Tachyon Condensation on Fuzzy Sphere and Noncommutative Solitons

TL;DR

This paper explores tachyon condensation and noncommutative solitons on fuzzy spheres within string theory, revealing how D-branes can form from brane-antibrane systems and non-BPS D-branes, with implications for noncommutative geometry.

Contribution

It demonstrates the formation of codimension two D-branes via tachyon condensation and identifies noncommutative tachyonic solitons with D0-branes on fuzzy spheres.

Findings

Tachyon condensation generates D2-branes as bound states of D0-branes.

Noncommutative tachyonic solitons correspond to D0-branes.

Effective field theory on a fuzzy sphere describes noncommutative solitons.

Abstract

We study a brane-antibrane system and a non-BPS D-brane in SU(2) WZW model. We first discuss the tachyon condensation using the vertex operator formalism and find the generation of codimension two D-branes after the condensation. Our result is consistent with the recent interpretation that a D2-brane is a bound state of D0-branes. Then we investigate the world volume effective theory on a non-BPS D-brane. It becomes a field theory on the ``fuzzy sphere'' when the level is sent to infinity. The most interesting feature is that there exist the noncommutative tachyonic solitons and we can identify them with D0-branes. We also discuss the brane-antibrane system from the world volume point of view and comment on the relation to the noncommutative version of the index theorem.