# Lifting 1/4-BPS States on K3 and Mathieu Moonshine

## TL;DR

This paper investigates how conformal perturbation theory lifts degeneracies of 1/4-BPS states in K3 sigma models, revealing their actual counts and implications for Mathieu moonshine.

## Contribution

It demonstrates that perturbing away from the orbifold point lifts degeneracies, allowing the elliptic genus to count actual BPS states, advancing understanding of K3's BPS spectrum.

## Key findings

- Degeneracy of 1/4-BPS states is fully lifted near the Kummer surface.
- Elliptic genus measures the actual number of BPS states after perturbation.
- Implications for symmetry surfing and Mathieu moonshine are discussed.

## Abstract

The elliptic genus of K3 is an index for the 1/4-BPS states of its sigma model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find that this fully lifts the accidental degeneracy of the 1/4-BPS states with h=1. At a generic point near the Kummer surface the elliptic genus thus measures not just their index, but counts the actual number of these BPS states. We comment on the implication of this for symmetry surfing and Mathieu moonshine.