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Note on Noncommutative Tachyon in Matrix Models

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.