New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories

by Dr Sungwoo Hong (University of Chicago)

Tuesday 14 Jun 2022, 16:00 → 17:30 Asia/Seoul

1423 in building 1 (KIAS)

Title: New Anomalies, TQFTs, and Confinement in Bosonic Chiral Gauge Theories

Speaker: Sungwoo Hong (University of Chicago)

Abstract: In this talk, I will introduce a class of four dimensional chiral gauge theories which is purely bosonic. By "bosonic" I mean that these theories do not admit any fermionic gauge invariant operators. Then I discuss possibly the most comprehensive set of `t Hooft anomalies that the theory possesses. For this, I will discuss general background 
fields that can be consistently activated. The final outcome of this is a combination of centers of color, non-abelian flavor symmetry, and U(1) symmetry of the theory, which we call a CFU background. Next, I will discuss anomaly matching assuming confinement as the IR phase. I will show that a combination of the following facts imposes serious 
challenges for the anomaly matching:
(1) Theory is bosonic, so no possible composite fermions to match continuous anomalies.
(2) Theorems regarding existence/absence of "symmetry preserving TQFTs"
(3) Possible vacuum operators and associated breaking of flavor symmetries.
(4) Dimensional analysis and RG flow.
Focusing on a example of SU(8) theory with one fermion in rank-2 symmetric and three fermions in the rank-2 antisymmetric representations, I will argue that if the theory confines then we can more or less determine the vacuum condensate operator, dimension 5 fermion bilinear operator, and thereby the pattern of chiral symmetry breaking. If, however, this dimension 5 operator decouples through the RG trajectory, then the theory most likely must flow to IR 
conformal field theory. Considering another example, SU(8) theory with two fermions in rank-2 symmetric and six fermions in the rank-2 antisymmetric representations, I will then argue that the theory is highly unlikely to confine and the most feasible possibility is to flow to the IR CFT. Interestingly, these rather remarkable results based on non-perturbative analysis are consistent with what the perturbative analysis about the IR fixed point suggests.