Recursion representation of the Neveu-Schwarz superconformal block

TL;DR

This paper develops a recursive framework for calculating four-point superconformal blocks in the N=1 Neveu-Schwarz algebra, expressing coefficients as sums over poles in conformal weight and central charge, with explicit residue calculations.

Contribution

It introduces a novel recursive method for superconformal blocks, providing explicit pole sum representations and residue formulas for the N=1 Neveu-Schwarz algebra.

Findings

Derived closed-form recurrence relations for block coefficients

Expressed coefficients as sums over poles in conformal weight and central charge

Calculated residues of poles explicitly

Abstract

Four-point super-conformal blocks for the N = 1 Neveu-Schwarz algebra are defined in terms of power series of the even super-projective invariant. Coefficients of these expansions are represented both as sums over poles in the "intermediate" conformal weight and as sums over poles in the central charge of the algebra. The residua of these poles are calculated in both cases. Closed recurrence relations for the block coefficients are derived.