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

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.

arXiv comment29+5 pp, a sign mistake corrected in eqs. (3.14) and (4.20), footnote 6 added to clarify this point, references added

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• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• Microstate Renormalization in Deformed D1-D5 SCFT
• The Stranger Things of Symmetric Product Orbifold CFTs
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• Dynamical evolution in the D1D5 CFT
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• On Rational Points in CFT Moduli Spaces
• SU(2) channels the cancellation of K3 BPS states
• Tracking the symmetries of ${\mathbb{Z}}_3$-orbifold K3s within the Mathieu groups