Sujay K. Ashok

A twisted non-compact elliptic genus

We give a detailed path integral derivation of the elliptic genus of the supersymmetric coset conformal field theory

Localization and real Jacobi forms

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S-duality, triangle groups and modular anomalies in \( \mathcal{N}=2 \) SQCD

, further twisted by a global U(1) symmetry. It gives rise to a Jacobi form in three variables, which is the modular completion of a mock modular form. The derivation provides a physical interpretation to the non-holomorphic part as arising from a difference in spectral densities for the continuous part of the right-moving bosonic and fermionic spectrum. The spectral asymmetry can also be read off directly from the reflection amplitudes of the theory. By performing an orbifold, we show how our twisted elliptic genus generalizes an existing example.

Elliptic genera of non-compact Gepner models and mirror symmetry

We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing Killing form, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.

D-branes in unoriented non-critical strings and duality in SO(N) and Sp(N) gauge theories

A bstractWe 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 Stückelberg 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 Kähler 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 Stückelberg fields from first principles.

Elliptic genera and real Jacobi forms

String theory on AdS3 space-times with boundary conditions that allow for black hole states has global asymptotic symmetries which include an infinite dimensional conformal algebra. Using the conformal current algebra for sigma-models on PSU(1,1|2), we explicitly construct the R-symmetry and Virasoro charges in the worldsheet theory describing string theory on AdS3 × S3 with Ramond-Ramond fluxes. We also indicate how to construct the full boundary superconformal algebra. The boundary superconformal algebra plays an important role in classifying the full spectrum of string theory on AdS3 with Ramond-Ramond fluxes, and in the microscopic entropy counting in D1-D5 systems.

Counting strings, wound and bound

A bstractWe study N=2