Sergey Alexandrov (Université de Montpellier, France) - Modular bootstrap for BPS black holes
BPS indices encoding the entropy of supersymmetric black holes in compactifications of Type II string theory on Calabi-Yau threefolds, known in mathematics as generalized Donaldson-Thomas invariants, possess remarkable (mock) modular properties. I'll explain the physical origin of mock modularity and show, for a set of one-parameter threefolds, how it can be used, together with wall-crossing and direct integration of topological string, to compute the BPS indices and other topological invariants. As a result, one obtains explicit (mock) modular functions encoding infinite sets of D4-D2-D0 BPS indices as well as new boundary conditions for the holomorphic anomaly equation of the topological string partition function allowing to overcome the limitations of the direct integration method. In the end, I'll present prelimenary results on the asymptotic growth of DT invariants hinting for the existence of some phase transitions.
Ralph Blumenhagen (Max-Planck-Institut für Physik, Munich, Germany) - Emergence of CY triple intersection numbers
To give more credence to the M-theoretic Emergence Proposal it is important to show that also classical kinetic terms in a low energy effective action arise as a quantum effect from integrating out light towers of states. We show that for compactifications of type IIA on Calabi-Yau manifolds, the classical weak coupling Yukawa couplings, which are the triple intersection numbers of the Calabi-Yau threefold, can be obtained from the 1/2-BPS protected one-loop Schwinger integral over bound states, after employing a novel regularization for the final infinite sum of Gopakumar-Vafa invariants. Approaching the problem in a consecutive manner from 6D decompactification over emergent string to the ultimate M-theory limits, we arrive at a mathematically concrete regularization that involves finite distance degeneration limits of Calabi-Yau threefolds in an intriguing way. We test and challenge this proposal by the concrete determination of the periods around such degeneration points for threefolds with one Kähler modulus and two examples.
Robert de Mello Koch (Huzhou University, China & University of the Witwatersrand, South Africa) - Hilbert Space at Finite N
We study the Hilbert space structure of gauge-invariant operators emergent in large- multi-matrix quantum mechanics. Concretely this entails solving the complete set of trace relations, at finite N. The result is that space of gauge invariant operators admits a Hironaka decomposition, with generators given by the primary and secondary invariants of the algebra of invariants. The growth in the number of secondary invariants indicates that most of these invariants have a dimension of order $N^2$ and hence correspond to new spacetime backgrounds. We also identify a class of light single-trace secondary invariants that behave like free creation operators at low energy but saturate beyond a critical excitation level, ceasing to generate new states. This -reducibility is a direct consequence of finite N trace identities and leads to a dramatic truncation of the high-energy spectrum of the emergent theory. The resulting number of independent degrees of freedom is far smaller than naïve semiclassical expectations, providing a concrete mechanism for how nonperturbative constraints shape the ultraviolet behaviour of emergent theories.
Luca Iliesiu (University of California, Berkeley, USA) - The evaporation of black holes in supergravity
In supergravity, charged rotating black holes are generically driven towards becoming extremal and supersymmetric through the emission of Hawking radiation. Eventually, as the black hole approaches the BPS bound and is close to becoming supersymmetric, quantum gravity corrections become critical to describing the emission of Hawking radiation, making the QFT in curved spacetime approximation inaccurate. In this paper, we compute how such quantum gravity corrections affect the spectrum of Hawking radiation for black holes in supergravity in flatspace. We show that due to such corrections, the spectrum of emitted Hawking radiation for both spin-0 and spin-1/2 particles deviates drastically at low temperatures from the naively expected black-body spectrum. Rather remarkably, the spectrum exhibits a discrete emission line from direct transitions from near-BPS to BPS states, providing the first controlled example where the discreteness of the black hole energies is visible in the emitted Hawking radiation. Similar quantum gravity effects drastically modify the absorption cross-section: BPS black holes are transparent to certain frequencies, while near-BPS black holes appear much larger than the semi-classical prediction.
Thomas Mohaupt (University of Liverpool, UK) - T-duality and Killing horizons
The Buscher rules become singular for null isometries. When applying T-duality to space-times containing Killing horizons, such as the Schwarzschild or Reissner-Nordstrom solution, the horizon is mapped to a curvature singularity, while the curvature singularity is also mapped to a curvature singularity. Both types of singularities arise at infinite distance in moduli space, but at finite distance in space-time. We argue that when embedding such space-times into type-II string theory, the singularities are related to towers of light states associated with strings becoming tensionless. We also report on recent and ongoing work on analysing these singularities in the framework of generalised geometry.
Hermann Nicolai (Max Planck Institute for Gravitational Physics, Potsdam, Germany) - N=8 supergravity, and beyond
This talk will provide a panoramic overview of the development of N = 8 supergravity and its relation to other maximally supersymmetric theories over the past 45 years, highlighting distinguishing features of this theory. I will also discuss its future perspectives for attempts at unification and quantising gravity.
Ioannis Papadimitriou (National and Kapodistrian University of Athens, Greece) - Near-extremal dynamics away from the horizon
Near-extremal black holes are usually studied by zooming into the throat that describes their near-horizon geometry. Within this throat, one can argue that two-dimensional JT gravity is the appropriate effective theory that dominates at low temperature. Here, we discuss how to capture this effective description by standing far away from the horizon. Our strategy is to construct a phase space within gravitational theories in AdS$_{d+1}$ that fixes the radial dependence while keeping the transverse dependence arbitrary. This allows us to implement a decoupling limit directly on the phase space while keeping the coordinates fixed. With this, we can relate the effective description in JT gravity to the CFT$_{d}$ description at the boundary of AdS$_{d+1}$, which we do explicitly in AdS$_{3}$ and non-rotating configurations in AdS$_{4}$.
Julio- Parra Martinez (Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France) - Soft theorems from Higher Symmetries
I will explain a direct connection between continuous higher symmetries and soft theorems in scattering amplitudes of Nambu-Goldstone-Bosons, including new examples in theories with higher-group symmetry.
Jan Plefka (Humboldt-Universitär zu Berlin, Germany) - High precision classical black hole scattering with worldline quantum field theory
The gravitational two-body problem has been fundamental to physics since Newton's time. With the advent of gravitational wave astronomy and the anticipated third generation of gravitational wave detectors in the 2030s, there is an increasing need for high-precision predictions from Einstein's theory of gravity regarding the encounters of black holes and neutron stars in our universe. Fascinatingly, perturbative quantum field theory methods have proven remarkably efficient for this classical physics problem. This unexpected connection has led to inspiring synergies between collider and gravitational wave physics. I will review our approach using a worldline quantum field theory inspired by string theory, which has emerged as the most efficient tool for quantifying the classical scattering of black holes. We have achieved the highest-precision results for the scattering angle, radiated energy, and recoil of such black hole encounters at the fifth order in Newton's gravitational coupling G, assuming a mass hierarchy between the two bodies. Our four-loop analytical calculations feature the appearance of a new class of mathematical functions related to Calabi-Yau manifolds for the first time in an observable quantity.
Gustavo Turiaci (University of Washington, Seattle, USA) - Supersymmetric gravitational indices
Hendrik van Zyl (University of Cape Town, South Africa) - Perspectives on Krylov Complexity
In recent years Krylov Complexity (and its counterpart for quantum states, spread complexity) has emerged as a quantity that can diagnose many significant features of quantum systems such as phase transitions, information scrambling and thermalization. The most common way that K-complexity is computed is by means of the Lanczos algorithm, a recursive algorithm that brings the Hamiltonian of the system into tri-diagonal form. In this talk I would like to highlight other computational techniques for spread complexity, some of which are well-explored and others which are recent developments. In particular, I will highlight a recent approximation scheme which obtains the Krylov basis as a limiting case of an orthogonal basis obtained from two operations, namely unitary time-evolution and superposition. This perspective may allow the spread complexity of quantum states to be measured experimentally.