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

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.

💡 Research Summary

The paper investigates correlation functions in the D1‑D5 symmetric‑orbifold CFT that involve fractional‑mode excitations of the R‑symmetry currents. Starting from the free orbifold point, the authors define fractional modes Jᵃ_{‑k/n} as diagonal combinations of the seed‑theory currents in the presence of an n‑cycle twist σ_{