Abstract
Applying supersymmetric localization for superstring worldsheet theory with N=(1,1) supersymmetries on a cylinder and with arbitrary boundary interactions, we find the most general formula for the Ramond-Ramond (RR) coupling of D-branes. We allow all massive excitations of open superstrings, and find that only a finite number of them can contribute to the formula. The formula is written by Quillen's superconnection which includes higher form gauge fields, and the resultant general Chern-Simons terms are consistent with RR charge quantization. Applying the formula to boundary string field theory of a BPS D9-brane or a D9-antiD9 brane system, we find that any D9-brane creation via massive mode condensation is impossible.
Highlights
RR coupling formula including the tachyon modes was given in the context of boundary string field theory (BSFT) [6,7,8,9]
Applying supersymmetric localization for superstring worldsheet theory with N = (1, 1) supersymmetries on a cylinder and with arbitrary boundary interactions, we find the most general formula for the Ramond-Ramond (RR) coupling of D-branes
The BSFT action for the RR sector is nothing but the partition function of the worldsheet theory with some fermion zero modes corresponding to the background RR-forms, so basically we evaluate the expectation value of the operator exp[−IB]
Summary
Our interest here is whether one can climb up the potential hill in the BSFT, to obtain a solution of the BSFT representing multiple D-branes, starting from a single D-brane. We consider only D9-branes as a starting point for the BSFT action. These include a BPS D9-brane, and a pair of a D9-brane and an anti-D9-brane (brane-antibrane pair). Our aim is to show whether multiple D-branes can be created in the BSFT or not. It is easy to create a charge of a D-brane with different spatial world volume dimensions. The question of our concern is: let us start with a D9-brane, and with a condensation of massive modes on the D9-brane, can we create a charge of multiple D9-branes?. We check whether string theory can have a power to obtain multiple D-brane charges starting from the (naive) Hilbert space of a single D-brane
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