1,493 research outputs found
Twining Genera of (0,4) Supersymmetric Sigma Models on K3
Conformal field theories with (0,4) worldsheet supersymmetry and K3 target
can be used to compactify the E8xE8 heterotic string to six dimensions in a
supersymmetric manner. The data specifying such a model includes an appropriate
configuration of 24 gauge instantons in the E8xE8 gauge group to satisfy the
constraints of anomaly cancellation. In this note, we compute twining genera -
elliptic genera with appropriate insertions of discrete symmetry generators in
the trace - for (0,4) theories with various instanton embeddings. We do this by
constructing linear sigma models which flow to the desired conformal field
theories, and using the techniques of localization. We present several examples
of such twining genera which are consistent with a moonshine relating these
(0,4) models to the finite simple sporadic group M24.Comment: 22 pages, 3 tables. We thank T. Eguchi and K. Hikami for permission
to copy our Tables 2 and 3 (M24 character table and q-expansions of some
twining genera in the (4,4) sigma model with K3 target) from their article
arXiv:1008.492
Maass-Jacobi Poincar\'e series and Mathieu Moonshine
Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to
each conjugacy class of the largest sporadic simple group of Mathieu. We
introduce a modification of this assignment, whereby weak Jacobi forms are
replaced by semi-holomorphic Maass-Jacobi forms of weight one and index two. We
prove the convergence of some Maass-Jacobi Poincar\'e series of weight one, and
then use these to characterize the semi-holomorphic Maass-Jacobi forms arising
from the largest Mathieu group.Comment: 27 pages, minor correction
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