# Supersymmetric field theories and generalized cohomology

@article{Stolz2011SupersymmetricFT, title={Supersymmetric field theories and generalized cohomology}, author={Stephan Stolz and Peter Teichner}, journal={arXiv: Algebraic Topology}, year={2011}, pages={279-340} }

This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field theories is given, refining Segal's axioms for conformal field theories. We state and give an outline of the proof of various results relating field theories to cohomology theories.

## 88 Citations

Supersymmetric Field Theories from Twisted Vector Bundles

- MathematicsCommunications in Mathematical Physics
- 2019

We give a description of the delocalized twisted cohomology of an orbifold and the Chern character of a twisted vector bundle in terms of supersymmetric Euclidean field theories. This includes the…

Supersymmetric Euclidean field theories and K-theory

- MathematicsJournal of Geometry and Physics
- 2019

The Chern–Gauss–Bonnet Theorem via Supersymmetric Euclidean Field Theories

- Mathematics
- 2013

We prove the Chern–Gauss–Bonnet Theorem using sigma models whose source supermanifolds have super dimension 0|2. Along the way we develop machinery for understanding manifold invariants encoded by…

Perturbative Quantum Gauge Theories on Manifolds with Boundary

- Mathematics
- 2015

This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic (BV–BFV) formalism.…

FROM SUPERSYMMETRIC FIELD THEORIES TO THE ELLIPTIC INDEX THEOREM WITH COMPLEX COEFFICIENTS

- Mathematics
- 2018

We present a cocycle model for elliptic cohomology with complex coefficients in which methods from physics can be used to rigorously construct cocycles. For example, quantizing a version of the free…

Dimensional reduction and the equivariant Chern character

- MathematicsAlgebraic & Geometric Topology
- 2019

We propose a dimensional reduction procedure in the Stolz--Teichner framework of supersymmetric Euclidean field theories (EFTs) that is well-suited in the presence of a finite gauge group or, more…

Mock modularity and a secondary elliptic genus

- Mathematics
- 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…

Orbifold construction for topological field theories

- MathematicsJournal of Pure and Applied Algebra
- 2019

Twisted equivariant elliptic cohomology from gauged perturbative sigma models I: Finite gauge groups

- Mathematics
- 2014

We use the geometry of gauged 2|1-dimensional sigma models to construct cocycles for the twisted equivariant elliptic cohomology with complex coefficients of a smooth manifold with an action by a…

Topological modular forms and the absence of a heterotic global anomaly

- Physics
- 2021

Spacetime theories obtained from perturbative string theory constructions are automatically free of perturbative anomalies, but it is not settled whether they are always free of global anomalies.…

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