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Title: Toda theory from six dimensions

Abstract

We describe a compactification of the six-dimensional (2,0) theory on a foursphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and twodimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.

Authors:
 [1];  [2]
  1. Inst. for Advanced Study, Princeton, NJ (United States). School for National Sciences
  2. Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1502497
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: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Field Theories in Higher Dimensions; Supersymmetric Gauge Theory; Topological Field Theories

Citation Formats

Córdova, Clay, and Jafferis, Daniel L. Toda theory from six dimensions. United States: N. p., 2017. Web. doi:10.1007/jhep12(2017)106.
Córdova, Clay, & Jafferis, Daniel L. Toda theory from six dimensions. United States. doi:10.1007/jhep12(2017)106.
Córdova, Clay, and Jafferis, Daniel L. Tue . "Toda theory from six dimensions". United States. doi:10.1007/jhep12(2017)106. https://www.osti.gov/servlets/purl/1502497.
@article{osti_1502497,
title = {Toda theory from six dimensions},
author = {Córdova, Clay and Jafferis, Daniel L.},
abstractNote = {We describe a compactification of the six-dimensional (2,0) theory on a foursphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and twodimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.},
doi = {10.1007/jhep12(2017)106},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2017,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 7 works
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Figures / Tables:

Figure 1 Figure 1: The six-dimensional geometry relevant to the AGT conjecture. The $S$4 is viewed as a fibration of $S$3 over a line. By reducing on $S$3 we obtain complex Chern-Simons theory on the product of the Riemann surface $Σ$ times an interval.

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