Abstract
It is possible to formulate light-cone gauge string field theory in noncritical dimensions. Such a theory corresponds to conformal gauge worldsheet theory with nonstandard longitudinal part. We study the longitudinal part of the worldsheet theory on higher genus Riemann surfaces. The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory.
Highlights
In this paper, we would like to study the X± CFT on higher genus Riemann surfaces
The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory
The results in this paper will be used in a forthcoming publication, in which we discuss the dimensional regularization of the multiloop amplitudes of light-cone gauge superstring field theory
Summary
As has been demonstrated in [1], all the properties of the worldsheet theory of the longitudinal variables can be deduced from the correlation function of the form. The insertions of TFLCTFLC at the interaction points in light-cone gauge perturbation theory arise by integrating superspace correlation function over the odd moduli parameters ξI , ξI . We can proceed in the same say as in the bosonic case and calculate the correlation functions of supersymmetric X± CFT, starting from (3.6). − g (z, ZN+1) + θΘN+1Sδ (z, ZN+1) In this way, it is possible to evaluate all the correlation functions of X +, X − with the source terms e−ip+r X −(Zr, Zr), e−ip−s X +(ws, ws) starting from (3.6). Which corresponds to the super Virasoro algebra with the central chargec = 12 − d These facts can be derived by calculating the expectation value of the energy-momentum tensor and their OPE’s. Dz −C T X ± + T LC + C∂C − 1 (DC) B
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