Related papers: Topological Quantum Field Theory And Strong Shift …
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional Riemannian gravity with a positive cosmological constant {\Lambda}. We complete the program to canonically quantize the theory in the BF…
We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…
By choosing an unconventional polarization of the connection phase space in (2+1)-gravity on the torus, a modular invariant quantum theory is constructed. Unitary equivalence to the ADM-quantization is shown.
We establish a connection between three-dimensional self-mirror symmetric $\mathcal N=4$ superconformal field theories (SCFTs) and time-reversal invariant topological quantum field theories (TQFTs) arising from universal mass deformations.…
Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of…
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this…
A class of quantum field theories invariant with respect to the action of an odd vector field Q on a source supermanifold $\Sigma$ is considered. We suppose that Q satisfies the conditions under which an integral of any Q-invariant function…
We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic $q$. Both types of invariants are labeled by extra data which plays an important role in the…
We propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg's concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action…
In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…
We study the cohomology of $G$-representation varieties and $G$-character stacks by means of a topological quantum field theory (TQFT). This TQFT is constructed as the composite of a so-called field theory and the 6-functor formalism of…
We study interacting massive N=(2,2) supersymmetric field theories in two dimensions which arise from deforming conformal field theories with a continuous spectrum. Firstly, we deform N=2 superconformal Liouville theory with relevant…
We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to…
Topological quantum field theory (TQFT) is a powerful tool to describe homologies, which normally involve complexes and a variety of maps/morphisms, what makes a functional integration approach with a sum over a single kind of maps…
We introduce a new computable invariant for strong shift equivalence of shifts of finite type. The invariant is based on an invariant introduced by Trow, Boyle, and Marcus, but has the advantage of being readily computable. We summarize…
The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin…
We study Quot schemes of vector bundles on algebraic curves. Marian and Oprea gave a description of a topological quantum field theory (TQFT) studied by Witten in terms of intersection numbers on Quot schemes of trivial bundles. Since these…
Motivated by suggestions of Paolo Cotta-Ramusino's work at the physical level of rigor relating BF theory to the Donaldson polynomials, we provide a construction applicable to the Turaev/Viro and Crane/Yetter invariants of *a priori* finer…
The topological aspects of Einstein gravity suggest that topological invariance could be a more profound principle in understanding quantum gravity. In this work, we explore a topological supergravity action that initially describes a…