• Corpus ID: 119182648

Mock modularity and a secondary elliptic genus

  title={Mock modularity and a secondary elliptic genus},
  author={Davide Gaiotto and Theo Johnson-Freyd},
  journal={arXiv: High Energy Physics - Theory},
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. 
Chern characters for supersymmetric field theories
We construct a map from d|1-dimensional Euclidean field theories to complexified K-theory when d = 1 and complex analytic elliptic cohomology when d = 2. This provides further evidence for the
APS η-invariant, path integrals, and mock modularity
Abstract We show that the Atiyah-Patodi-Singer η-invariant can be related to the temperature-dependent Witten index of a noncompact theory and give a new proof of the APS theorem using scattering
Chern characters and supersymmetric field theories
We construct a map from $d|1$-dimensional Euclidean field theories to complexified K-theory when $d=1$ and complex analytic elliptic cohomology when $d=2$. This provides further evidence for the
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
Three Avatars of Mock Modularity
Mock theta functions were introduced by Ramanujan in 1920 but a proper understanding of mock modularity has emerged only recently with the work of Zwegers in 2002. In these lectures we describe three
Snowmass White Paper: Moonshine
We present a brief overview of Moonshine with an emphasis on connections to physics. Moonshine collectively refers to a set of phenomena connecting group theory, analytic number theory, and vertex
In my research, I apply higher algebra to the study of quantum field theory, and I apply quantum field theory to the study of higher algebra — two areas that have a rich history of interaction
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 $SO(3)$
Fun with F24
We study some special features of $F_{24}$, the holomorphic $c=12$ superconformal field theory (SCFT) given by 24 chiral free fermions. We construct eight different Lie superalgebras of "physical"
Topological Mathieu Moonshine.
We explore the Atiyah-Hirzebruch spectral sequence for the $tmf^\bullet[\frac12]$-cohomology of the classifying space $BM_{24}$ of the largest Mathieu group $M_{24}$, twisted by a class $\omega \in


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