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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. https://doi.org/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. https://doi.org/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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text, January 2010

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preprint, January 2010

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text, January 2010

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text, January 2010

SUSY Gauge Theories on Squashed Three-Spheres
text, January 2011

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text, January 2011

From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
text, January 2011

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text, January 2011

The gravity dual of supersymmetric gauge theories on a squashed three-sphere
text, January 2011

3-Manifolds and 3d Indices
preprint, January 2011

Quivers, YBE and 3-manifolds
text, January 2012

Network and Seiberg Duality
text, January 2012

Bootstrapping the superconformal index with surface defects
text, January 2012

Gluing equations for PGL(n,C)-representations of 3-manifolds
text, January 2012

RG Domain Walls and Hybrid Triangulations
preprint, January 2013

3d Chern-Simons Theory from M5-branes
text, January 2013

New Integrable Models from the Gauge/YBE Correspondence
text, January 2013

Holography of Wrapped M5-branes and Chern-Simons theory
text, January 2014

3d-3d Correspondence Revisited
text, January 2014

Holography of 3d-3d correspondence at Large N
text, January 2014

The Superconformal Index of the (2,0) Theory with Defects
text, January 2014

Taming Supersymmetric Defects in 3d-3d Correspondence
text, January 2015

Khovanov-Rozansky Homology and Topological Strings
text, January 2004

(1,1)-knots via the mapping class group of the twice punctured torus
preprint, January 2002

Cluster ensembles, quantization and the dilogarithm
preprint, January 2003

The quantum dilogarithm and representations quantum cluster varieties
text, January 2007

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    K-Decompositions and 3d Gauge Theories
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    Comments on Exchange Graphs in Cluster Algebras
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    All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
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    BPS Graphs: From Spectral Networks to BPS Quivers
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    Symmetry enhancement and closing of knots in 3d/3d correspondence
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    Janus and J-fold Solutions from Sasaki-Einstein Manifolds
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