Fermions on the Worldsheet of Effective Strings via Coset Construction

TL;DR

This paper develops a detailed coset construction for fermions on string worldsheets, demonstrating how nonlinear symmetries restrict interactions and identifying the critical dimension for fermionic strings through one-loop integrability.

Contribution

It provides a comprehensive CCWZ-based framework for fermions on effective string worldsheets, including non-supersymmetric cases and the derivation of critical dimension via integrability.

Findings

Nonlinear realizations restrict fermionic interactions.

Supersymmetric models exemplify the construction with Goldstinos.

Critical dimension D=10 identified through one-loop integrability.

Abstract

In this paper the detailed CCWZ procedure for introducing fermions on the world sheet of a string propagating in flat space-time is presented. The theory of nonlinear realizations is used to derive the transformation as well as the interactions of fermionic matter fields under arbitrary spinorial representations of the unbroken subgroup. This demonstrates that even for non-supersymmetric spinors, the interactions are still severely restricted by the nonlinearly realized symmetry. We also explain how supersymmetric models provide an example for this construction with Goldstinos as matter fields, and how one can use the $\kappa$-symmetry of the Green Schwarz action in particular, to verify this nonlinear transformation for a specific matter field representation. We finally restrict the target space dimension without reference to supersymmetry, but rather by imposing one-loop integrability on a fermionic string that nonlinearly realizes Poincare symmetry. This singles out the critical dimension $D=10$ for heterotic, GS and RNS supersymmetric strings.