma
Jorge Casalderrey Solana (Oxford)
We analyse classical string configurations with non-trivial transverse dynamics in AdS5-Schwarzschild. These strings develop kink-like structures which, via the gauge/gravity duality, can be interpreted as the propagation of hard gluons produced in association with a quark-antiquark pair in a strongly coupled N=4 SYM plasma. We observe the appearance of two physically distinct regimes of the in-plasma dynamics, depending on whether the medium is able to resolve the transverse structure of the string prior to its total quench. From these studies we extract the medium resolution scale of the strongly coupled SYM plasma, defined as the smallest angular separation between two jets that the medium can resolve. Our analysis constitutes the first study of proxies for three-jet events in a holographic context.
Quantum Mechanics, Born Again
Tim Hollowood (Swansea)
I will start by explaining why the interpretational problem of quantum mechanics is much worse than the so-called measurement problem. However, the problem is not really with quantum mechanics itself but rather how the classical world arises from it. Then I will describe a way to think about the quantum to classical transition that is inspired by Wilson's approach to quantum field theory, i.e. effective theories; cut offs; coarse graining, etc. The usual rules of the Copenhagen Interpretation emerge from the view point I establish, but the approach has important things to say about the foundations of statistical mechanics as well.
Dynamics of confined double-shells systems, critical behavior and chaos
Jorge Rocha (Barcelona)
I will present a study of gravitational collapse in confined spaces employing the simplest possible two-body setting: a system composed of two thin shells in spherical symmetry. Confinement is introduced either by putting the system inside a totally reflecting spherical cavity or by formulating the problem in anti-de Sitter (AdS) spacetime. The two shells interact only through their gravitational attraction. The problem amounts to solving just two decoupled ODEs but it features highly non-trivial dynamics: depending on initial data, one observes prompt collapse, perpetual oscillations or black hole formation on arbitrarily long timescales. This confined double-shell system exhibits critical behavior reminiscent of the ``turbulent'' dynamics of massless scalar fields in AdS, as well as chaotic behavior. The AdS and the cavity settings show qualitatively similar dynamics, but there are some quantitative differences.
Computing black hole one-loop determinants from quasi-normal modes
Philip Szepietowski (Utrecht)
Denef, Hartnoll and Sachdev (DHS) provided a beautiful expression for the one-loop determinant of an operator in a black hole background in terms of the associated quasinormal mode (QNM) frequencies. Several checks of this proposal have been performed in the literature for cases where the full QNM spectrum is known analytically. However, in many interesting cases (such as asymptotically AdS black holes in dimensions greater than three) the QNM frequencies are only known numerically -- with analytic results known only in various limiting approximations. In this talk I will discuss work in progress towards applying the formalism of DHS to situations where the QNM spectrum is not fully known analytically and will describe a proposed procedure for computing such one-loop determinants numerically.
Constraints from unitarity in conformal field theories
Andrei Parnachev (Trinity College Dublin)
We discuss implications of unitarity in CFTs and derive
a number of constraints, including positivity of energy flux constraint.
Soft Limits in Multi-Field Inflation
Zachary Kenton (Queen Mary)
Soft limits of inflationary correlation functions are sensitive to the number of light fields during inflation. I will begin with the calculation of the soft (squeezed) limit of the bispectrum in multifield inflation. I will then discuss the soft limits of the trispectrum and higher n-point functions. I’ll show novel relations and inequalities between soft limits of n-point functions and soft limits of lower-point functions. We apply our results to observational probes and compare our results with previous formulae, finding a 20% theoretical correction to observable parameters for squeezings relevant to future cosmological experiments. This work is based on our paper http://arxiv.org/abs/1507.08629 and work soon to appear.
Conformal Manifolds in Four Dimensions and Chiral Algebras
Matthew Buican (Queen Mary)
Any N = 2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral algebra is a Virasoro algebra. In this talk, I will consider the chiral algebras associated with interacting N = 2 SCFTs possessing an exactly marginal deformation that can be interpreted as a gauge coupling (i.e., at special points on the resulting conformal manifolds, free gauge fields appear that decouple from isolated SCFT building blocks). At any point on these conformal manifolds, I will argue that the associated chiral algebras possess at least three generators. In addition, I will show that there are examples of SCFTs realizing such a minimal chiral algebra: they are certain points on the conformal manifold obtained by considering the low-energy limit of type IIB string theory on a particular three complex-dimensional hyper surface singularity I will describe. The associated chiral algebra is the A(6) theory of Feigin, Feigin, and Tipunin. As byproducts of this discussion, I will argue that (i) a collection of isolated theories can be conformally gauged only if there is a SUSY moduli space associated with the corresponding symmetry current moment maps in each sector, and (ii) N = 2 SCFTs with a ≥ c have hidden fermionic symmetries (in the sense of fermionic chiral algebra generators).
Effective theories for bubbles, branes and black holes
Jay Armas (ULB Brussels)
Black holes in certain regimes of parameter space are described by long-wavelength effective theories. The resulting dynamics, after integrating out the short-wavelength degrees of freedom, is usually of hydrodynamic and/or elastic character while the resulting theories are relativistic generalisations of theories of fluid mechanics, soap bubbles, fluid droplets or of elasticity of biophysical membranes. I will review the several different contexts in which these effective theories can be useful, either in pure gravity, string theory or in the AdS/CFT correspondence and discuss the several different types of (in some cases novel) theories of hydrodynamics that have been developed from gravity. In particular, using these theories, I will highlight recent developments in the classification of horizon geometries, in the perturbative construction of non-trivial black holes solutions in pure gravity and the role of minimal surface theory. Furthermore, I will discuss the role of hydrodynamic theories with boundaries and, if time permits, I will also discuss different methods for evaluating the equilibrium partition function and the equations of motion for hydrodynamic fluctuations of branes in string theory.
Black hole instabilities and weak cosmic censorship in higher dimensions
Markus Kunesch (DAMTP)
In this talk I will present the results of fully nonlinear numerical simulations of black rings and Myers-Perry black holes in five and six dimensions. Most importantly, our simulations of black rings provide the first concrete evidence that the weak cosmic censorship conjecture can be violated in five dimensional asymptotically flat spacetimes. Furthermore, we have discovered a new instability in black rings which stretches the ring without substantially changing its thickness. This instability completely dominates the evolution for rings of intermediate thickness and always leads to the collapse to a black hole of spherical topology. For very thin rings the Gregory-Laflamme instability becomes dominant and eventually gives the ring a fractal structure of bulges connected by necks which become ever thinner over time. I will argue that this suggests that very thin black rings break and hence violate weak cosmic censorship.
D-branes in background fluxes and Nielsen-Olesen instabilities
In quantum field theory, charged particles with spin ≥1 may become tachyonic in the present of magnetic fluxes above some critical field, signaling an instability of the vacuum. The phenomenon is generic, in particular, similar instabilities are known to exist in open and closed string theory, where a spinning string state can become tachyonic above a critical field. In compactifications involving RR fluxes, the quantum states which could become tachyonic by the same Nielsen-Olesen mechanism are Dp branes. By constructing an appropriate background with RR magnetic flux, and computing its energy spectrum, we argue that there are high spin Dp quantum states which become very light at critical fields.
Holographic Thermal QCD at Finite Gauge Coupling('MQGP' Limit) and G-structures
Aalok Mishra (Indian Institute of Technology)
We will discuss the delocalized Strominger-Yau-Zaslow mirror of the McGill type IIB dual of large-N thermal QCD involving N black D3-branes, M D5 (and anti-D5) branes wrapping a two-cycle and N_f D7 (and anti-D7) branes embedded via the Ouyang embedding in a non-Kaehler resolved warped deformed conifold (NKRWDC), and its M-theoretic uplift to black M3-branes. We will do so in a large-N limit referred to as the MQGP limit involving gs<~1. We will discuss torsion class chasing from type IIB to type IIA and a local G_2 structure of the M-theory uplift. Using the prescription of Son et al, we will discuss evaluation of a host of transport coefficients from appropriate correlation functions at leading and next-to-leading order in N in the MQGP limit.
Towards expressing amplitudes in a compact form
Chrysostomos Kalousios (ICTP-SAIFR, Sao Paulo)
In a series of papers by Cachazo-He-Yuan it was suggested that tree level massless scattering in arbitrary dimensions can be elegantly expressed in terms of solutions of a polynomial set of equations, called scattering equations. Recent progress has been made towards an explicit evaluation of arbitrary point amplitudes. I will present such a method and argue that one can use elementary algebraic operations to compactly express massless scattering.