Nonassociative Star Product Deformations for DBrane WorldVolumes in Curved Backgrounds
Abstract
We investigate the deformation of Dbrane worldvolumes in curved backgrounds. We calculate the leading corrections to the boundary conformal field theory involving the background fields, and in particular we study the correlation functions of the resulting system. This allows us to obtain the worldvolume deformation, identifying the open string metric and the noncommutative deformation parameter. The picture that unfolds is the following: when the gauge invariant combination ω=B+F is constant one obtains the standard Moyal deformation of the brane worldvolume. Similarly, when dω= 0 one obtains the noncommutative Kontsevich deformation, physically corresponding to a curved brane in a flat background. When the background is curved, H=dω≠ 0, we find that the relevant algebraic structure is still based on the Kontsevich expansion, which now defines a nonassociative star product with an A_{∞} homotopy associative algebraic structure. We then recover, within this formalism, some known results of Matrix theory in curved backgrounds. In particular, we show how the effective action obtained in this framework describes, as expected, the dielectric effect of Dbranes. The polarized branes are interpreted as a soliton, associated to the condensation of the brane gauge field.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2002
 DOI:
 10.1007/s002201000569
 arXiv:
 arXiv:hepth/0101219
 Bibcode:
 2002CMaPh.225...33C
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Symplectic Geometry
 EPrint:
 Latex, 50 pages