This series consists of talks in the area of Quantum Fields and Strings.
Painlevé equations can be obtained both from time-dependent classical Hamiltonian systems and from isomonodromic deformation problems. These realizations lead to a precise matching between Painlevé equations and Hitchin systems associated to four-dimensional N=2 SQCD as well as Argyres-Douglas theories. Long-time analysis of the Painlevé Hamiltonians dynamics allows to extract the unrefined "instanton" partition function for these theories at all strong-coupling points
We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d (2,0) type J theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of JJ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of JJ type. We can obtain the Schur and Hall-Littlewood index of these theories by computing the vacua character of the corresponding chiral algebra.
In my talk I will consider resurgence properties of Chern-Simons
theory on compact 3-manifolds. I will also describe what role
resurgence plays in the problem of categorification of Chern-Simons
theory, that is the problem of generalizing Khovanov homology of knots
to compact 3-manifolds.
We discuss information loss from black hole physics in AdS3, focusing on two sharp signatures infecting CFT2 correlators at large central charge c: `forbidden singularities' arising from Euclidean-time periodicity due to the effective Hawking temperature, and late-time exponential decay in the Lorentzian region. We show that these signatures can be derived from the behavior of the Virasoro conformal blocks at large central charge. At finite c, we compute non-perturbative effects that resolve the unitarity-violation from forbidden singularities.
We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally supersymmetric N=4 Yang-Mills theory, three-dimensional conformal field theories and QCD.
In previous work it has been observed that the singularity structure of multi-loop scattering amplitudes in planar N=4
super-Yang-Mills theory is evidently dictated by cluster algebras. In my talk I will discuss the interplay between this mathematical
observation and the physical principle that the singularities of Feynman integrals are encoded in the Landau equations.
I will discuss the recent progress on understanding scattering amplitudes in N=4 SYM beyond the planar limit. I will show that the singularity structure of these amplitudes is very similar to the planar amplitudes suggesting new hidden symmetries to be present in the complete N=4 SYM theory. I will also talk about the extension of this work to N=8 SUGRA by studying the on-shell diagrams in this theory as well as some of the properties of the integrands of loop amplitudes.
The mathematical notion of moonshine relates the theory of finite groups with that of modular objects. The first example, 'Monstrous Moonshine', was clarified in the context of two dimensional conformal field theory in the 90's. In 2010, interest in moonshine in the physics community was reinvigorated when Eguchi et. al. observed representations of the finite group M24 appearing in the elliptic genus of nonlinear sigma models on K3.