Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon

Abstract

We explicitly construct the four and two fermion zero modes for the mixed-flux generalization of the Hofman-Maldacena giant magnon on two of the AdS${}_3$ backgrounds with maximal amount of supersymmetry, AdS${}_3\times$S${}^3\times$T${}^4$ and AdS${}_3\times$S${}^3\times$S${}^3\times$S${}^1$. We also show how to get the $\mathfrak{psu}(1|1{)}^4$ and $\mathfrak{su}(1|1{)}^2$ superalgebras from the semiclassically quantized fermion zero modes.

51 pages, 1 figure; references added, typos corrected, minor change to introduction

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