• Corpus ID: 119182648

Mock modularity and a secondary elliptic genus

@article{Gaiotto2019MockMA,
  title={Mock modularity and a secondary elliptic genus},
  author={Davide Gaiotto and Theo Johnson-Freyd},
  journal={arXiv: High Energy Physics - Theory},
  year={2019}
}
The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of some of these invariants. The theory of mock modular forms makes a surprise appearance, shedding light on the integrality properties of some well-known examples. 
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References

SHOWING 1-10 OF 56 REFERENCES
Secondary invariants for string bordism and topological modular forms
Elliptic genera and quantum field theory
It is shown that in elliptic cohomology — as recently formulated in the mathematical literature — the supercharge of the supersymmetric nonlinear signa model plays a role similar to the role of the…
Secondary invariants for string cobordism and tmf
Using spectral invariants of Dirac operators we construct a secondary version of the Witten genus, namely a bordism invariant of string manifolds in dimensions 4m−1. We prove a secondary index…
Supersymmetric field theories and generalized cohomology
This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field…
Notes on the K3 Surface and the Mathieu Group M 24
We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M 24. The reason remains a…
Liouville field, modular forms and elliptic genera
When we describe non-compact or singular Calabi–Yau manifolds by CFT, continuous as well as discrete representations appear in the theory. These representations mix in an intricate way under the…
Localization and real Jacobi forms
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…
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,…
4-manifolds and topological modular forms
We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with…
Kac-Moody algebras, conformal symmetry and critical exponents
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