Covariant BRST Quantization of Closed Strings in the PP-Wave Background

TL;DR

This paper develops a covariant BRST quantization method for closed strings in a pp-wave background with flux, constructing new free-mode representations and analyzing anomalies to determine spacetime dimensions.

Contribution

It introduces a covariant quantization framework for closed strings in a fluxed pp-wave background, including new free-mode representations and anomaly calculations.

Findings

Constructed covariant free-mode representations.

Calculated Virasoro algebra anomaly.

Determined spacetime dimensions from BRST nilpotency.

Abstract

We canonically quantize closed string theory in the pp-wave background with a non-zero flux of the three-form field strength by using the covariant BRST operator formalism. In this canonical quantization, we completely construct new covariant free-mode representations, for which it is particularly important to take account of the commutation relations of the zero mode of the light-cone string coordinate X^{-} with other modes. All covariant string coordinates are composed of the free-modes. Moreover, employing these covariant string coordinates for the energy-momentum tensor, we calculate the anomaly in the Virasoro algebra and determine the number of dimensions of spacetime and the ordering constant from the nilpotency condition of the BRST charge in the pp-wave background.