Gauge Invariant Action for the Open Bosonic String
Abstract
The issue of spacetime gauge invariance for the bosonic string has been earlier addressed using the loop variable formalism. In this paper the question of obtaining a gauge invariant action for the open bosonic string is discussed. The derivative with respect to ln a (where a is a worldsheet cutoff) of the partition function — which is first normalized by dividing by the integral of the twopoint function of a marginal operator — is a candidate for the action. Applied to the zeromomentum tachyon it gives a tachyon potential that is similar to those that have been obtained using Witten's background independent formalism. This procedure is easily made gauge invariant in the loop variable formalism by replacing ln a by Σ which is the generalization of the Liouville mode that occurs in this formalism. We also describe a method of resumming the Taylor expansion that is done in the loop variable formalism. This allows one to see the pole structure of string amplitudes that would not be visible in the original loop variable formalism.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2008
 DOI:
 10.1142/S0217751X08039323
 arXiv:
 arXiv:0712.1650
 Bibcode:
 2008IJMPA..23.1001S
 Keywords:

 String theory;
 loop variables;
 gauge invariance;
 action;
 High Energy Physics  Theory
 EPrint:
 19 pages, Latex file