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BPS Jumping Loci are Automorphic

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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 T2 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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Authors and Affiliations

  1. Stanford Institute for Theoretical Physics, Stanford University, Palo Alto, CA, 94305, USA

    Shamit Kachru

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Arnav Tripathy

Authors
  1. Shamit Kachru
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  2. Arnav Tripathy
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Correspondence to Arnav Tripathy.

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Communicated by X. Yin

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Kachru, S., Tripathy, A. BPS Jumping Loci are Automorphic. Commun. Math. Phys. 360, 919–933 (2018). https://doi.org/10.1007/s00220-018-3090-3

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