Tracy-Widom distribution in supersymmetric gauge theories

• Gregory P. Korchemsky (Saclay, IPhT)

Room: Aula C It was recently recognized that various observables in four-dimensional supersymmetric gauge theories can be computed for an arbitrary 't Hooft coupling as determinants of certain semi-infinite matrices. I will show that these quantities can be expressed as Fredholm determinants of the so-called Bessel kernel and they are closely related to celebrated Tracy-Widom distribution (more precisely, its finite temperature generalization) describing level-spacing distributions in matrix model.

Corrections to the thermodynamics of AdS$_5$ black holes and the superconformal index

• Alejandro Ruiperez (Roma Tor Vergata)

Room: Aula C We consider a four-derivative extension of minimal gauged supergravity in five dimensions and use it to evaluate the on-shell action of AdS$_5$ black holes, showing that it fully matches the result from the superconformal index ``on the second sheet” after imposing supersymmetry. We then compute the corrected black hole thermodynamics and we find a formula of the BPS entropy as a function of the charges. The latter is shown to match both the Legendre transform of the superconformal index and the Wald entropy. Based on 2208.01007 [hep-th] and on work in progress.

Higher rank equivariant Donaldson-Witten theory

• Ekaterina Sysoeva (SISSA)

Room: Aula C Partition function and correlation functions of the topologically twisted $\mathcal{N} = 2$ super Yang-Mills theory on a smooth four-manifold with gauge group $SU(2)$, also known as Donaldson-Witten theory, provide us a way to compute topological invariants of many manifolds classifying their smooth structure (Donaldson invariants). Equivariantisation of this theory, on the one hand, can be considered as a tool to find the original invariants by means of the equivariant localisation, and on the other hand, is interesting by itself, since it also has a topological counterpart (equivariant Donaldson invariants). While for the equivariant Donaldson-Witten theory with $SU(2)$, gauge group quite a lot of results were found, there is still not much known in the case of the higher rank gauge symmetry. After giving an introduction on the subject I will present our recent results for the higher rank theory, which include generalisation of the recurrence relation for the partition function on $\mathbb{C}^2$ (Zamolodchikov relation) and a proposal for the equivariant Donaldson invariants of the compact toric manifolds.

Meeting organizzativo PRIN

• Massimo Bianchi (Università di Roma Tor Vergata)

Room: Sala Wataghin

Holography with heavy states as a tool to study black holes

• Rodolfo Russo (Queen Mary University of London)

Room: Aula C In holographic CFTs it is interesting to study operators whose dimension scales as the central charge when the latter is taken to be large. As an example of such operators, I consider multi-particle states formed by a large number of BPS single-particle constituents. Focusing on the example of the (AdS_3 x S^3)/CFT_2 duality, I discuss how the gravitational backreaction of these heavy states is described by regular geometries that encode interesting CFT data. The quadratic fluctuations around these geometries capture the heavy-light four point correlators. Finally I comment on similarities and differences between these correlators and similar quantities calculated in the background of asymptotically AdS black holes.

Fate of Radiating Black Holes With Minimum Mass in Einstein-dilaton-Gauss-Bonnet Theory of Gravity

• Fabrizio Corelli (Sapienza Università di Roma)

Room: Aula C Einstein-dilaton-Gauss-Bonnet (EdGB) is a theory of modified gravity in which a dilaton-type scalar field is nonminimally coupled to quadratic curvature terms via an exponential function. Black holes (BHs) in this theory are particularly interesting since they possess a critical configuration with minimum mass and finite Hawking temperature. This means that a critical BH loses mass due to Hawking's radiation, but it is not clear what is its fate after this process, since it cannot reach a final configuration with lower mass. In a recent work we studied this problem by means of fully nonlinear numerical evolutions of spherically symmetric BH spacetimes. Specifically, by simulating the collapse of wave packets of a phantom scalar field we have been able to dynamically reduce the BH mass, reproducing the effect of Hawking's evaporation. In this talk I will present our results with a particular focus on the case in which the BH mass falls below the critical value. In particular, I will show that a high-curvature elliptic region emerges from the apparent horizon, and I will discuss how this could hint to an incompatibility between EdGB gravity and Hawking evaporation. I will also mention some alternative scenarios for a stable evolution, and future possible research directions.