Seminar on QFT and Geometry

Speaker:Myungbo Shim
Organizer:Myungbo Shim, Nicolai Reshetikhin, Babak Haghighat
Time:2024/06/28 (Fri) 15:00 ~17:00 PM
Venue:Jingzhai 218

Upcoming talk

Title: Survey of some 3d N=2 localization

Speaker: Myungbo Shim
Time: 2024/06/28 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218

Abstract: We review general results of N=2 supersymmetric localization on non singular 3-manifolds(closed, oriented). In specific, review the general philosophy and collect some formulae which frequently appear in other contexts involving 3d supersymmetric partition functions. We discuss some generalization to singular manifolds or 3-manifolds with boundary (for example, a half index)

Past Talks:

Title: Twisted formalism of 3d supersymmetric theories - 3

Speaker: Myungbo Shim
Time: 2024/06/14 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218

Abstract: Finishing the review of twisted formalism, and discussing the general structures of consequences of HT-twists and Topological twists; vertex algebra endowed with shifted Poisson structures, bulk-boundary map, derived structures, and some RG properties as well as SUSY compatible boundary conditions. We will wrap up this topic with discussions on future applications for us.

Title: The Coordinate Bethe Ansatz for the Heisenberg XXX model

Speaker: Xiao-yue Sun

Time: 2024/06/07 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218


Bethe ansatz equations often appear in the study of the vacuum structure of supersymmetric gauge theories and the gluing conditions in three-dimensional manifolds. In this talk, I will discuss solving Heisenberg spin chains using the coordinate Bethe ansatz in detail.

Title: Non-hyperbolic 3-manifolds and bulk dual 3D field theories of 2D Virasoro minimal models

Speaker: Dongmin Gang (SNU)

Time: 2024/05/29 (Wed) 15:00 ~17:00 PM

Venue: C548, Shuangqing Research Complex


Using 3D-3D correspondence, we construct 3D dual bulk field theories of general Virasoro minimal models $M(P,Q)$. They correspond to Seifert fiber spaces $S^2 ((P,R-P),(Q,-S),(3,1))$ with two integers $(R,S)$ satisfying $PS-QR =1$. For unitary case, i.e. $|P-Q|=1$, the bulk theory has a mass gap and flows to an unitary topological field theory (TQFT) in the IR which is expected to support the chiral Virasoro minimal model at the boundary upon a proper boundary condition. For non-unitary case, i.e. $|P-Q|>1$, the bulk theory flows to a 3D $\CN=4$ rank-0 superconformal field theory, whose topologically twisted theory supports the chiral minimal model at the boundary. We also give concrete field theory description of the 3D bulk theory using $T[SU(2)]$ theories.

Title: Twisted formalism of 3d supersymmetric theories - 2

Speaker: Myungbo Shim
Time: 2024/05/10 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218

Abstract: Based on  [2204.02997]  and [1706.09977], we are going to review the construction of holomorphic-topological (HT) Chern-Simons-Matter theories on 3-manifolds with transverse holomorphic foliation (THF) via BV-BRST formalism with short brief introduction. We introduce twisted (super)fields for non-supersymmetric CSM and generalize them to HT-twisted N=2 CSM theories.

Title: Twisted formalism of 3d supersymmetric theories - 1

Speaker: Myungbo Shim
Time: 2024/04/26 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218

Abstract: Recently, vertex operator algebras from 3d supersymmetric theories gained a lot of attention. One way to study them directly is using twisted formalism and compute OPE. We are going to review [2204.02997]  (with relevant references) from scratch to utilize this technique to research holomorphically or topologically twisted SQFTs in 3d.

Title: Topological Twisted Indices from 3-manifolds- 2

Speaker: Myungbo Shim
Time: 2024/04/19 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218

Abstract:Last time, we reviewed the topologically twisted indices from the holonomy matrix method for 3-manifolds constructed by Dehn surgery of knot/link complements. This time, we are going to review the other method using the ideal triangulation based on Dimofte-Gaiotto-Gukov and Dimofte-Garoufalidis.Specifically, we'll review combinatorial data of ideal triangulation of 3-manifolds with n-cusped boundaries.

Title: 3d-3d correspondence and 2d N = (0,2) boundary conditions

Speaker: Hee Joong Chung (Jeju National University)
Time: 2024/03/29 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218

Abstract : After a brief introduction on the 3d-3d correspondence and analytically continued Chern-Simons partition function, we interpret quiver forms or fermionic sums that appear in the generating function of Donaldson-Thomas invariant or characters of CFT in terms of half-index of 3d N=2 theories with certain 2d N = (0,2) boundary conditions. We apply this relation to the 3d-3d correspondence and obtain a Lagrangian description of 3d N=2 theories T[M_3] for 3-manifolds M_3 in several contexts.

Title: Topological Twisted Indices from 3-manifolds
Speaker: Myungbo Shim
Time: 2024/03/15 (Fri) 15:00 ~17:00 PM
Venue: Jingzhai 218
Abstract:Topologically twisted indices of 3d N=2 SCFTs are BPS partition function on a circle bundle over the Riemann surfaces of genus g. In 3d-3d correspondences, it can be obtained from topological invariants of 3-manifolds called Reidemeister-Ray-Singer torsion or simply analytic torsion. We review how to compute the torsion from 3-manifolds which are described as Dehn surgery of knot/link complements in two different ways for (P)SL(2,C) Chern-Simons theories.