skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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:
 [1];  [2]
  1. Univ. of California, Davis, CA (United States)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
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. https://doi.org/10.1007/JHEP08(2019)132.
Dimofte, Tudor, & Paquette, Natalie M. (0,2) dualities and the 4-simplex. United States. https://doi.org/10.1007/JHEP08(2019)132
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.
@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 = {2019},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

N = 2 dualities
journal, August 2012


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

  • Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew
  • Communications in Mathematical Physics, Vol. 299, Issue 1
  • DOI: 10.1007/s00220-010-1071-2

Vortex Counting and Lagrangian 3-Manifolds
journal, October 2011

  • Dimofte, Tudor; Gukov, Sergei; Hollands, Lotte
  • Letters in Mathematical Physics, Vol. 98, Issue 3
  • DOI: 10.1007/s11005-011-0531-8

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

  • Terashima, Yuji; Yamazaki, Masahito
  • Journal of High Energy Physics, Vol. 2011, Issue 8
  • DOI: 10.1007/JHEP08(2011)135

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

  • Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
  • Communications in Mathematical Physics, Vol. 325, Issue 2
  • DOI: 10.1007/s00220-013-1863-2

3-Manifolds and 3d indices
journal, January 2013

  • Dimofte, Tudor; Gaiotto, Davide; Gukov, Sergei
  • Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 5
  • DOI: 10.4310/ATMP.2013.v17.n5.a3

Fivebranes and 3-manifold homology
journal, July 2017

  • Gukov, Sergei; Putrov, Pavel; Vafa, Cumrun
  • Journal of High Energy Physics, Vol. 2017, Issue 7
  • DOI: 10.1007/JHEP07(2017)071

Khovanov-Rozansky Homology and Topological Strings
journal, October 2005

  • Gukov, Sergei; Schwarz, Albert; Vafa, Cumrun
  • Letters in Mathematical Physics, Vol. 74, Issue 1
  • DOI: 10.1007/s11005-005-0008-8

M5-branes on S 2 × M 4: Nahm’s equations and 4d topological sigma-models
journal, September 2016

  • Assel, Benjamin; Schäfer-Nameki, Sakura; Wong, Jin-Mann
  • Journal of High Energy Physics, Vol. 2016, Issue 9
  • DOI: 10.1007/JHEP09(2016)120

(0, 2) trialities
journal, March 2014

  • Gadde, Abhijit; Gukov, Sergei; Putrov, Pavel
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)076

RG domain walls and hybrid triangulations
journal, January 2015

  • Dimofte, Tudor; Gaiotto, Davide; Veen, Roland van der
  • Advances in Theoretical and Mathematical Physics, Vol. 19, Issue 1
  • DOI: 10.4310/ATMP.2015.v19.n1.a2

Dual boundary conditions in 3d SCFT’s
journal, May 2018

  • Dimofte, Tudor; Gaiotto, Davide; Paquette, Natalie M.
  • Journal of High Energy Physics, Vol. 2018, Issue 5
  • DOI: 10.1007/JHEP05(2018)060

Walls, lines, and spectral dualities in 3d gauge theories
journal, May 2014

  • Gadde, Abhijit; Gukov, Sergei; Putrov, Pavel
  • Journal of High Energy Physics, Vol. 2014, Issue 5
  • DOI: 10.1007/JHEP05(2014)047

Holomorphic blocks in three dimensions
journal, December 2014

  • Beem, Christopher; Dimofte, Tudor; Pasquetti, Sara
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)177

Twisted Hilbert spaces of 3d supersymmetric gauge theories
journal, August 2018

  • Bullimore, Mathew; Ferrari, Andrea
  • Journal of High Energy Physics, Vol. 2018, Issue 8
  • DOI: 10.1007/JHEP08(2018)018

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

  • Lawrie, Craig; Schäfer-Nameki, Sakura; Weigand, Timo
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)111

Theories of class F and anomalies
journal, October 2018

  • Lawrie, Craig; Martelli, Dario; Schäfer-Nameki, Sakura
  • Journal of High Energy Physics, Vol. 2018, Issue 10
  • DOI: 10.1007/JHEP10(2018)090

Affine Structures in 3-Manifolds: V. The Triangulation Theorem and Hauptvermutung
journal, July 1952

  • Moise, Edwin E.
  • The Annals of Mathematics, Vol. 56, Issue 1
  • DOI: 10.2307/1969769

The topology of four-dimensional manifolds
journal, January 1982


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

  • Manolescu, Ciprian
  • Journal of the American Mathematical Society, Vol. 29, Issue 1
  • DOI: 10.1090/jams829

P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst
journal, March 1991


On realizations of Pachner moves in 4d
journal, November 2015


The Volume Spectrum of Hyperbolic 4-Manifolds
journal, January 2000


Hyperbolic four-manifolds with one cusp
journal, August 2013


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

  • Benedetti, Riccardo; Petronio, Carlo
  • Manuscripta Mathematica, Vol. 88, Issue 1
  • DOI: 10.1007/BF02567824

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

  • Dijkgraaf, Robbert; Witten, Edward
  • Communications in Mathematical Physics, Vol. 129, Issue 2
  • DOI: 10.1007/BF02096988

Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models
journal, June 2019

  • Brunner, Ilka; Schulz, Jonathan; Tabler, Alexander
  • Journal of High Energy Physics, Vol. 2019, Issue 6
  • DOI: 10.1007/JHEP06(2019)046

Supersymmetric, integrable boundary field theories
journal, January 1996


Elliptic Genera of Two-Dimensional $${\mathcal{N} = 2}$$ N = 2 Gauge Theories with Rank-One Gauge Groups
journal, November 2013

  • Benini, Francesco; Eager, Richard; Hori, Kentaro
  • Letters in Mathematical Physics, Vol. 104, Issue 4
  • DOI: 10.1007/s11005-013-0673-y

Instantons and affine Lie algebras
journal, March 1996


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

  • Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)151

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