Talk 1:

Room: Building 774 Salle 35, Time: 11:00 CET

Speaker: Bercel Bodis, Wigner Research Centre for Physics and Budapest University of Technology and Economics Budapest 

Title: Fredholm determinant in four-dimensional supersymmetric gauge theories

Abstract: In holographic dualities, non-perturbative coefficients at large ’t Hooft coupling play an important role, as they encode different saddle point corrections for the string worldsheet. However, calculating these corrections from the string theory side turns out to be extremely difficult. In my talk, I present a systematic method to determine these corrections for a special class of observables in four-dimensional N=2 and N=4 supersymmetric Yang-Mills theories to arbitrary order. This method is based on the fact that, for arbitrary ’t Hooft coupling, these observables can be expressed in the form of a Fredholm determinant. From this representation, a large number of constraints can be derived in the form of differential and integral equations. These exact relations, together with certain analytical properties, completely determine the non-perturbative corrections of these observables. With this method, it is possible to effectively determine the entire transseries of several observables in four-dimensional supersymmetric gauge theories.

Talk 2

Room: Salle Itzykson Time: 14:00 CET

Speaker: Alessandro Testa, IPhT and Parma 

Title: Solving N=2 superconformal long circular quiver theories by Tracy-Widom distributions

Abstract: In this talk, I will discuss correlation functions of chiral primary half-BPS operators in four-dimensional N = 2 superconformal circular, cyclic symmetric quiver theories. Using supersymmetric localization, these functions can be expressed as matrix integrals which, in the planar limit, reduce to Fredholm determinants of certain semi-infinite matrices. This powerful representation allows us to investigate these correlators across the parameter space of the quiver theory, including both weak and strong coupling regimes and various limits of the number of nodes and the operator scaling dimensions. At strong coupling, the standard semiclassical AdS/CFT expansion diverges in the long quiver limit. However, by incorporating both perturbative corrections (in negative powers of the ’t Hooft coupling) and an infinite tower of nonperturbative, exponentially suppressed contributions, we derive a remarkably simple expression for the correlation functions in this limit. These functions exhibit exponential decay with increasing node separation and admit an interpretation within a five-dimensional effective theory. We determine the mass spectrum of excitations propagating along the emergent fifth dimension within this theory, finding it to be given by the zeros of Bessel functions.

On behalf of the organisers Benjamin BASSO, Julius JULIUS, Gabriel LEFUNDES and Didina SERBAN

**In case you wish to be added/removed from this mailing list, please write to Julius JULIUS ()**