Perturbative worldvolume dynamics of the bosonic membrane and string
Abstract
We study the worldvolume theory of a bosonic membrane perturbatively and discuss if one can obtain any conditions on the number of spacetime dimensions from the consistency of the theory. We construct an action which is suitable for such a study. In order to study the theory perturbatively we should specify a classical background around which perturbative expansion is defined. We will discuss the conditions which such a background should satisfy to deduce the critical dimension. Unfortunately, we do not know any background satisfying such conditions. In order to get indirect evidences for the critical dimension of the membrane, we next consider two string models obtained via doubledimensional reduction of the membrane. The first one reduces to the Polyakov string theory in the conformal gauge. The second one is described by the Schild action. We show that the critical dimension is 26 for these string theories, which implies that the critical dimension is 27 for the membrane theory.
 Publication:

Nuclear Physics B
 Pub Date:
 October 2001
 DOI:
 10.1016/S05503213(01)00400X
 arXiv:
 arXiv:hepth/0107103
 Bibcode:
 2001NuPhB.614..171H
 Keywords:

 High Energy Physics  Theory
 EPrint:
 30 pages, 1 figure, LATEX2e, axodraw.sty used, references added