Academic Year 2024/2025

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.

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.

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.

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].

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.