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# Advances in Theoretical and Mathematical Physics

## Volume 21 (2017)

### Number 7

### Special Issue: Proceedings of the Strings 2016 Conference in Beijing

Guest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University)

### The hidden symmetry of the heterotic string

Pages: 1729 – 1745

DOI: http://dx.doi.org/10.4310/ATMP.2017.v21.n7.a5

#### Authors

#### Abstract

We propose that Borcherds’ Fake Monster Lie algebra is a broken symmetry of heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study the fully flavored counting function for BPS instantons contributing to a certain loop amplitude. The result is controlled by $\Phi_{12}$, an automorphic form for $O (2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier coefficients are graded dimensions of a second-quantized Fock space for this large symmetry algebra. This construction provides a concrete realization of Harvey and Moore’s proposed relationship between Generalized Kac–Moody symmetries and supersymmetric string vacua.

Published 19 March 2018