Violation of Lorentz invariance in type II Green-Schwarz superstrings in curved D=10, N=2 superspace

Abstract

The divergent part of the d=2 one loop effective action of the σ-model describing type II (both IIA and IIB) Green-Schwarz superstrings propagating in a background D=2, N=2 curved superspace is computed, using Kallosh's gauge fixing procedure to fix the fermionic κ-symmetry of the quantum fluctuations. We obtain a divergent contribution, which manifestly violates spacetime Lorentz invariance, and which cannot be absorbed into a variation of the classical string action under a superspace diffeomorphism, even though the background fields are on their mass shell. We argue that this Lorentz “anomaly” is an artifact of the gauge-fixing procedure which is manifestly Lorentz non-covariant. We delineate the reasons why such Lorentz violations did not surface in earlier calculations involving N=1 heterotic Green-Schwarz superstrings.