Gauge invariant finite size spectrum of the giant magnon

TL;DR

This paper demonstrates that finite size corrections to the giant magnon spectrum in classical string theory are gauge invariant and physically meaningful, matching gauge theory predictions and confirming their robustness.

Contribution

It establishes gauge invariance of finite size effects for the giant magnon and connects string theory results with gauge theory computations.

Findings

Finite size corrections are gauge invariant.

Quantum numbers are independent of gauge choice.

Results agree with gauge theory via the Hubbard model.

Abstract

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the $R$-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.