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arXiv · 2602.09260

Four-point functions with fractional R-symmetry excitations in the D1-D5 CFT

V. A. Souza Alves·Andre Alves Lima·G. M. Sotkov·M. Stanishkov
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Abstract

We study correlation functions with fractional-mode excitations of the R-symmetry currents in D1-D5 CFT. We show how fractional-mode excitations lift to the covering surface associated with correlation functions as a specific sum of integer-mode excitations, with coefficients that can be determined exactly from the covering map in terms of Bell polynomials. We consider the four-point functions of fractional excitations of two chiral/anti-chiral NS fields, Ramond ground states and the twist-two scalar modulus deformation operator that drives the CFT away from the free point. We derive explicit formulas for classes of these functions with twist structures $(n)$-$(2)$-$(2)$-$(n)$ and $(n_1)(n_2)$-$(2)$-$(2)$-$(n_1)(n_2)$, the latter involving double-cycle fields. The final answer for the four-point functions always depends only on the lift of the base-space cross-ratio. We discuss how this relates to Hurwitz blocks associated with different conjugacy classes of permutations, the corresponding OPE channels and fusion rules.

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V. A. Souza Alves, Andre Alves Lima, G. M. Sotkov, M. Stanishkov. 2026-02-09. Four-point functions with fractional R-symmetry excitations in the D1-D5 CFT. https://arxiv.org/abs/2602.09260

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