String Field Theory Vertices for Fermions of Integral Weight

TL;DR

This paper develops string field theory vertices for fermionic systems with specific conformal weights, analyzing their properties and connections to bosonic coefficients, with implications for various string theory formalisms.

Contribution

It constructs and analyzes Witten-type vertices for fermionic first order systems, revealing their relation to bosonic coefficients and implications for string field theory.

Findings

Neumann coefficients linked to bosonic coefficients

Reparametrization anomaly cancels with bosonic contributions

Overlap equations for interaction vertices verified

Abstract

We construct Witten-type string field theory vertices for a fermionic first order system with conformal weights (0,1) in the operator formulation using delta-function overlap conditions as well as the Neumann function method. The identity, the reflector and the interaction vertex are treated in detail paying attention to the zero mode conditions and the U(1) charge anomaly. The Neumann coefficients for the interaction vertex are shown to be intimately connected with the coefficients for bosons allowing a simple proof that the reparametrization anomaly of the fermionic first order system cancels the contribution of two real bosons. This agrees with their contribution c=-2 to the central charge. The overlap equations for the interaction vertex are shown to hold. Our results have applications in N=2 string field theory, Berkovits' hybrid formalism for superstring field theory, the \eta\xi-system and the twisted bc-system used in bosonic vacuum string field theory.