Related papers: Topological quantum field theory for dormant opers
We construct a weak categorification of the quantum toroidal algebra action on the Grothendieck group of moduli space of stable (or framed) sheaves over an algebraic surface, which is constructed by Schiffmann-Vasserot and Negu\c{t}. The…
Given a topological group G, its orbit category Orb_G has the transitive G-spaces G/H as objects and the G-equivariant maps between them as morphisms. A well known theorem of Elmendorf then states that the category of G-spaces and the…
We derive (quasi-)quantum groups in 2+1 dimensional topological field theory directly from the classical action and the path integral. Detailed computations are carried out for the Chern-Simons theory with finite gauge group. The principles…
This is a paper in a series to study quantum vertex algebras and their relations with various quantum algebras. In this paper, we introduce a notion of T-type quantum vertex algebra and a notion of $G$-covariant $\phi$-coordinated quasi…
We construct a topological quantum field theory based on the moduli space of $\mathrm{Spin}(7)$-instantons on 8-dimensional manifolds. Using the Mathai-Quillen formalism, we derive the action of the theory in purely geometric terms, which…
In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov. Our approach follows the construction carried out by the authors together with A. Kupiainen in…
We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes…
We show that the equations of motion defined over a specific field space are realizable as operator conditions in the physical sector of a generalized Floer theory defined over that field space. The ghosts associated with such a…
We call a reductive complex group $G$ quasi-toral if $G^0$ is a torus. Let $G$ be quasi-toral and let $V$ be a faithful $1$-modular $G$-module. Let $N$ (the shell) be the zero fiber of the canonical moment mapping $\mu\colon V\oplus…
A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the "nonlinear Sigma-model" or "lattice-CFT", is given. Underlying this approach to CFT is a unitary modular functor, the…
The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d…
We present a topological quantum field theory which corresponds to the moduli problem associated to Witten's monopole equations for four-manifolds. The construction of the theory is carried out in purely geometrical terms using the…
We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres-Douglas theories on $S^1 \times M_3$ with a non-trivial holonomy of a discrete global symmetry along the $S^1$.…
We construct a category $\mathrm{HomCob}$ whose objects are {\it homotopically 1-finitely generated} topological spaces, and whose morphisms are {\it cofibrant cospans}. Given a manifold submanifold pair $(M,A)$, we prove that there exists…
Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime…
The cohomology theory TMF of topological modular forms is a derived algebro-geometric interpretation of the classical ring of complex modular forms from number theory. In this article, we refine the classical Adams operations, Hecke…
The goal of this article is to motivate and describe how Gromov-Witten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and…
A smooth GKM stack is a smooth Deligne-Mumford stack equipped with an action of an algebraic torus $T$, with only finitely many zero-dimensional and one-dimensional orbits. (i) We define the stacky GKM graph of a smooth GKM stack, under the…
Motivated by the similarity between CSW theory and the Chern Simons state for General Relativity in the Ashtekar variables, we explore what the universe would look like if it were in a state corresponding to a 3D TQFT. We end up with a…