On Marginal Deformations in Superstring Field Theory
Amer Iqbal, Asad Naqvi
TL;DR
The paper investigates marginal Wilson-line deformations in open superstring field theory using level truncation, comparing BPS and non-BPS D-branes. On a BPS D-brane, the Wilson-line effective potential becomes progressively flatter with higher levels and shows no branching at the levels studied. On a non-BPS D-brane, two branches appear: an M-branch with zero tachyon vev and a V-branch with nonzero tachyon vev, although the V-branch exists only within a finite range of the marginal parameter $|w|$ and eventually merges with the M-branch. From the V-branch, the authors extract a nonzero mass for the $U(1)$ gauge field in the tachyon-condensed vacuum, suggesting stabilization as the level is increased, though further higher-level analysis is needed for stronger evidence.
Abstract
We use level truncated superstring field theory to obtain the effective potential for the Wilson line marginal deformation parameter which corresponds to the constant vacuum expectation value of the U(1) gauge field on the D-brane in a particular direction. We present results for both the BPS and the non-BPS D-brane. In the case of non-BPS D-brane the effective potential has branches corresponding to the extrema of the tachyon potential. In the branch with vanishing tachyon vev (M-branch), the effective potential becomes flatter as the level of the approximation is increased. The branch which corresponds to the stable vacuum after the tachyon has condensed (V-branch) exists only for a finite range of values of marginal deformation parameter. We use our results to find the mass of the gauge field in the stable tachyonic vacuum. We find this mass to be of a non-zero value which seems to stabilize as the level approximation is improved.