Quantum aspects of a noncommutative supersymmetric kink

TL;DR

This paper investigates quantum corrections to a supersymmetric kink in noncommutative 1+1D phi^4 theory, finding that quantum energy remains unaffected by noncommutativity and renormalization parallels the commutative case.

Contribution

It introduces a method to define supercharges and Hamiltonian in a noncommutative supersymmetric theory with infinite derivatives, and shows quantum corrections match the commutative case.

Findings

Quantum energy of the kink is independent of noncommutativity.

Renormalization process is identical to the commutative case.

Vacuum expectation value aligns with quantum energy of the kink.

Abstract

We consider quantum corrections to a kink of noncommutative supersymmetric phi^4 theory in 1+1 dimensions. Despite the presence of an infinite number of time derivatives in the action, we are able to define supercharges and a Hamiltonian by using an unconventional canonical formalism. We calculate the quantum energy E of the kink (defined as a half-sum of the eigenfrequencies of fluctuations) which coincides with its' value in corresponding commutative theory independently of the noncommutativity parameter. The renormalization also proceeds precisely as in the commutative case. The vacuum expectation value of the new Hamiltonian is also calculated and appears to be consistent with the value of the quantum energy E of the kink.