Zero modes for the giant magnon

TL;DR

This paper explicitly constructs fermionic and bosonic zero modes for the giant magnon, facilitating direct quantization and revealing the underlying superalgebra structure in the context of AdS/CFT correspondence.

Contribution

It provides explicit solutions for fermionic and bosonic zero modes of the giant magnon, and demonstrates how to derive the superalgebra from these modes.

Findings

Explicit fermionic zero mode solutions constructed.

Simplified Lagrangian allows direct quantization.

Superalgebra derived from zero modes.

Abstract

We explicitly construct the eight fermion zero mode solutions for the Hofman-Maldacena giant magnon. The solutions are naturally gauge fixed under the \kappa-symmetry. Substituting the solutions back into the Lagrangian leads to a simple expression that can be quantized directly. We also show how to construct the SU(2|2)\times SU(2|2) superalgebra from these zero modes. For completeness we also find the four bosonic zero mode solutions.