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arXiv · 1706.02706

BPS jumping loci are automorphic

Shamit Kachru·Arnav Tripathy
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Abstract

We show that BPS jumping loci -- loci in the moduli space of string compactifications where the number of BPS states jumps in an upper semi-continuous manner -- naturally appear as Fourier coefficients of (vector space-valued) automorphic forms. For the case of $T^2$ compactification, the jumping loci are governed by a modular form studied by Hirzebruch and Zagier, while the jumping loci in K3 compactification appear in a story developed by Oda and Kudla-Millson in arithmetic geometry. We also comment on some curious related automorphy in the physics of black hole attractors and flux vacua.

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Shamit Kachru, Arnav Tripathy. 2017-06-08. BPS jumping loci are automorphic. https://doi.org/10.1007/s00220-018-3090-3

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