Calculus of conformal fields on a compact Riemann surface

2017/08/24 by Nam‐Gyu Kang, Kang, Nam-Gyu, Nikolai Makarov +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1708.07361

openalex publication_date 2017/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present analytical implementation of conformal field theory on a compact Riemann surface. We consider statistical fields constructed from background charge modifications of the Gaussian free field and derive Ward identities which represent the Lie derivative operators in terms of the Virasoro fields and the puncture operators associated with the background charges. As applications, we derive Eguchi-Ooguri's version of Ward's equations and certain types of BPZ equations on a torus.

Cited by

• Multiple chordal SLE(0) and classical Calogero-Moser system
• Multiple chordal SLE(κ) and quantum Calogero-Moser system

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