I will continue the discussions on line defects and surface defects in class S theories, making connections to the construction of the quantum trace map, as well as to the exact WKB method for higher order ODEs.
Inflation can be viewed as a natural "cosmological particle detector" which can probe energies as high as its Hubble scale. In this talk, I study the imprints of heavy relativistic particles during inflation on primordial correlators in situations where the scalar fluctuations have a reduced speed of sound. Breaking dS boosts allows new types of footprints of massive fields to emerge. In particular, I show that heavy particles that are lighter than Hubble divided by the speed of sound leave smoking gun imprints in the three-point function of curvature perturbations (due to the exchange of those fields) in the form of resonances in the squeezed limit which are vividly distinct from the previously explored signatures of heavy fields in de Sitter correlators. Throughout I use and extend the cosmological bootstrap techniques derived from locality, unitarity, and analyticity in order to find fully analytical formulae for the desired boost breaking correlators.
In the first part of my talk I'll briefly review some aspects of the relations
between N=4, d=4 SYM and vertex operator algebras (VOAs) discussed
in recent work of Gaiotto and collaborators. The resulting picture predicts
conjectural generalisations of the geometric Langlands correspondence.
We will focus on a class of examples figuring prominently in recent work
of Creutzig-Dimofte-Garner-Geer, labelled by parameters n (rank) and k.
For the case k=1,n=2 we will point out that the conformal blocks of the
relevant VOA, twisted by local systems, represent sections of natural
holomorphic line bundles over the moduli spaces of local systems closely
related to the isomonodromic tau functions. Observing the crucial role of
(quantised) cluster algebras in the definition of the holomorphic line
bundles suggests natural generalisations of this story to higher values
of the parameters k and n.
I will give an introduction to 4d N=2 class-S theories. I will describe the construction of such theories, the roles played by extended defects such as line defects and surface defects, as well as connections to Hitchin systems.
In 1965, Lévy-Leblond introduced the ultra-relativistic cousin of the Poincaré symmetry and named it the Carrollian symmetry after Lewis Carroll (the pseudonym of the author of Alice’s adventures in Wonderland and Through the Looking-Glass). It can be seen as the counterpart of the non relativistic Galilean symmetry. Since then, Carrollian symmetry has become an active research topic in various fields, ranging from field theories, hydrodynamics, and more recently, gravity and black holes. In this talk, I will give an introductory review of the Carrollian symmetry and Carrollian physics, especially focusing on the emergence of Carrollian hydrodynamics in gravity and black holes