Foams and KZ-equations in Rozansky-Witten theories

Fuente: arXiv
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Main Authors: Gukov, Sergei, Haghighat, Babak, Reshetikhin, Nicolai
Format: Preprint
Published: 2024
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author Gukov, Sergei
Haghighat, Babak
Reshetikhin, Nicolai
author_facet Gukov, Sergei
Haghighat, Babak
Reshetikhin, Nicolai
contents In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic perspective. This approach illuminates various aspects of decorated TQFTs via geometry of the target space $X$ of RW theory. Through the formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric framework, we derive the corresponding braiding and associator morphisms. We discuss applications where the target space of RW theory emerges as the Coulomb branch of a compactified 6d SCFT or Little String Theory, with the latter being particularly intriguing as it results in a compact $X$.
format Preprint
id arxiv_https___arxiv_org_abs_2407_19757
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Foams and KZ-equations in Rozansky-Witten theories
Gukov, Sergei
Haghighat, Babak
Reshetikhin, Nicolai
High Energy Physics - Theory
In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic perspective. This approach illuminates various aspects of decorated TQFTs via geometry of the target space $X$ of RW theory. Through the formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric framework, we derive the corresponding braiding and associator morphisms. We discuss applications where the target space of RW theory emerges as the Coulomb branch of a compactified 6d SCFT or Little String Theory, with the latter being particularly intriguing as it results in a compact $X$.
title Foams and KZ-equations in Rozansky-Witten theories
topic High Energy Physics - Theory
url https://arxiv.org/abs/2407.19757