Title and Abstract
W-algebras and 4d N=2 SCFTs from M5 branes
In this talk, we will review the correspondence between 4d N=2 superconformal field theories (SCFTs) and 2d vertex operator algebras (VOAs). For 4d SCFTs from M5 branes, corresponding VOAs are W-algebras with an explicit construction. Observables in both Higgs and Coulomb branches of SCFTs are identified with data in VOAs. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can also be derived from 4d theory.
Magnetically charged AdS4 Blackholes made of M5-branes
In this talk, I will talk about mictrostates counting of magnetically charged blackholes in AdS4 made of M5-branes wrapped on hyperbolic 3-manifolds.
Scale vs Conformal from the viewpoint of (topological) twist
Most rectangles are not a square, but why do “most” scale invariant field theories have conformal invariance? We believe unitarity or reflection positivity plays an important role here, but if we abandon the unitarity or reflection positivity, can we construct scale invariant field theories without conformal invariance at will? In this talk, I’ll show a general recipe to construct scale invariant field theories without conformal invariance by deforming the (topologically) twisted conformal field theory. I’ll discuss the corresponding (topologically) twisted supergravity (M-theory) solution as well as a perturbative realization in field theories (which we may find in nature).
Three dimensional gravity and the orbit method
Three dimensional gravity has been a fruitful arena to address conceptual questions in quantum gravity. We will revisit pure quantum gravity in 3d, following the approach of first implementing constraints and then quantizing, as advocated by Coussaert, Henneaux and van Driel some time ago. This led them to reduce pure AdS3 gravity to Liouville theory. We will reconsider this derivation taking special care of zero-mode solutions representing BTZ black holes. We find a surprising connection between gravity in 3d and a piece of group theory known as the orbit method. The boundary dynamics of three dimensional gravity can be understood as the geometric quantization on the coadjoint orbit of the Virasoro group. We’ll comment on extensions to supergravity and gravity in three dimensional flat space.