V. A. Belavin, “<nobr>$N=1$</nobr> supersymmetric conformal block recursion relations”, TMF, 2007, Volume 152, Number 3,Pages <nobr>476

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$N=1$ supersymmetric conformal block recursion relations

V. A. Belavin^ab

^a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
^b International School for Advanced Studies (SISSA)

Abstract: We present explicit recursion relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry.

Keywords: $N{=}1$ superconformal field theory, four-point conformal block function, recursion relation.

Received: 01.12.2006

DOI: 10.4213/tmf6104