Related papers: A Supersymmetric Quantum Field Theory Formulation …
Supersymmetric gauge theories have played a central role in applications of quantum field theory to mathematics. Topologically twisted supersymmetric gauge theories often admit a rigorous mathematical description: for example, the Donaldson…
We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal…
We study the path integral of a twisted $N=2$ supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the $SU(2)$ theory on a compact oriented simply…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and…
We present a detailed description of the three inequivalent twists of N=4 supersymmetric gauge theories. The resulting topological quantum field theories are reobtained in the framework of the Mathai-Quillen formalism and the corresponding…
We construct a new off-shell twisted hypermultiplet with a scalar and an anti-self-dual tensor superfields. Using the N=2 twisted superspace formalism, we construct a Donaldson-Witten theory coupled to the hypermultiplet. We show that this…
Twisted four-dimensional supersymmetric Yang-Mills theory famously gives a useful point of view on the Donaldson and Seiberg-Witten invariants of four-manifolds. In this paper we generalize the construction to include a path integral…
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…
In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric theories. We discuss…
We propose a N=2 twisted superspace formalism with a central charge in four dimensions by introducing a Dirac-K\"ahler twist. Using this formalism, we construct a twisted hypermultiplet action and find an explicit form of fermionic scalar,…
We define a holographic dual to the Donaldson-Witten topological twist of $\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$ gauged…
We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the…
We discuss gauge theory with a topological N=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space $\cal M$ and the partition function equals the Euler number of $\cal M$. We explicitly…
((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 present a summary of the applications of duality to Donaldson-Witten theory and its generalizations. Special emphasis is made on the computation of Donaldson invariants in terms of Seiberg-Witten invariants using recent results in N=2…
Twists of four-dimensional supersymmetric quantum field theories (SQFTs) isolate protected sectors with rich algebraic structures. We develop a unified framework for analyzing symmetries and anomalies in four-dimensional holomorphically…
We take a fresh look at the relation between generalised K\"ahler geometry and $N=(2,2)$ supersymmetric sigma models in two dimensions formulated in terms of $(2,2)$ superfields. Dual formulations in terms of different kinds of superfield…
Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…
We study the Donaldson-Witten function in four-dimensional topological gauge theory which is constructed from N=2 supersymmetric SU(2) gauge theory with $N_f < 4$ massless fundamental hypermultiplets. When $N_f = 2,3$, the strong-coupling…