Related papers: 2-Representations and Equivariant 2D Topological F…
Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We compute the equivariant cohomology of many…
In this paper we propose a naive construction of 2-dimensional extended topological quantum field theories (TQFTs), which can be further generalized to the higher-dimension extended TQFTs.
A new conformal field theory description of two-dimensional turbulence is proposed. The recently established class of rational logarithmic conformal field theories provides a unique candidate solution which resolves many of the drawbacks of…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
In this paper, we apply the method of Fourier transform and basis rewriting developed in arXiv:1910.13441 for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group…
We define a new topological polynomial extending the Bollobas-Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behavior under partial duality. This allows to write down a completely…
Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations…
For $G$ a finite group, we show that functions on fields for the 2-dimensional supersymmetric sigma model with background $G$-symmetry determine cocycles for complex analytic $G$-equivariant elliptic cohomology. Similar structures in…
We define four distinct oriented bivariant theories associated with algebraic cobordism in its two versions (the axiomatic $\Omega$ and the geometric $\omega$), when applied to quasi-projective varieties over a field $k$. Specifically, we…
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 algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
We study torus-equivariant algebraic $K$-theory of affine Schubert varieties in the perfect affine Grassmannians over $\mathbb{F}_p$. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the…
In this paper, we introduce Topological Quantum Field Theories (TQFTs) generalizing the arithmetic computations done by Hausel and Rodr\'iguez-Villegas and the geometric construction done by Logares, Mu\~noz, and Newstead to study…
We generalize the electromagnetic duality between a massless, canonical scalar field and a 2-form gauge field in 4-dimensional spacetime to scalar-tensor theories. We derive the action of 2-form gauge field that is dual to two kinds of…
Let $G=SU(2)$ and let $\Omega G$ denote the space of based loops in SU(2). We explicitly compute the $R(G)$-module structure of the topological equivariant $K$-theory $K_G^*(\Omega G)$ and in particular show that it is a direct product of…
We investigate the 3d lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation $\D{G}$ of the quantum double of a finite commutative group $G$ as the underlying…
We introduce invariants of Hurwitz equivalence classes with respect to arbitrary group $G$. The invariants are constructed from any right $G$-modules $M$ and any $G$-invariant bilinear function on $M$, and are of bilinear forms. For…
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in…