Worldsheet one-loop energy correction to IIA Giant Magnon

TL;DR

This paper calculates one-loop quantum corrections to the energy of a giant magnon in type IIA string theory on AdS4 x CP3, using QFT techniques and comparing with algebraic curve results.

Contribution

It provides a detailed perturbative calculation of one-loop energy corrections for the giant magnon in AdS4 x CP3, including handling coordinate-dependent coefficients.

Findings

One-loop energy correction computed for the giant magnon.

Agreement with algebraic curve method results.

Analysis includes velocity parameter expansion.

Abstract

We compute one-loop corrections to the energy of a IIA giant magnon solution in the $AdS_4 \times CP^3$ background by using the standard quantum field theory (QFT) techniques. The string action is expanded around the solution to the quadratic order in the fluctuation fields. The resulting action has 2D coordinate dependent-coefficients, a feature that complicates the analysis. The solution contains a worldsheet velocity parameter $v$, and is expanded in terms of the parameter. A perturbative analysis is carried out by treating the $v$-dependent parts as vertices. The energy is computed by first putting the system in a box of length $L$ and Fourier-transforming the fields into the discrete momentum modes. We compare our result with the results obtained by the algebraic curve method.