Quantum Flat Connections, KZ equations, and Integrability

Fuente: arXiv
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Autori principali: Banerjee, Sibasish, Haghighat, Babak, Latifi, Anouchah
Natura: Preprint
Pubblicazione: 2026
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author Banerjee, Sibasish
Haghighat, Babak
Latifi, Anouchah
author_facet Banerjee, Sibasish
Haghighat, Babak
Latifi, Anouchah
contents N=2 supersymmetric Yang-Mills theories are described in terms of a Hitchin system over a Riemann surface C. Focusing on strongly coupled Argyres-Douglas theories, we show that the corresponding flat bundle over C can be quantized such that the resulting quantum flat connection is integrable. For $sl_2$, the quantum connection takes values in $gl_2$(A) where A is an associative algebra which we explicitly describe for the cases of Painlevé I, II and IV. Moreover, we find that the quantum connection is equivalent to irregular versions of Knizhnik-Zamolodchikov (KZ) connections. Utilizing a suitable gauge transformation, one can show that the corresponding KZ equations give rise to BPZ equations.
format Preprint
id arxiv_https___arxiv_org_abs_2604_26159
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Quantum Flat Connections, KZ equations, and Integrability
Banerjee, Sibasish
Haghighat, Babak
Latifi, Anouchah
High Energy Physics - Theory
Representation Theory
N=2 supersymmetric Yang-Mills theories are described in terms of a Hitchin system over a Riemann surface C. Focusing on strongly coupled Argyres-Douglas theories, we show that the corresponding flat bundle over C can be quantized such that the resulting quantum flat connection is integrable. For $sl_2$, the quantum connection takes values in $gl_2$(A) where A is an associative algebra which we explicitly describe for the cases of Painlevé I, II and IV. Moreover, we find that the quantum connection is equivalent to irregular versions of Knizhnik-Zamolodchikov (KZ) connections. Utilizing a suitable gauge transformation, one can show that the corresponding KZ equations give rise to BPZ equations.
title Quantum Flat Connections, KZ equations, and Integrability
topic High Energy Physics - Theory
Representation Theory
url https://arxiv.org/abs/2604.26159