A Twisted Non-compact Elliptic Genus

Abstract

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

16 pages, minor improvements

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Cited by in corpus (36)

• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• 2d Index and Surface operators
• The Omega deformed B-model for rigid N=2 theories
• String theory at the tip of the cigar
• Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
• A holomorphic anomaly in the elliptic genus
• Localization and real Jacobi forms
• Lessons on Black Holes from the Elliptic Genus
• A 2d (0,2) appetizer
• Wall-crossing made smooth
• Mirror Symmetry and Bosonization in 2d and 3d
• Single-centered black hole microstate degeneracies from instantons in supergravity
• Moonshine in Fivebrane Spacetimes
• Elliptic genera and real Jacobi forms
• Elliptic Genera of Non-compact Gepner Models and Mirror Symmetry
• K3 String Theory, Lattices and Moonshine
• Comments on Non-holomorphic Modular Forms and Non-compact Superconformal Field Theories
• APS $\eta$-invariant, path integrals, and mock modularity
• The Black Hole Interior and a Curious Sum Rule
• Superstrings in Thermal Anti-de Sitter Space
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Higher Poles and Crossing Phenomena from Twisted Genera
• Umbral Moonshine and K3 Surfaces
• Counting Strings, Wound and Bound
• ADE Double Scaled Little String Theories, Mock Modular Forms and Umbral Moonshine
• Compact Formulas for the Completed Mock Modular Forms
• New supersymmetric index of heterotic compactifications with torsion
• An Elliptic Triptych
• Three-Charge Black Holes and Quarter BPS States in Little String Theory
• Squashed toric sigma models and mock modular forms
• Squashed Toric Manifolds and Higher Depth Mock Modular Forms
• Mock modularity from black hole scattering states
• Umbral Moonshine and String Duality
• TASI Lectures on Moonshine
• Non-Compact SCFT and Mock Modular Forms
• Quantum Black Hole Entropy and Localization in Supergravity