Exact Rolling Tachyon in Noncommutative Field Theory

TL;DR

This paper derives exact homogeneous rolling tachyon solutions in noncommutative DBI field theory on unstable D-branes, revealing specific solution forms and electric field constraints.

Contribution

It provides explicit exact solutions for rolling tachyons in noncommutative DBI theory with constant electric fields, covering all homogeneous configurations.

Findings

Solutions include hyperbolic cosine, sine, and exponential forms.

Only constant electric fields satisfy the equations of motion.

Exact solutions exist for all homogeneous configurations.

Abstract

We study the exact rolling tachyon solutions in DBI type noncommutative field theory with a constant open string metric and noncommutative parameter on an unstable D$p$-brane. Functional shapes of the obtained solutions span all possible homogeneous rolling tachyon configurations; that is, they are hyperbolic-cosine, hyperbolic-sine, and exponential under $1/\cosh$ runaway NC tachyon potential. Even if general DBI type NC electric field is turned on, only a constant electric field satisfies the equations of motion, and again, exact rolling tachyon solutions are obtained.