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Calculus of conformal fields on a compact Riemann surface

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arxiv 1708.07361 v2 pith:CWQPRHAF submitted 2017-08-24 math-ph math.CVmath.MPmath.PR

classification math-phmath.CVmath.MPmath.PR
keywords fieldsbackgroundcompactconformalderiveequationsfieldoperators
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Multiple chordal SLE($\kappa$) and quantum Calogero-Moser system

    math.PR 2025-05 reject novelty 6.0 of 10

    Multiple chordal SLE(kappa) partition functions with a marked boundary point are claimed to solve null vector equations and, after a gauge transform, to become quantum Calogero-Moser eigenstates.

  2. Multiple chordal SLE(0) and classical Calogero-Moser system

    math.PR 2025-05 conditional novelty 5.0 of 10

    Multiple chordal SLE(0) systems of type (n,m) have traces given by the real locus of rational functions with n prescribed critical points and m poles, and their growth-point dynamics is the classical Calogero-Moser system.

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