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We propose a field theory for describing the tachyon on a brane–antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: (a) absence of plane-wave solutions around the minimum, and (b) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial configuration towards the minimum of the potential. Classical solutions in this field theory include nonrelativistic matter with arbitrary spatial distribution of energy.
Ashoke Sen (2002) studied this question.