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

## TL;DR

This paper constructs fermion zero modes for the mixed-flux AdS3 giant magnon and derives associated superalgebras, enhancing understanding of supersymmetry in these string backgrounds.

## Contribution

It explicitly constructs fermion zero modes for the mixed-flux AdS3 giant magnon and derives the related superalgebras from semiclassical quantization.

## Key findings

- Explicit fermion zero modes for AdS3 backgrounds
- Derivation of superalgebras from zero modes
- Enhanced understanding of supersymmetry in mixed-flux backgrounds

## 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.