String field theory vertices for fermions of integral weight

Abstract

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 ηξ-system and the twisted bc-system used in bosonic vacuum string field theory.

String Field Theory Projectors for Fermions of Integral Weight

“…8 This is a distinguished feature of N=2 string field theory. A similar cancellation has been observed for the anomaly of midpoint preserving reparametrizations in [36]. Both cancellations are consequences of relation (2.7).…”

“…in terms of Neumann coefficients N rs kl with 1 ≤ r, s ≤ 3. For the nonzero-mode part of these coefficients it was shown in [36] (cf. also [37]) that they are related to the bosonic coefficients N rs mn by N rs mn = 2 m n V rs mn , m, n ≥ 1 .…”

“…In this section we reformulate the interaction vertex of the fermionic first order system [36] in the continuous Moyal basis. General methods for the diagonalization of the fermionic vertex were presented in [47,43,37].…”

“…Such a first order system appears in bosonic string field theory as the twisted bc system, in the fermionic sector of N=2 string field theory [34] and as the auxiliary ηξ ghost system of N=1 strings which is introduced in the process of fermionization of the superconformal ghosts [35]. We use a reformulation of the interaction vertex for such a system, which has been constructed explicitly in [36] (see also [37]), in terms of a continuous Moyal basis [38][39][40][41][42][43][44]. 2 The diagonalization of the vertex is greatly simplified due to an intimate relation of the bosonic matter Neumann matrices and those for the fermionic (1, 0)-system [36,37].…”

“…The U (1) charges of the insertions of the correlation functions have to sum up to +1 in order to give a nonvanishing result. -The somewhat unusual factors of 2 in the next two formulas stem from our normalization (2.5).14 Recall that the second factor originates from the nontrivial background charge of the system[36].…”