Exact Tachyon Condensation on Noncommutative Torus

TL;DR

This paper constructs exact solutions for tachyon condensation on noncommutative tori, providing a precise geometric description of D-brane bound states and illustrating the role of Morita equivalence in noncommutative geometry.

Contribution

It introduces an exact noncommutative solution framework for tachyon condensation on tori, highlighting the use of gauge Morita equivalence to generate bound states.

Findings

Exact solutions describe tachyon condensation on various D-branes.

Bound states of D-branes are obtained through these solutions.

Morita equivalence underpins the geometric framework.

Abstract

We construct the exact noncommutative solutions on tori. This gives an exact description of tachyon condensation on bosonic D-branes, non-BPS D-branes and brane-antibrane systems. We obtain various bound states of D-branes after the tachyon condensation. Our results show that these solutions can be generated by applying the gauge Morita equivalence between the constant curvature projective modules. We argue that there is a general framework of the noncommutative geometry based on the notion of Morita equivalence which underlies this specific example.