# BKM Lie superalgebras from counting twisted CHL dyons

Suresh Govindarajan (Madras)

24.06.2010 at 16:15

Following Sen, we study the counting of (`twisted') BPS states that contribute to twisted
helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The
generating functions of half-BPS states, twisted as well as untwisted, are given in terms of
multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These
multiplicative eta products enable us to construct Siegel modular forms that count twisted
quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a
special class of Siegel modular forms, the dd-modular forms, that have been classified by
Clery and Gritsenko. We show that each one of these dd-modular forms arise as the Weyl-
Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie
superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the
walls of marginal stability in the corresponding CHL model for twisted dyons as well as
untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that
are consistent with physical expectations.

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