(0,2) dualities and the 4simplex
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 4manifold: the 4simplex. We then begin to flesh out a dictionary between more general triangulated 4manifolds 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 halfindices. We also describe how to produce standalone 2d theories (as opposed to interfaces) capturing the geometry of 4simplices and Pachner moves by making additional fieldtheoretic choices, and find in this context that the Pachner moves recover abelian \( \mathcal{N} \) = (0, 2) trialities of GaddeGukovPutrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4manifold geometry that has been developed in recent years.
 Authors:

 Univ. of California, Davis, CA (United States)
 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 10298479
 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 4simplex. United States: N. p., 2019.
Web. https://doi.org/10.1007/JHEP08(2019)132.
Dimofte, Tudor, & Paquette, Natalie M. (0,2) dualities and the 4simplex. United States. https://doi.org/10.1007/JHEP08(2019)132
Dimofte, Tudor, and Paquette, Natalie M. Fri .
"(0,2) dualities and the 4simplex". 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 4simplex},
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 4manifold: the 4simplex. We then begin to flesh out a dictionary between more general triangulated 4manifolds 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 halfindices. We also describe how to produce standalone 2d theories (as opposed to interfaces) capturing the geometry of 4simplices and Pachner moves by making additional fieldtheoretic choices, and find in this context that the Pachner moves recover abelian \( \mathcal{N} \) = (0, 2) trialities of GaddeGukovPutrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4manifold 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}
}
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