Elliptic genera and real Jacobi forms

We construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional N=(2,2) supersymmetric theories. They arise in a family labeled by two integers N and k which determine the central charge of the infrared fixed point through the formula c=3N(1+ 2N/k). We decompose the real Jacobi form into a mock modular form and a term arising from the continuous spectrum of the conformal field theory. We argue that the Jacobi form represents the elliptic genus of a theory defined on a 2N dimensional background with U(N) isometry, containing a complex projective space section, a circle fiber and a linear dilaton direction. We also present formulas for the elliptic genera of orbifolds of these models.Comment: 32 page

Localization and real Jacobi forms

We calculate the elliptic genus of two dimensional abelian gauged linear sigma models with (2,2) supersymmetry using supersymmetric localization. The matter sector contains charged chiral multiplets as well as Stueckelberg fields coupled to the vector multiplets. These models include theories that flow in the infrared to non-linear sigma models with target spaces that are non-compact Kahler manifolds with U(N) isometry and with an asymptotically linear dilaton direction. The elliptic genera are the modular completions of mock Jacobi forms that have been proposed recently using complementary arguments. We also compute the elliptic genera of models that contain multiple Stueckelberg fields from first principles.Comment: 19+1 pages, LaTeX. Minor correctio

Counting Strings, Wound and Bound

We analyze zero mode counting problems for Dirac operators that find their origin in string theory backgrounds. A first class of quantum mechanical models for which we compute the number of ground states arises from a string winding an isometric direction in a geometry, taking into account its energy due to tension. Alternatively, the models arise from deforming marginal bound states of a string winding a circle, and moving in an orthogonal geometry. After deformation, the number of bound states is again counted by the zero modes of a Dirac operator. We count these bound states in even dimensional asymptotically linear dilaton backgrounds as well as in Euclidean Taub-NUT. We show multiple pole behavior in the fugacities keeping track of a U(1) charge. We also discuss a second class of counting problems that arises when these backgrounds are deformed via the application of a heterotic duality transformation. We discuss applications of our results to Appell-Lerch sums and the counting of domain wall bound states.Comment: 38 page

Long Strings and Quasinormal Winding Modes

We compute the path integral for a particle on the covering group of SL(2,R) using a decomposition of the Lie algebra into adjoint orbits. We thus intuitively derive the Hilbert space of the particle on the group including discrete and continuous representations. Next, we perform a Lorentzian hyperbolic orbifold of the partition function and relate it to the Euclidean BTZ partition function. We use the particle model to inform further discussion of the spectral content of the one loop vacuum amplitude for strings on BTZ black hole backgrounds. We argue that the poles in the loop integrand code contributions of long string modes that wind the black hole. We moreover identify saddle point contributions of quasinormal winding modes.Comment: 31 page

Kokkelsterfte in de Oosterschelde juni 2010

Op 15 juni 2010 is door medewerkers van Rijkswaterstaat grote kokkelsterfte (Cerastoderma edule) gemeld bij de Slikken van de Dortsman (Stavenisse) in de Oosterschelde. Een veldbezoek op 17 juni 2010 door medewerkers van IMARES bevestigde deze sterfte. Verspreid over een groot gebied werden tienduizenden kokkels dood aangetroffen op het sediment oppervlak met het vlees nog aanwezig in de schelp. Een eerste onderzoek door het CVI gaf aan dat kokkels van de locatie Slikken van de Dortsman zwaar geïnfecteerd waren met een aantal soorten trematoden, zowel qua prevalentie (aantallen kokkels in de partij) als intensiteit (aantallen parasieten per kokkel). Eind juni 2010 werden in het kader van dit onderzoek acht locaties bezocht in de Oosterschelde