The hidden symmetry of the heterotic string

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We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of heterotic string theory compactified on T⁷ × T². As evidence, we study the fully flavored counting function for BPS instantons contributing to a certain loop amplitude. The result is controlled by Φ₁₂, an automorphic form for O(2, 26, 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.