Related papers: Supersymmetric field theories from twisted vector …
We study orbifolds of two-dimensional topological field theories using defects. If the TFT arises as the twist of a superconformal field theory, we recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory as well as…
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…
I define topological twists of supersymmetric field theories in the case when the supercharges involved obey an ``open'' algebra. Using the Batalin-Vilkovisky field-antifield formalism, I construct twisted theories algorithmically from the…
We construct spaces of 1-dimensional supersymmetric Euclidean field theories and show that they represent real or complex K-theory. A noteworthy feature of our bordism category is that the identity bordism of a point is connected to…
Vector supersymmetry is typical of topological field theory. Its role in the construction of gauge invariant quantities is explained, as well as its role in the cancellation of the ultraviolet divergences. The example of the Chern-Simons…
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 generally, for field theories over an…
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 Stolz--Teichner program, while also…
In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth…
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 families of 0|n-dimensional Euclidean field…
It has been argued by Witten and others that in the presence of a nontrivial B-field, D-brane charges in type IIB string theories are measured by twisted K-theory. In joint work with Bouwknegt, Carey and Murray it was proved that twisted…
Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…
We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…
We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations)…
Topological phases of matter in (2+1) dimensions are commonly equipped with global symmetries, such as electric-magnetic duality in gauge theories and bilayer symmetry in fractional quantum Hall states. Gauging these symmetries into local…
For two complex vector bundles admitting a homomorphism, whose singularity locates in the disjoint union of some odd--dimensional spheres, we give a formula to compute the relative Chern characteristic number of these two complex vector…
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…
We derive the basic correlation functions of twist fields coming from arbitrary twisted sectors in symmetric $Z_N$ orbifold conformal field theories, keeping all the admissible marginal perturbations, in particular those corresponding to…
We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the…
The structure of topological quantum field theories on the compact Kahler manifold is interpreted. The BRST transformations of fields are derived from universal bundle and the observables are found from the second Chern class of universal…