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arXiv · 2604.26159

Quantum Flat Connections, KZ equations, and Integrability

Sibasish Banerjee·Babak Haghighat·Anouchah Latifi
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Abstract

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 Painlev\'e 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.

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Sibasish Banerjee, Babak Haghighat, Anouchah Latifi. 2026-04-28. Quantum Flat Connections, KZ equations, and Integrability. https://arxiv.org/abs/2604.26159

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