Nilpotent Symmetries of a Model of 2D Diffeomorphism Invariant Theory: BRST Approach

TL;DR

This paper develops a comprehensive BRST and anti-BRST symmetry framework for a 2D diffeomorphism invariant bosonic string theory, introducing novel off-shell nilpotent and anticommuting transformations and deriving related invariants and charges.

Contribution

It provides the first complete derivation of proper anti-BRST transformations and Curci-Ferrari restrictions for this model, extending previous work limited to BRST symmetry.

Findings

Proper off-shell nilpotent (anti-)BRST transformations derived.

Curci-Ferrari type restrictions identified and formulated.

Explicit conserved (anti-)BRST and ghost charges obtained.

Abstract

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss the full set of proper BRST and anti-BRST transformations for a 2D diffeomorphism invariant theory which is described by the Lagrangian density of a standard bosonic string. The above (anti-)BRST transformations are off-shell nilpotent and absolutely anticommuting. The latter property is valid on a submanifold of the space of the quantum fields where the 2D version of the universal (anti-)BRST invariant Curci-Ferrari (CF) type of restrictions are satisfied. We derive the precise forms of the BRST and anti-BRST invariant Lagrangian densities as well as the exact expressions for the conserved (anti-)BRST and ghost charges. The lucid derivation of the proper anti-BRST symmetry transformations and the emergence of the CF-type restrictions are completely novel results for our present bosonic string which has already been discussed earlier in literature where only the BRST symmetry transformations have been pointed out. We briefly mention the derivation of the CF-type restrictions from the modified version of Bonora-Tonin superfield approach, too.