Aspects of defects in 3d-3d correspondence

doi:10.1007/JHEP10(2016)062

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

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Abstract

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d (2, 0) theory of type A _N-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:

Gang, Dongmin ^[1]; Kim, Nakwoo ^[2]; Romo, Mauricio ^[3]; Yamazaki, Masahito ^[3]

Univ. of Tokyo (Japan)
Kyung Hee Univ., Seoul (Korea); Korea Inst. for Advanced Study, Seoul (Korea)
Inst. for Advanced Study, Princeton, NJ (United States); Univ. of Tokyo (Japan)

Publication Date:: 2016-10-12

Research Org.:: Inst. for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

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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