Note on Noncommutative Tachyon in Matrix Models

TL;DR

This paper investigates the transformation properties of the tachyon field in matrix models, revealing it as a nontrivial tensor that cannot be gauged away, and discusses its relation to tachyon condensation.

Contribution

It demonstrates that the spacetime symmetry on branes appears as a combination of matrix transformations and gauge transformations, affecting the tachyon's behavior.

Findings

Tachyon transforms as a tensor of different ranks under rotations.

Tachyon cannot be gauged away in the matrix model.

Conjecture that the tachyon relates to the usual scalar tachyon via a field redefinition.

Abstract

The solution representing a brane-anti-brane system in matrix models breaks the usual matrix spacetime symmetry. We show that the spacetime symmetry on the branes is not breaking, rather appears as a combination of the matrix spacetime transformation and a gauge transformation. As a result, the tachyon field, itself an off-diagonal entry in longitudinal matrices, transforms nontrivially under rotations, decomposing into tensors of different ranks. We also show that the tachyon field can never be gauged away, and conjecture that this field is related to the usual complex scalar tachyon by a field redefinition. We also briefly discuss tachyon condensation.