The non-compact elliptic genus: mock or modular

@article{Troost2010TheNE,
  title={The non-compact elliptic genus: mock or modular},
  author={Jan Troost},
  journal={Journal of High Energy Physics},
  year={2010},
  volume={2010},
  pages={1-18}
}
  • J. Troost
  • Published 21 April 2010
  • Mathematics
  • Journal of High Energy Physics
We analyze various perspectives on the elliptic genus of non-compact supersymmetric coset conformal field theories with central charge larger than three. We calculate the holomorphic part of the elliptic genus via a free field description of the model, and show that it agrees with algebraic expectations. The holomorphic part of the elliptic genus is directly related to an Appell-Lerch sum and behaves anomalously under modular transformations. We analyze the origin of the anomaly by calculating… 

A holomorphic anomaly in the elliptic genus

A bstractWe consider a class of gauged linear sigma models (GLSMs) in two dimensions that flow to non-compact (2, 2) superconformal field theories in the infra-red, a prototype of which is the SL(2,

Topological string theory, modularity and non-perturbative physics

In this thesis the holomorphic anomaly of correlators in topological string theory, matrix models and supersymmetric gauge theories is investigated. In the first part it is shown how the techniques

Lessons on black holes from the elliptic genus

A bstractWe further study the elliptic genus of the cigar SL(2, ℝ)k/U(1) coset supercon-formal field theory. We find that, even in the small curvature, infinite level limit, there are holomorphic and

Holomorphic anomalies, fourfolds and fluxes

Abstract We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition

Duality and mock modularity

We derive a holomorphic anomaly equation for the Vafa-Witten partition function for twisted four-dimensional $\mathcal{N} =4$ super Yang-Mills theory on $\mathbb{CP}^{2}$ for the gauge group $SO(3)$

A twisted non-compact elliptic genus

We give a detailed path integral derivation of the elliptic genus of the supersymmetric coset conformal field theory $$ {{{{\text{SL}}\left( {2,\mathbb{R}} \right)}} \left/ {{{\text{U}}(1)}} \right.}

Compact formulas for the completed mock modular forms

A bstractIn this paper we present a new compact expression of the elliptic genus of SL(2)/U(1)-supercoset theory by making use of the ‘spectral flow method’ of the pathintegral evaluation. This new

Higher poles and crossing phenomena from twisted genera

A bstractWe demonstrate that Appell-Lerch sums with higher order poles as well as their modular covariant completions arise as partition functions in the cigar conformal field theory with worldsheet

Elliptic genera and real Jacobi forms

A bstractWe construct real Jacobi forms with matrix index using path integrals. The path integral expressions represent elliptic genera of two-dimensional $ \mathcal{N} $ = (2, 2) supersymmetric

Elliptic genera of non-compact Gepner models and mirror symmetry

A bstractWe consider tensor products of N = 2 minimal models and non-compact conformal field theories with N = 2 superconformal symmetry, and their orbifolds. The elliptic genera of these models give
...

References

SHOWING 1-10 OF 82 REFERENCES

Non-compact WZW conformal field theories

We discuss non-compact WZW sigma models, especially the ones with symmetric space H C /H as the target, for H a compact Lie group. They offer examples of non-rational conformal field theories. We

Higher-Level Appell Functions, Modular Transformations, and Characters

We study modular transformation properties of a class of indefinite theta series involved in characters of infinite-dimensional Lie superalgebras. The level-ℓ Appell functions satisfy open

N = 2 gauged WZW models and the elliptic genus

Algebraic Geometry and Effective Lagrangians

The partition function of the supersymmetric two-dimensional black hole and little string theory

We compute the partition function of the supersymmetric two-dimensional euclidean black hole geometry described by the SL(2,)/U(1) superconformal field theory. We decompose the result in terms of

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

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

The Partition Function of the Two-Dimensional Black Hole Conformal Field Theory

The partition function of the conformal field theory on the two-dimensional euclidean black hole background is computed using path-integral techniques and confirmation for the bound on the spin of the discrete representations and the density of the continuous representations is determined.

Notes on non-critical superstrings in various dimensions

We study non-critical superstrings propagating in d ? 6 dimensional Minkowski space or equivalently, superstrings propagating on the two-dimensional euclidean black hole tensored with d-dimensional

String theory. Vol. 1: An introduction to the bosonic string

String Theory comprises two volumes which give a comprehensive and pedagogic account of the subject. Volume 1, first published in 1998, provides a thorough introduction to the bosonic string. The
...