Academic Year 2024/2025

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

A-model topological string amplitudes enumerate holomorphic curves with Lagrangian boundary conditions in Calabi-Yau threefolds. Through string dualities, these open string correlators are linked to the dynamics of certain BPS sectors in M-theory, as well as to aspects of three-dimensional N=2 supersymmetric quantum field theories. This talk will explore the physical implications of recent advances arising from novel connections between topological strings and the mathematics of quivers, skein modules, and Legendrian contact homology.

In this talk, I will show an approach to compute Hawking radiation based on on-shell scattering amplitudes. The Hawking spectrum is obtained by exponentiating a series of Feynman diagrams describing a massless scalar field scattering through a collapse background. Using semiclassical methods, we obtain a generalized an in-in generalisation of an amplitude closely connected to the Bogoliubov coefficients. Finally, I will show how subdominant one-loop correction can be interpreted as finite-size corrections sensitive to the radius of the black hole.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

Kaluza-Klein theory has a variety of different static black hole solutions and for fixed circle size, multiple solutions with the same mass co-exist. In my talk, I will conjecture that for fixed mass and sufficiently small circle size, the only black holes are the homogeneous ones and I will give evidence that this is indeed the case. Firstly, I will consider a scalar field model with a potential that allows tachyonic behaviour on a product of Minkowski with a circle. This toy model gives an analogous set of static homogeneous and inhomogeneous solutions. I will prove homogeneity of the solutions for small circle size. Turning to the full gravitational theory, I will show that as the circle size becomes small, the solution becomes increasingly homogeneous. To conclude, a new approach to uniqueness theorems will be introduced, using Sobolev spaces and elliptic analysis, leading to a local rigidity statement.

I will discuss different ways to resum expansions with zero, finite or infinite radius of convergence using only a finite number of terms. In real applications, one can usually only calculate O(10) coefficients, so the goal is to construct resummations which converge quickly. One can do this by incorporating additional information about the function into the resummation. Several new resummation methods have been developed in recent years. One can, for example, use coefficients from both the small x and the large x expansions. One can also use resurgence, which relates late terms in the small x expansion to early terms in an expansion around a different point. I will illustrate these ideas with applications in strong-field-QED, but the ideas are general.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

I will discuss the large-N limit of two-dimensional symmetric product orbifolds. The goal is to single out which symmetric product orbifold theory could lead to a strongly coupled point in their moduli space, whose dual could be a semi-classical theory of AdS_3 gravity. To this end, we consider the symmetric product orbifold of N=(2,2) SCFT_2, and classify them according to two criteria. The first criterion is the existence of a single-trace twisted exactly marginal operator in their moduli space. The second criterion is a sparseness condition on the growth of light states in the elliptic genera. In this context, we encounter a strange variety: theories that obey the first criterion but the second criterion falls into a Hagedorn-like growth. I will explain why this may be counter-intuitive and discuss how it might be accounted for in conformal perturbation theory. I will also present a new infinite class of theories that obey both criteria, which are necessary conditions for their moduli spaces to contain a supergravity points.

Often in a physical problem there are some degrees of freedom that we treat as unobservable because the energy required to excite them is much greater than the energy scale of the problem. For example, when modelling a pendulum with a rigid arm we ignore the vibrational modes of the arm. Or in quantum physics it may be that the energy scales available to us, for example in a collider, are not sufficient to create a particular heavy particle. These unobservable degrees of freedom can still affect the physics that we do observe at subleading order. A tool that is often used by to study this is the machinery of effective field theory (EFT). In this talk I will discuss work with Harvey Reall in which we studied a classical EFT for a model problem and gave a prescription to handle the ill-posed PDE problems that typically arise.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

I will present an integrable long-range version of the XX model, arising as the free-fermion point of the Haldane--Shastry spin chain. It has a description via non-unitary fermions, based on the free-fermion Temperley--Lieb algebra. Even and odd length behave very differently; I will mostly focus on odd length. I will explicitly give two commuting hamiltonians. While non-unitary, their spectrum is real by PT-symmetry. One hamiltonian is chiral and quadratic in fermions, while the other is parity-invariant and quartic. Their one-particle spectra have two linear branches, realising a massless relativistic dispersion on the lattice. The appropriate fermionic modes arise from 'quasi-translation' symmetry, which replaces ordinary translation symmetry. The model exhibits exclusion statistics, like the isotropic Haldane--Shastry chain, with even more 'extended symmetry' and larger degeneracies.

Automorphic Lie algebras are a class of infinite-dimensional Lie algebras over the complex numbers that naturally arise in mathematical physics, particularly in the context of integrable systems. These algebras originally appeared in the context of reduction of Lax pairs. They can be thought of as Lie algebras of meromorphic maps (usually with prescribed poles) from a compact Riemann surface $X$ into a finite-dimensional Lie algebra $\mathfrak{g}$ which are equivariant with respect to a finite group $G$ acting on $X$ and on $\mathfrak{g}$, both by automorphisms. Independently of their origins in integrable systems, they show up in algebra as equivariant map algebras. In this talk we will highlight some motivations from integrable systems to study these algebras. We will mainly focus on elliptic automorphic Lie algebras, which, for example, appear in the context of Landau-Lifshitz type of equations. We show that well-known algebras, such as Holod's hidden symmetry algebra of the Landau-Lifshitz equation and the Wahlquist-Estabrook prolongation algebra of the same equation, have a particularly simple structure which is revealed when adopting the automorphicity viewpoint: they turn out to be isomorphic to a current algebra $\mathfrak{sl}(2,\mathbb{C})\otimes R$, where $R$ a suitable ring of elliptic $D_2$-invariant functions, where $D_2$ is the dihedral group of order 4.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

We elucidate the relationship between 2d integrable field theories and 2d integrable lattice models, in the framework of the 4d Chern-Simons theory. The 2d integrable field theory is realized by coupling the 4d theory to multiple 2d surface order defects, each of which is then discretized into 1d defects. We find that the resulting defects can be dualized into Wilson lines, so that the lattice of discretized defects realizes integrable lattice models. Our discretization procedure works systematically for a broad class of integrable models (including trigonometric and elliptic models), and uncovers a rich web of new dualities among integrable field theories. We also study the anomaly-inflow mechanism for the integrable models, which is required for the quantum integrability of field theories. By analyzing the anomalies of chiral defects, we derive a new set of bosonization dualities between generalizations of massless Thirring models and coupled Wess-Zumino-Witten (WZW) models. We study an embedding of our setup into string theory, where the thermodynamic limit of the lattice models is realized by polarizations of D-branes.

The post-Newtonian expansion has been instrumental in understanding and producing predictions for general relativity since its inception. Post-Newtonian gravity continues to be a vital tool for many applications of general relativity today, not least gravitational wave physics. Modern post-Newtonian theory (of the type that directly solves for the metric) is dominated by approaches that rely entirely on applying the harmonic gauge condition from the very outset. These approaches have been enormously successful in producing high order corrections. However, despite what some believe, harmonic gauge is not the only gauge for which the post-Newtonian field equations reduce to a reasonable set of PDEs. In this talk, I will present a new framework for post-Newtonian gravity using the covariant 1/c-expansion, which is based on Newton-Cartan type geometry, in combination with a multipolar post-Minkowskian expansion. This new framework allows us to work in any gauge with a Newtonian limit. I will show that in any such gauge the field equations reduce to a set of Poisson and relativistic wave equations. These equations are then solved near and far from the compact matter source and glued together using matched asymptotic expansion methods. I will then highlight one specific gauge choice, namely the transverse gauge (a GR equivalent to the Coulomb gauge), and argue why this is an interesting alternative to the standard harmonic gauge. Finally, I will go through the ways that this framework can be generalised further and what new doors this has opened for the applications of non-relativistic gravity.

A session during which speakers give a short introduction to their talks for PhD students and postdocs.

The study of spectral statistics is of importance in physics due to its simplicity, universality, and utility as a diagnosis of quantum chaos and localization. Recently, as a probe of spectral statistics, the spectral form factor (SFF) has been instrumental in pinpointing novel signatures of quantum chaos in the presence of many-body interactions, in demonstrating the random matrix theory behaviour of black holes, and in shedding light on the existence of the many-body localization phase in the thermodynamic limit. In this talk, I will give an overview on the generic behavior of the SFF in closed and open strongly-interacting many-body quantum chaotic systems, and its experimental measurements in quantum simulators. Specifically, I will report a mapping between the SFF of quantum many-body chaotic systems and the partition function of classical ferromagnetic spin chains, and describe how non-Hermitian random matrix universality emerges from Hermitian quantum many-body chaotic systems.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

I'll briefly review the classical double copy, which maps exact solutions of classical gauge theories like electromagnetism, to solutions of general relativity. We will discuss why a position-space map is feasible, and then relate several gravitational objects (including horizons, Penrose limits, and asymptotics) to their gauge theory analogues.

In this talk I will explain how the size of the Einstein-Rosen (ER) bridge dual to the Double Scaled SYK (DSSYK) model saturates at late times because of finiteness of the underlying quantum Hilbert space. To this end, I will extend recent work implying that the ER bridge size is equal to the spread complexity of the dual DSSYK theory with an appropriate initial state. I will show that the auxiliary "chord basis'' used to solve the DSSYK theory is the physical Krylov basis of the spreading quantum state. ER bridge saturation then follows from tapering of the Lanczos spectrum, derived by methods adapted from Random Matrix Theory (RMT). The results amount to an exact resummation of a class of non-perturbative effects in the dual gravitational description.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

The averaged null energy operator (ANEC) is a light-ray integral of the null energy, which is known to have far-reaching consequences in CFT, such as the Lorentzian Inversion Formula. It is also closely connected to modular Hamiltonian in QFT. In this talk, I will discuss a new connection between the ANEC operator and monotonicity of the renormalization group. In particular, I will show how the 2d c-theorem and 4d a-theorem can be derived using the ANEC. This derivation relies on contact terms appearing in specific ANEC correlators. I will also review a new infinite set of constraints that can be derived from the ANEC in 2d QFT. This program hints at a more general role for light-ray operators in QFT, which I will argue for.

We discuss the structure of 2-> N scattering in QCD and gravity in high energy Regge asymptotics and outline remarkable similarities between the two. In the QCD case, the rapid growth of the N-gluon amplitude, described by the BFKL equation, leads to the emergence of nonperturbative classical lumps that unitarize the cross-section at fixed impact parameter. We describe the resulting shockwave picture of gluon radiation in hadron-hadron collisions that leads to the formation of a quark-gluon plasma. The ``gravitational BFKL” 2->N amplitude grows far more rapidly and it has been argued on general grounds that classicalization and unitarization must result similarly to the QCD case. We compute gravitational radiation and shockwave propagators in the collision of gravitational shockwaves and demonstrate their double copy structure to QCD in the Regge regime. Both soft (Weinberg) and semi-hard (Lipatov) radiation can be understood as classical double copies of QCD radiation.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

Celestial Holography posits the existence of a holographic description of gravitational theories in asymptotically flat space-times. To date, top-down constructions of such dualities involve a combination of twisted holography and twistor theory. The gravitational theory is the closed string B model living in a suitable twistor space, while the dual is a chiral 2d gauge theory living on a stack of D1 branes wrapping a twistor line. I’ll talk about a variant of these models that yields a theory of self-dual Einstein gravity (via the Plebanski equations) in four dimensions. This is based on work in progress with Roland Bittleston, Kevin Costello and Atul Sharma.

The supersymmetric IKKT matrix model provides a holographic framework in which all spacetime dimensions are emergent. Despite being much more technically tractable than large N field theory path integrals, the model remains poorly understood. This is largely because the ’timeless’ nature of the model means that the standard renormalisation group interpretation of the emergent ‘radial’ dimension is not immediately applicable. I will discuss a supersymmetric deformation of the IKKT integral that gives a practical handle on the model. I will show how well-established phenomena, including brane polarisation in the presence of background fluxes, arise in this context and thereby allow the rudiments of a holographic dictionary to be established.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

In this talk, I will discuss charged superradiant instabilities suffered by black holes in asymptotically AdS_5 * S^5. Hairy black hole solutions (constructed within gauged supergravity) have previously been proposed as endpoints to this instability. In this work, we demonstrate that these hairy black holes are themselves unstable to the emission of large dual giant gravitons. We propose that the endpoint to this instability is given by Dual Dressed Black Holes (DDBH)s; configurations consisting of one, two, or three very large dual giant gravitons surrounding a core AdS black hole with one, two, or three SO(6) chemical potentials equal to unity. We conjecture that DDBHs dominate the phase diagram of N = 4 Yang-Mills over a range of energies around the BPS plane, and provide an explicit construction of this phase diagram, briefly discussing the interplay with supersymmetry. We also construct the 10-dimensional DDBH supergravity solutions.

Twisting of supersymmetric quantum field theories produces field theories living on spacetimes where certain directions are topological, some other directions are holomorphic, and some directions are neither. The operator product expansions of local operators on such theories have rich behaviour, aspects of which may be captured by certain sheaf cohomology classes. Based on 2401.11917 and ongoing joint work with Luigi Alfonsi, Laura Olivia Felder, and Charles Alastair Stephen Young.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

The presence of integrability in a given model provides a series of powerful tools to study its spectrum and properties. This is the case, for instance, in a series of discrete models called integrable spin chains. Examples include the Hubbard model, the Potts model and the Heisenberg spin chain. Usually, in these systems, a particle in a given site of the chain only interacts with the ones in its first neighbor sites; they are called Nearest-Neighbour spin chains. Certain applications in gauge theories and condensed matter, however, require understanding long-range deformations. In this talk, I will start with an introduction to integrable spin chains and then present a procedure to include long range interactions such that integrability is perturbatively preserved. I will show two examples: the spin-1/2 and the spin-1 isotropic chains, and discuss their properties.

Celestial holography posits that the 4D S-matrix may be calculated holographically by a 2D conformal field theory. However, bulk translation invariance forces low-point massless celestial amplitudes to be distributional, which is an unusual property for a 2D CFT. In this talk, I show that translation-invariant MHV gluon amplitudes can be extracted from smooth 'leaf' amplitudes, where a bulk interaction vertex is integrated only over a hyperbolic slice of spacetime. After describing gluon leaf amplitudes' soft and collinear limits, I will show that MHV leaf amplitudes can be generated by a simple 2D system of free fermions and the semiclassical limit of Liouville theory, showing that translation-invariant, distributional amplitudes can be obtained from smooth correlation functions. An important step is showing that, in the semiclassical limit of Liouville theory, correlation functions of light operators are given by contact AdS Witten diagrams. This talk is based on a series of papers with Atul Sharma, Andrew Strominger, and Tianli Wang [2312.07820, 2402.04150,2403.18896].

We discuss aspects of Carroll and BMS invariant field theories that might be relevant for flat space holography.

We show that supersymmetric gauge theories on the blowup of the complex plane obey Painleve’ equations in bilinear form. We discuss the modular properties of the solutions to these equations in relation with holomorphic anomaly equations for topological string amplitudes. These solutions provide a non-perturbative completion of the partition function for topological strings geometrically engineering this class of gauge theories. The approach we use can be applied also for non-Lagrangian gauge theories, explicit results will be shown for the simplest Argyres-Douglas theory case.

One of the few cases of AdS/CFT where both sides of the duality are under good control relates tensionless $k=1$ strings on AdS$_3$ to a two-dimensional symmetric product CFT. Building on prior observations, we propose an exact duality between string theory on a spacetime which is not asymptotically AdS and a non-conformal field theory. The bulk theory is constructed as a marginal deformation of the $k=1$ AdS$_3$ string while the spacetime dual is a single trace $T \bar{T}$-deformed symmetric orbifold theory. As evidence for the duality, we match the one-loop bulk and boundary torus partition functions. This correspondence provides a framework to both learn about quantum gravity beyond AdS and understand how to define physical observables in $T \bar{T}$-deformed field theories.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

In a supergravity theory, supersymmetric bosonic solutions are those solutions for which all fermions vanish and which are preserved by some supersymmetries of the theory. These supersymmetries can be understood as spinor fields on the Lorentzian base manifold satisfying a certain differential equation (and possibly some additional constraints) which are known as Killing spinors because they "square" to Killing vectors. These spinors, together with the Killing vectors which preserve all of the bosonic data of the solution, can be assembled into a Lie superalgebra known as the Killing superalgebra which has been used as a tool in the effort to classify supersymmetric bosonic solutions. Importantly, the closure and Jacobi identities of these brackets are not automatic; they typically require at least some of the supergravity equations of motion. In Riemannian geometry, a related but distinct concept of Killing spinor exists, but these cannot in general be assembled into a Killing superalgebra as there is no appropriate analogue of the equations of motion. Nonetheless, it has been shown that the "triality" of so(8) and the exceptional Lie algebras F4 and E8 find geometric realisations as an analogous structure on higher-dimensional spheres. In this talk, I will describe recent work unifying these ideas, exploring the question of what kind of "Killing spinors" define Killing (super)algebras for general signature and choice of spinor squaring maps, describing their structure and some homological tools used to study them, and providing some examples in both Riemannian and Lorentzian signatures in 2 dimensions. This talk is based on the following preprints: arXiv:2409.11306, arXiv:2410.01765

We start with an introduction to supersymmetric conformal field theories, and the motivations for considering them. Then we review a construction of a two-dimensional chiral algebra (the holomorphic sector of a 2d CFT) inside four-dimensional conformal theories with 8 or more supercharges. While the chiral algebra is not unitary, it inherits an extra structure from the fact that the parent four-dimensional theory is unitary. We use these unitarity requirements to constrain the landscape of four-dimensional superconformal theories.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

Spectral triples are a mathematical framework for the Dirac operator that includes a generalisation to non-commutative geometry. The finite spectral triples are ones in which the Dirac operator is a finite-dimensional matrix. Interesting examples include the internal space of the standard model and spacetimes with a high-energy cutoff due to non-commutativity. The talk will discuss 1) a construction of spin groups from two commuting Clifford algebra actions, with an application to unification groups in the standard model, and 2) fermion integrals for finite spectral triples in general.

The collinear singularities of form factors in certain self-dual QCDs determine an abstract chiral algebra. In this talk I will realize an example concretely as the large N limit of an algebra of operators living on a 2d holomorphic surface defect. The construction goes via twisted holography for the type I topological string on a Calabi-Yau 5-fold related to twistor space. I will explain how this realization can be exploited to compute QCD form factors in flat space, and helicity amplitudes on a range of self-dual backgrounds. This is joint work with Kevin Costello and Keyou Zeng.