In person, Tuesdays, 12:00-2:00pm. 

Note: dates are subject to change, to give flexibility for topics to possibly run over into a second session.

Semester 1  in 54/5027 (5A)

27/09/22 - Group organizational meeting (via Teams)

04/10/22 - Zhiwei Wang

11/10/22 - Radu-Nicolae Moga

18/10/22 - Enrico Parisini

25/10/22 - Mritunjay Verma

01/11/22 - Jianrong Li (String seminar)

08/11/22 - Davide Bufalini

15/11/22 - Filip Landgren

22/11/22 - Yossi Nir (String Seminar) 

29/11/22 - Zezhuang Hao

06/12/22 - Arvind Shekar

[Winter break: 12 Dec 2022 - 13 January 2023]
[Exam period: 16-27 Jan 2023]

Semester 2 location varying from week to week, as indicated below.

31/01/23 - Ernesto Bianchi, 54/8033 (8B)

07/02/23 - Callum Hunter, 54/8033 (8B)

14/02/23 - David Sola Gil, 58/1023

21/02/23 - Alex Davey, 54/8033 (8B)

28/02/23 - Adam Bzowski (String Seminar), 54/8033 (8B)

07/03/23 - Pratyusha Chowdhury , 04/1035

14/03/23 - Alexander Tyukov, 02/5033

21/03/23 - Jack Holden, 02/5053

[Spring break: 24 March - 21 April 2023]

25/04/23 - No talk due to Eurostrings 2023

02/05/23 - Mritunjay Verma & Journal Club  ** Ketley room, 1pm-3pm**

09/05/23 - Federico Capone (String Seminar) & Journal Club   ** 100/5017, 1pm-3pm**

16/05/23 - Benjamin Withers & Journal Club   ** 54 / 7033 (7C), 1pm-3pm**

Topics: (reverse chronological order)

Benjamin Withers: Bounds on relativistic transport from causality

Abstract: I will present recent work deriving bounds on hydrodynamic transport coefficients of relativistic QFTs at finite temperature. The requirement that hydrodynamics emerges from a causal microscopic theory excludes most of transport coefficient space. I will discuss what is left behind.

Federico Capone: Phase Space Renormalization and Finite BMS charges in Six Dimensions

Abstract: In this talk I show how to settle the long-standing open question regarding the existence of BMS symmetries in higher dimensional non-linear gravity. For this purpose, we need a systematic analysis of the solution space at null infinity and the development of the phase space renormalization formalism. With the latter, divergences in the symplectic form are removed using an adapted notion of local and covariant counterterms. Finite BMS charges are then obtained. From this, the derivation of soft scattering theorems as Ward identities of the asymptotic symmetries follows smoothly.

Mritunjay Verma: S-matrix bootstrap techniques

Abstract: I shall review some basic tools and techniques used in the S-matrix bootstrap program. After introducing some basics of S-matrix, I shall consider various bounds and constraints which are obtained by imposing the requirements such as unitarity and crossing symmetry. In particular, I shall consider Froissart-Martin bound, Froissart-Gribov inversion formula and show how to constrain the coefficients appearing in low energy effective field theories using dispersion relations. 

Jack Holden: Small black holes, partial confinement and instanton condensation

Abstract: We argue that small 1/16-BPS black holes in $AdS_5$ should be understood as a partially confined phase in the dual field theory. These black holes are analogous to small thermal black holes in $AdS_5$, which are defined by their negative specific heat. We use the superconformal index to show that the small black hole saddle coincides with the condensation of instantons, or equivalently multi-cut eigenvalue distributions in the complex plane. We discuss the implications of this for characterising the ‘transition’ between the big and small black holes. This offers a synthesis to the disagreement between two schools of thought as to where the ‘Gross-Witten-Wadia’ transition lies in the black hole phase diagram. It is argued that these conclusions are likely to carry over to the thermal black hole phase diagram.

Alexander Tyukov: Holographic correlators in AdS_3 from fuzzball geometries

Abstract: In the first part I will review the fuzzball proposal and the way it attempts to resolve the black hole entropy problem and the information paradox. Then I will give a brief overview of the holographic description of fuzzball geometries in terms of pure states of dual D1D5 CFT. In the second part I will talk about how to use holography to calculate the heavy-heavy-light-light (HHLL) correlators by studying the supergravity fluctuations around the non-trivial fuzzball geometry. Finally, I will describe how to reconstruct the light-light-light-light (LLLL) correlator from the limit of HHLL correlator thus bypassing the use of Witten diagrams.   

Pratyusha Chowdhury: Mellin Amplitudes in AdS/CFT

Abstract: AdS doesn’t have a S-Matrix, but it has a close analogue - correlation function in the dual CFT. These are computed with the help of Witten diagrams but are often very hard and cumbersome. In this talk I will review the importance of Mellin Representation to study scattering amplitudes in AdS. I will start with a brief introduction to Mellin transform of CFT correlators. Further, I will show that in Mellin space these correlators have simple analytical structures and obey the factorization property similar to the flat space scattering amplitudes. Finally, I will arrive at some diagrammatic rules analogous to the Feynman rules for tree level Mellin amplitudes (in scalar theories) making it very easy to compute higher point correlators in Mellin space, which would be otherwise not possible in position space.

Alex Davey: Machine learning and string theory

Abstract: I will give a brief introduction to machine learning, focusing on neural networks. Then, I will discuss some recent literature applying machine learning to topics including numerical Calabi-Yau metrics and conformal bootstrap.

David Sola Gil: Black Hole Microstate Counting in AdS.

Abstract: Since the 70s black holes in GR are regarded as thermodynamic objects. In particular, they have an entropy: the Bekenstein-Hawking entropy, which depends on the area of the black hole horizon and the fundamental constants $c$, $k_B$, $\hbar$ and $G_N$. It is a current challenge for all theories of quantum gravity, including string theory, to account for this entropy from the statistical mechanics point of view and to identify the corresponding microstates.

Following the well-known paper of Strominger and Vafa in 1996, this has been achieved for several examples of asymptotically flat BPS black holes using String Theory. However, it was not until 20 years later that we managed to count microstates for  asymptotically AdS BPS black holes, by relying on the AdS/CFT correspondence.

This will be an introductory talk in the field. I aim to provide an overview of the terminology and main techniques employed for microstate counting in asymptotically AdS black holes. In addition, I will summarize the recent findings for these and briefly review an open question in the formalism.  

Callum Hunter: N−point Amplitudes in Pure Spinor SYM: A Pragmatic Approach

Abstract: In this talk I will introduce the required techniques to calculate Super Yang-Mills N-point amplitudes in D=10 using the perturbiner formalism using pure spinors. I will introduce the non-linear equations of motion for SYM and how one can use a generating series of Berends-Giele currents to solve these non-linear equations – it is this perturbiner method for solving the equations of motion that allow us to generate n-point amplitudes from compact expressions. I will demonstrate how to take the tree-level generating series and produce the n-point tree-level amplitudes. The pure spinor formalism also lends itself to determining higher-order corrections to SYM via its particularly simple BRST operator. I will show how one can take this operator and determine alpha’^2 and alpha’^3 corrections before going on to discuss the extension to alpha’^4 corrections and the complexities therein, including new identities derived in order to properly canonicalize the corrections.

Ernesto Bianchi: Bulk renormalization and the AdS/CFT correspondence

Abstract: We develop a systematic renormalization procedure for QFT in anti-de Sitter spacetime. UV infinities are regulated using a geodesic point-splitting method, which respects AdS isometries, while IR infinities are regulated by cutting off the radial direction (as in holographic renormalization). The renormalized theory is defined by introducing $Z$ factors for all parameters in the Lagrangian and the boundary conditions of bulk fields (sources of dual operators), and a boundary counterterm action, $S_{\rm ct}$, such that the limit of removing the UV and IR regulators exists. The results are in general scheme dependent (mirroring the analogous result in flat space) and require renormalization conditions. These may be provided by the dual CFT (or by string theory in AdS).  Our analysis amounts also to a first principles derivation of the Feynman rules regarding Witten diagrams. The presence and treatment of IR divergences is essential for correctly accounting for anomalous dimensions of dual operators. We apply the method to scalar $\Phi^4$ theory and obtain the renormalized 2-point function of the dual operator to 2-loops, and the renormalized 4-point function to 1-loop order, for operators of any dimension $\Delta$ and bulk spacetime dimension up to $d+1=7$.

Arvind Shekar: Entanglement Entropy and theories that yield islands on d dimensional AdS black hole

The study of entropy and entanglement entropy (EE) in field theories along with gravity has been fruitful in uncovering the inconsistencies within our theories such as the information paradox and has also provided us with a direction to resolve them. Motivated by studies of EE using the AdS/CFT conjecture, there has been a recent (2019) proposal first studied in (1+1) dim JT gravity called islands that possibly resolves the information paradox.  Our exploration of CFT EE on AdS_3 and BTZ backgrounds did not yield islands. So, what are the constraints on a QFT living on an AdS black hole background in general dimensions if it must yield islands (one way to resolve the paradox)?  I will present the ideas behind this and motivate our results based on our work exploring this while restricted to static AdS black holes in general dimensions. In the process we will also understand the subtleties behind calculating EE in an arbitrary radial region in this background (the study of EE in spacetime dim>2 has so far been restricted to flat backgrounds due to the technicalities involved). Before this, I will discuss entanglement entropy in QM, QFTs - why it is a suitable measure and what are its properties, when is it a well-defined quantity, how to calculate it, what it implies for black holes, what we know from AdS/CFT.  

Zezhuang Hao: Signatures of Physics: Euclidean, Minkowski and Klein

We will start from an introduction on how people usually do wick rotation between Euclidean and Minkowski. Then move on to the Klein.  Recent results (by S.Pasterski and H.Verlinde) show that out-of-time-ordered celestial correlators exhibit characteristics of maximal quantum chaos on the celestial torus. We will study their paper. Various problems concerning the central charge of celestial CFT will also be discussed.  

Filip Landgren: Renormalized entanglement entropy and islands in AdS3\CFT2. 

Abstract: Islands, as a potential resolution to the information paradox, has been extensively studied in 2d. A reason the study of islands has not been properly extended to 3d is due to the difficulty of computing the entanglement entropy of a CFT3 on an AdS3 background, which the Hawking radiation is being modelled as. I will present how to make this calculation as well as show that islands are absent in this construction when uplifting the well-studied 2d result to 3d. 

Davide Bufalini: Microstate correlators from the worldsheet

To account for all the bulk microstates of a three-charge black hole, the supergravity approximation may not suffice and full control over string theory may be essential. Recently, a specific family of black hole microstates was shown to admit an exact string worldsheet description. The worldsheet theory is a coset of the well-studied AdS3×𝕊3×𝕋4 model. This allows full control over the entire 𝛼′ corrections. I will show how to construct the physical vertex operators of these coset models, and how to compute an extensive set of novel heavy-light correlators. I will present a closed formula for correlators with an arbitrary number “n” of light insertions on top of the microstate background, written as a function of the corresponding n-point function on pure AdS3×𝕊3×𝕋4. A subset of these provides the first match between worldsheet correlators in black hole microstates and the holographically dual conformal field theory, in a highly non-trivial way.

Mritunjay Verma: Massive amplitudes from momentum space CFTs

There are evidences  that the perturbative S-matrices in the flat space can be obtained by taking the flat limits of CFT correlators. Some progress has been made in this direction for scalar and gauge fields. Most of these works have made use of the position and mellin spaces. In this work, we consider the CFT correlators involving non conserved tensorial oparators in momentum space and use these to obtain the flat space amplitudes involving spinning massive states by analysing the flat limit of AdS. 

Enrico Parisini: An embedding formalism for CFTs in general backgrounds and states

Conformal field theories exhibit a high level of control provided by conformal symmetry. However, in many relevant situations conformal symmetry is broken by either the state or the background of the theory, and most of the mathematical control is lost. In this talk I will present a framework generalising the embedding space formalism to compute the observables of CFTs in non-trivial states and on generic backgrounds. In this construction (d+2)-dimensional Minkowski is replaced by a more general Ricci-flat metric, the ambient space by Fefferman and Graham. As a test of the formalism, I will apply it to the case of 2-point functions in CFTs at finite temperature, showing exact agreement with a holographic computation and expectations from the thermal OPE.

Radu-Nicolae Moga: Grand Unification from Heterotic String Theory

Grand unified theories (GUTs) arising from string theory compactifications share many of the desirable features of traditional supersymmetric GUTs. At the same time, the additional structures arising from string theory make these GUTs much more versatile. String GUTs provide simple mechanisms for breaking the unified symmetry and can elegantly deal with problems such as the doublet-triplet Higgs splitting or rapid proton decay. This talk will review the early attempts at unification and then discuss the phenomenological advantages of SU(5) GUTs obtained as four-dimensional compactifications of the heterotic string on smooth Calabi-Yau threefolds with abelian holomorphic vector bundles. One of the salient features of this class of models is the presence of several Green-Schwarz anomalous U(1) symmetries which in the effective four-dimensional theory act as global symmetries (i.e. gauge symmetries with ultra-heavy gauge bosons). The U(1) symmetries have a rich phenomenology and this talk will present an example of resulting constraints on the allowed operators in the low-energy Lagrangian.

Zhiwei Wang: Quantum scrambling and high temperature & Energy definition for dynamical spacetimes

Black holes are conjectured to be the fastest quantum scramblers in nature, with the stretched horizon being the scrambling boundary. Under this assumption, we show that any infalling body must couple to virtually the entire black hole Hilbert space even prior to the Page time in order for there to be any hope of preserving the often-cited claim of the equivalence principle that such bodies should experience `no drama' as they pass a black hole's horizon. Further, under the scrambling assumption, we recover the usual firewall result at the black hole's Page time for an initially pure-state black hole without the need for any complexity or computational assumptions. For a black hole that is initially impure, we find that the onset of the firewall is advanced to times prior to the standard Page time. Finally, if black holes really do efficiently scramble quantum information, this suggests that, in order to preserve this claim of the equivalence principle even prior to the onset of a full-blown firewall, the quantum state of a black hole interior must be a Bose-Einstein condensate.

Noether's theorem identifies fundamental conserved quantities, called Noether charges, from a Hamiltonian. To-date Noether charges remain largely elusive within theories of gravity: We do not know how to directly measure them, and their physical interpretation remains unsettled in general spacetimes. Here we show that the surface gravity as naturally defined for a family of observers in arbitrarily dynamical spacetimes is a directly measurable Noether charge. This Noether charge reduces to the accepted value on stationary horizons, and, when integrated over a closed surface, yields an energy with the characteristics of gravitating mass. Stokes' theorem then identifies the gravitating energy density as the time-component of a locally conserved Noether current in general spacetimes. Our conclusion, that this Noether charge is extractable from astronomical observations, holds the potential for determining the detailed distribution of the gravitating mass in galaxies, galaxy clusters and beyond.

References:
1. Black holes, fast scrambling and the breakdown of the equivalence principle,
ZW Wang, S Das, SL Braunstein arXiv preprint arXiv:2206.02053
2. Noether charge astronomy, ZW Wang, SL Braunstein arXiv preprint arXiv:2105.14985