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Title: Aspects of defects in 3d-3d correspondence

Abstract

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d (2, 0) theory of type AN-1 on a 3-manifold M . The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group SL(N,C) ) on M and a 3d N=2 theory T N [M ]. We study this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory T [SU(N )], 5d N=2 SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, which can be used to compute in the presence of maximal and certain class of non-maximal punctures when N > 2. We also highlight the non-Abelian description of the 3d N=2 T N [M ] theory with defect included, when such a description is available. This paper is a companion to our shorter paper, which summarizes our main results.

Authors:
 [1];  [2];  [3];  [3]
+ Show Author Affiliations
  1. Univ. of Tokyo (Japan)
  2. Kyung Hee Univ., Seoul (Korea); Korea Inst. for Advanced Study, Seoul (Korea)
  3. Inst. for Advanced Study, Princeton, NJ (United States); Univ. of Tokyo (Japan)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1424004
Grant/Contract Number:  
sc0009988
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 10; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Chern-Simons Theories; M-Theory; Wilson; ’t Hooft and Polyakov loops

Citation Formats

Gang, Dongmin, Kim, Nakwoo, Romo, Mauricio, and Yamazaki, Masahito. Aspects of defects in 3d-3d correspondence. United States: N. p., 2016. Web. doi:10.1007/JHEP10(2016)062.
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Gang, Dongmin, Kim, Nakwoo, Romo, Mauricio, & Yamazaki, Masahito. Aspects of defects in 3d-3d correspondence. United States. doi:10.1007/JHEP10(2016)062.
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Gang, Dongmin, Kim, Nakwoo, Romo, Mauricio, and Yamazaki, Masahito. Wed . "Aspects of defects in 3d-3d correspondence". United States. doi:10.1007/JHEP10(2016)062. https://www.osti.gov/servlets/purl/1424004.
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@article{osti_1424004,
title = {Aspects of defects in 3d-3d correspondence},
author = {Gang, Dongmin and Kim, Nakwoo and Romo, Mauricio and Yamazaki, Masahito},
abstractNote = {In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d (2, 0) theory of type AN-1 on a 3-manifold M . The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group SL(N,C) ) on M and a 3d N=2 theory T N [M ]. We study this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory T [SU(N )], 5d N=2 SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, which can be used to compute in the presence of maximal and certain class of non-maximal punctures when N > 2. We also highlight the non-Abelian description of the 3d N=2 T N [M ] theory with defect included, when such a description is available. This paper is a companion to our shorter paper, which summarizes our main results.},
doi = {10.1007/JHEP10(2016)062},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2016,
place = {United States},
year = {2016},
month = {10}
}
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DOI:  10.1007/JHEP10(2016)062
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