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The $\mathbb{CP}^{N-1}$ model is an analytically tractable $2d$ quantum field theory which shares several properties with $4d$ Yang-Mills theory. By virtue of its classical integrability, this model also admits a family of integrable…

Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the…

We show that topological strings on a class of non-compact Calabi-Yau threefolds is equivalent to two dimensional bosonic U(N) Yang-Mills on a torus. We explain this correspondence using the recent results on the equivalence of the…

The dimension of the Hilbert space of QFT scales exponentially with the volume of the space in which the theory lives, yet in supersymmetric theories, one can define a graded dimension (such as the supersymmetric index) that counts just the…

While the achievements in the study of N=4 Super Yang-Mills through the application of integrability are impressive, the precise origins of the exact solvability remain shrouded in mystery. In this note, we propose that viewing the problem…

We determine the $d+1$ dimensional topological field theory, which encodes the higher-form symmetries and their 't Hooft anomalies for $d$-dimensional QFTs obtained by compactifying M-theory on a non-compact space $X$. The resulting theory,…

In this note we consider the symplectic reduction of a four-dimensional holomorphic Chern-Simons theory recently introduced in arXiv:1908.02289 for describing integrable field theories. We work out explicitly the case of the lambda deformed…

We formulate the ten-dimensional super-Yang-Mills theory in a twisted superspace with 8+1 supercharges. Its constraints do not imply the equations of motion and we solve them. As a preliminary step for a complete formulation in a twisted…

We present a twistor space that describes super null-lines on six-dimensional N=(1,1) superspace. We then show that there is a one-to-one correspondence between holomorphic vector bundles over this twistor space and solutions to the field…

This report investigates general relativity and the Yang-Mills theory in four-dimensional space-time using a common mathematical framework, the Chern-Weil theory for principal bundles. The whole theory is described owing to the fibre bundle…

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…

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In…

Planar maximally supersymmetric Yang-Mills theory (N=4 SYM) is a special quantum field theory. A few of its remarkable features are conformal symmetry at the quantum level, evidence of integrability and, moreover, it is a prime example of…

A new set of tetrads is introduced within the framework of SU(2) X U(1) Yang-Mills field theories in four dimensional Lorentz curved spacetimes. Each one of these tetrads diagonalizes separately and explicitly each term of the Yang-Mills…

We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that Riemann surface. Firstly, we argue that the algebraic structure that underlies the…

This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…

We consider $SU(N)$ Yang-Mills theories in $(2n+1)$-dimensional Euclidean spacetime, where $N\geq n+1$, coupled to an even flavour number of Dirac fermions. After integration over the fermionic degrees of freedom the wave functional for the…

Considering the model of a scalar massive Fermion, it is shown that by means of deformation techniques it is possible to obtain all integrable quantum field theoretic models on two-dimensional Minkowski space which have factorizing…

We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of…

In this paper, we present a series of solutions of type IIB Supergravity, obtained through the TsT deformation of a seed background that is holographically dual to ${\cal N}=4$ Super Yang-Mills theory compactified on a circle (with a…