Elliptic genera and real Jacobi forms

A bstract We construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional = (2, 2) supersymmetric theories. They arise in a family labeled by two integers N and k which determine the central charge of the infrared fixe...

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Bibliographic Details
Published in:The journal of high energy physics 2014, Vol.2014 (1), p.1-32, Article 82
Main Authors: Ashok, Sujay K., Troost, Jan
Format: Article
Language:English
Subjects:
Asymptotic properties
Classical and Quantum Gravitation
Dilatons
Elementary Particles
High energy physics
High Energy Physics - Theory
Infrared
Integrals
Modular
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Slopes
String Theory
Two dimensional
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Summary:A bstract We construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional = (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 = 3 N (1 + 2 N / 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. For a given N and k we argue that the Jacobi form represents the elliptic genus of a theory defined on a 2 N dimensional linear dilaton background with U ( N ) isometry, an asymptotic circle of radius and linear dilaton slope . We also present formulas for the elliptic genera of their orbifolds.
ISSN:1029-8479
1126-6708
1029-8479
DOI:10.1007/JHEP01(2014)082