Abstract
We consider the theory of bosonic closed strings on the flat background ℝ25,1. We show how the BRST complex can be extended to a complex where the string center of mass operator,x μ0 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 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 backgroundi.e., the Poincaré algebra.
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Supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative agreement #DF-FC02-94ER40818
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Astashkevich, A., Belopolsky, A. String center of mass operator and its effect on BRST cohomology. Commun. Math. Phys. 186, 109–136 (1997). https://doi.org/10.1007/BF02885675
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DOI: https://doi.org/10.1007/BF02885675