(0,2) dualities and the 4-simplex

Dimofte, Tudor; Paquette, Natalie M.

doi:10.1007/JHEP08(2019)132

Title: (0,2) dualities and the 4-simplex

Abstract

We propose that a simple, Lagrangian 2d $ \mathcal{N} $ = (0, 2) duality interface between the 3d $ \mathcal{N} $ = 2 XYZ model and 3d $ \mathcal{N} $ = 2 SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundary and 2d $ \mathcal{N} $ = (0, 2) interfaces. In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3), (2, 4), and (2, 4) Pachner moves. We check these dualities using supersymmetric half-indices. We also describe how to produce stand-alone 2d theories (as opposed to interfaces) capturing the geometry of 4-simplices and Pachner moves by making additional field-theoretic choices, and find in this context that the Pachner moves recover abelian $ \mathcal{N} $ = (0, 2) trialities of Gadde-Gukov-Putrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4-manifold geometry that has been developed in recent years.

Authors:

Dimofte, Tudor ^[1]; Paquette, Natalie M. ^[2]

Univ. of California, Davis, CA (United States)
California Inst. of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Fri Aug 23 00:00:00 EDT 2019

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

OSTI Identifier:: 1596454

Grant/Contract Number:: SC0011632

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: 2019; Journal Issue: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Duality in Gauge Field Theories; Supersymmetric Gauge Theory; Supersymmetry and Duality

Citation Formats


                    Dimofte, Tudor, and Paquette, Natalie M. (0,2) dualities and the 4-simplex.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP08(2019)132.

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                    Dimofte, Tudor, & Paquette, Natalie M. (0,2) dualities and the 4-simplex.  United States.  https://doi.org/10.1007/JHEP08(2019)132

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                    Dimofte, Tudor, and Paquette, Natalie M. Fri .  
"(0,2) dualities and the 4-simplex".  United States.  https://doi.org/10.1007/JHEP08(2019)132.  https://www.osti.gov/servlets/purl/1596454.

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@article{osti_1596454,

  title        = {(0,2) dualities and the 4-simplex},

  author       = {Dimofte, Tudor and Paquette, Natalie M.},

  abstractNote = {We propose that a simple, Lagrangian 2d \( \mathcal{N} \) = (0, 2) duality interface between the 3d \( \mathcal{N} \) = 2 XYZ model and 3d \( \mathcal{N} \) = 2 SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundary and 2d \( \mathcal{N} \) = (0, 2) interfaces. In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3), (2, 4), and (2, 4) Pachner moves. We check these dualities using supersymmetric half-indices. We also describe how to produce stand-alone 2d theories (as opposed to interfaces) capturing the geometry of 4-simplices and Pachner moves by making additional field-theoretic choices, and find in this context that the Pachner moves recover abelian \( \mathcal{N} \) = (0, 2) trialities of Gadde-Gukov-Putrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4-manifold geometry that has been developed in recent years.},

  doi          = {10.1007/JHEP08(2019)132},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 8,

  volume       = 2019,

  place        = {United States},

  year         = {Fri Aug 23 00:00:00 EDT 2019},

  month        = {Fri Aug 23 00:00:00 EDT 2019}

}

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Title: (0,2) dualities and the 4-simplex

Abstract

Citation Formats

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K-decompositions and 3d gauge theories journal, November 2016

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory journal, July 2010

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Chiral 2d theories from N = 4 SYM with varying coupling journal, April 2017

A finite graphic calculus for 3-manifolds journal, December 1995

Pin(2)-Equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture journal, April 2015

$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls journal, August 2011

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A calculus for ideal triangulations of three-manifolds with embedded arcs: Calculus for ideal triangulations journal, June 2005

Topological gauge theories and group cohomology journal, April 1990

Instantons and affine Lie algebras journal, March 1996

Symmetry enhancement and closing of knots in 3d/3d correspondence journal, July 2018

3d-3d correspondence revisited journal, April 2016

Six-dimensional origin of N $$ \mathcal{N} $$ = 4 SYM with duality defects journal, December 2016

Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories journal, September 1999

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Index for three dimensional superconformal field theories with general R-charge assignments journal, April 2011

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A strong coupling test of S-duality journal, December 1994

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N = 2 dualities
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The Volume Spectrum of Hyperbolic 4-Manifolds
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On realizations of Pachner moves in 4d
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The topology of four-dimensional manifolds
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Walls, lines, and spectral dualities in 3d gauge theories
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Twisted Hilbert spaces of 3d supersymmetric gauge theories
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Khovanov-Rozansky Homology and Topological Strings
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M5-branes on S 2 × M 4: Nahm’s equations and 4d topological sigma-models
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Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
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Dual boundary conditions in 3d SCFT’s
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Chiral 2d theories from N = 4 SYM with varying coupling
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A finite graphic calculus for 3-manifolds
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$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls
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Theories of class F and anomalies
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Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models
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Supersymmetric, integrable boundary field theories
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Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups
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RG domain walls and hybrid triangulations
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Holomorphic blocks in three dimensions
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(0, 2) trialities
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A calculus for ideal triangulations of three-manifolds with embedded arcs: Calculus for ideal triangulations
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Topological gauge theories and group cohomology
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Instantons and affine Lie algebras
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3d-3d correspondence revisited
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