Related papers: Lectures in Topological Quantum Field Theory
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge…
((1+1)-dimensional ${\cal N}=1$ super-symmetric field theory and (3+1)-dimensional ${\cal N}=2$ super-symmetric gauge theory are discussed in a, more or less, unified way, designed to identify the quantum BPS states in both systems.…
We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…
The goal of this paper is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately…
This article surveys invariants of four-manifolds and their relation to Donaldson-Witten theory, and other topologically twisted Yang-Mills theories. The article is written for the second edition of the Encyclopedia of Mathematical Physics,…
A new type of topological matter interactions involving second-rank antisymmetric tensor matter fields with an underlying $N_T \geq 1$ topological supersymmetry are proposed. The construction of the 4-dimensional, $N_T = 1$ Donaldson-Witten…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
A class of two dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang-Mills systems, is presented. Locally, the solutions of the classical equations of motion are given. A general…
We present a non-abelian generalization of Witten monopole equations and we analyze the associated moduli problem, which can be regarded as a generalization of Donaldson theory. The moduli space of solutions for SU(2) monopoles on K\"ahler…
These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory, and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of…
Topological quantum field theories containing matter fields are constructed by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$ chiral (antichiral) multiplets lead to topological sigma models while $N=2$ twisted…
Description of two three-dimensional topological quantum field theories of Witten type as twisted supersymmetric theories is presented. Low-energy effective action and a corresponding topological invariant of three-dimensional manifolds are…
We study a topological Yang-Mills theory with $N=2$ fermionic symmetry. Our formalism is a field theoretical interpretation of the Donaldson polynomial invariants on compact K\"{a}hler surfaces. We also study an analogous theory on compact…
This work is a continuation of our previous paper arXiv:1812.06473 where we have constructed ${\cal N}=2$ supersymmetric Yang-Mills theory on 4D manifolds with a Killing vector field with isolated fixed points. In this work we expand on the…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold.…
A simple field theoretical approach to Mathai-Quillen topological field theories of maps $X: M_I \to M_T$ from an internal space to a target space is presented. As an example of applications of our formalism we compute by applying our…
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 begin with the construction of Mathai-Quillen's Thom form. We also study the case with group actions, with a review of equivariant cohomology and then Mathai-Quillen's construction in this setting. Next, we show that much of the above…
These lectures give an introduction to duality in Quantum Field Theory. We discuss the phases of gauge theories and the implications of the electric-magnetic duality transformation to describe the mechanism of confinement. We review the…