Topological DBI actions and nonlinear instantons.pdfVIP

a r X i v : h e p - t h / 0 1 0 5 1 4 3 v 2 2 1 M a y 2 0 0 1 Topological DBI actions and nonlinear instantons A. Imaanpur ? Department of Physics, School of Sciences, Tarbiat Modares University, P.O.Box 14155-4838, Tehran, Iran, and Institute for Studies in Theoretical Physics and Mathematics P.O.Box 19395-5531, Tehran, Iran February 7, 2008 Abstract We consider Euclidean D4 and D6-branes filling the whole R4 and R6 space, re- spectively. In both cases, with a constant background B-field turned on for D4-branes, we propose actions which are the same as the DBI actions up to some constant or total derivative terms. These extra terms allow us to write the action as a square of nonlinear instanton equations. As such, the actions can easily be supersymmetrized using the methods of topological field theory. 1 Introduction D-branes in string theory are effectively described by the Dirac-Born-Infeld action. The action has also a supersymmetric extension which consists of two parts; the Dirac-Born-Infeld (DBI) part, and the Wess-Zumino part. Both parts of the action are invariant under the rigid spacetime supersymmetry transformations, however, for a specific choice of normalization of the Wess-Zumino term, the whole action turns out to have an extra local symmetry known as κ-symmetry. The κ-symmetry allows one to remove the redundant fermionic degrees of freedom [1]. Here we are only concerned with the bosonic part of the DBI action. Later on, we will explain on an alternative way to supersymmetrize the action using the methods of topological field theory [2, 3]. When a constant background B-field is turned on, the only change in the DBI action is to replace F – the field strength of the U(1) gauge field – by F + B everywhere in the action. Using the Seiberg-Witten map, one could also recast the action in terms of the open string variables and noncommutative filed strength F? [4]. In this description, the effect of B appears only through the open string metric, coupl