Extended SL(2,R)/U(1) characters, or modular properties of a simple non-rational conformal field theory

Abstract

We define extended SL(2,R)/U(1) characters which include a sum over winding sectors. By embedding these characters into similarly extended characters of N=2 algebras, we show that they have nice modular transformation properties. We calculate the modular matrices of this simple but non-trivial non-rational conformal field theory explicitly . As a result, we show that discrete SL(2,R) representations mix with continuous SL(2,R) representations under modular transformations in the coset conformal field theory. We comment upon the significance of our results for a general theory of non-rational conformal field theories.

arXiv commentJHEP style, 25 pages, 2 figures, v2: minor corrections, reference added, version to appear in JHEP

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Cited by in corpus (21)

• The non-compact elliptic genus: mock or modular
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• D-branes in N=2 Liouville and its mirror
• D-branes and extended characters in SL(2,R)/U(1)
• Non-compact String Backgrounds and Non-rational CFT
• Non-holomorphic Modular Forms and SL(2,R)/U(1) Superconformal Field Theory
• D-branes in Little String Theory
• Heterotic Resolved Conifolds with Torsion, from Supergravity to CFT
• N=2 Liouville Theory with Boundary
• D-branes and BCFT in Hpp-wave backgrounds
• Liouville Field, Modular Forms and Elliptic Genera
• Double-Scaling Limit of Heterotic Bundles and Dynamical Deformation in CFT
• Elliptic genera and real Jacobi forms
• Notes on the Verlinde formula in non-rational conformal field theories
• Conformally invariant boundary conditions in the antiferromagnetic Potts model and the $SL(2,\mathbb{R})/U(1)$ sigma model
• Comments on Non-holomorphic Modular Forms and Non-compact Superconformal Field Theories
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Heterotic warped Eguchi-Hanson spectra with five-branes and line bundles
• Modular Bootstrap of Boundary N=2 Liouville Theory
• Compact Formulas for the Completed Mock Modular Forms
• On modular properties of the AdS3 CFT