String center of mass operator and its effect on BRST cohomology

TL;DR

This paper extends the BRST complex for bosonic closed strings to include a well-defined string center of mass operator, revealing a cohomology that better reflects physical states and symmetries, especially at zero momentum.

Contribution

It introduces an extended BRST complex incorporating the string center of mass operator, clarifying the structure of zero-momentum states and their relation to background symmetries.

Findings

No doubling of physical states in the extended cohomology.

Zero-momentum ghost number one states correspond to Poincare generators.

Extended cohomology provides a more physical description of states.

Abstract

We consider the theory of bosonic closed strings on the flat background R(25,1). We show how the BRST complex can be extended to a complex where the string center of mass operator, x^mu_0, is well defined. We investigate the cohomology of the extended complex. We demonstrate that this cohomology has a number of interesting features. Unlike in the standard BRST cohomology, there is no doubling of physical states in the extended complex. The cohomology of the extended complex is more physical in a number of of aspects related to the zero-momentum states. In particular, we show that the ghost number one zero-momentum cohomology states are in one to one correspondence with the generators of the global symmetries of the background i.e., the Poincare algebra.