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High Energy Physics - Theory, hep-th
Abstract:
We study the second quantized version of the twisted twining genera of
generalized Mathieu moonshine, and verify that they give rise to Siegel modular
forms with infinite product representations. Most of these forms are expected
to have an interpretation as twisted partition functions counting 1/4 BPS dyons
in type II superstring theory on K3\times T^2 or in heterotic CHL-models. We
show that all these Siegel modular forms, independently of their possible
physical interpretation, satisfy an "S-duality" transformation and a
"wall-crossing formula". The latter reproduces all the eta-products of an older
version of generalized Mathieu moonshine proposed by Mason in the '90s.
Surprisingly, some of the Siegel modular forms we find coincide with the
multiplicative (Borcherds) lifts of Jacobi forms in umbral moonshine.
