Related papers: The Makeenko-Migdal equation for Yang-Mills theory…

We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We…

Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the…

We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory…

We perform the Kaluza-Klein reduction of M-theory on warped Calabi-Yau fourfolds with non-trivial four-form flux turned on. The resulting scalar- and superpotential is computed and compared with the superpotential obtained by Gukov, Vafa…

This article is devoted to the energy critical hyperbolic Yang--Mills system in the $(4+1)$ dimensional Minkowski space, which is considered by the authors in a sequence of four papers. The final outcome of these papers is twofold: (i) the…

Using the theory of minimal models of quasi-projective surfaces we give a new proof of the theorem of Lin-Zaidenberg which says that every topologically contractible algebraic curve in the complex affine plane has equation $X^n=Y^m$ in some…

This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general Dichotomy Theorem for the energy critical $4+1$ dimensional hyperbolic Yang--Mills…

Matrix theory compactifications on tori have associated Yang-Mills theories on the dual tori with sixteen supercharges. A noncommutative description of these Yang-Mills theories based in deformation quantization theory is provided. We show…

We study the four-dimensional Yang-Mills theory in the presence of a three-dimensional membrane of fermions by lattice Monte Carlo simulations. We analyze the phase structure of this theory at finite temperature. Below the phase transition…

On a Riemannian manifold of dimension $n$ we extend the known analytic results on Yang-Mills connections to the class of connections called $\Omega$-Yang-Mills connections, where $\Omega$ is a smooth, not necessarily closed, $(n-4)$-form.…

In this short note we provide an expository account of the work of Leonard Gross and the author on the Yang-Mills heat equation over smooth three-manifolds with boundary.

We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such…

In this paper, we study the combinatorial Yamabe flow on infinite triangulated surfaces in Euclidean background geometry, aiming for solving discrete Yamabe problem on noncompact surfaces. Under suitable conditions, we establish the…

We derive an action describing edge dynamics on interfaces for gauge theories (Maxwell and Yang-Mills) using the path integral. The canonical structure of the edge theory is deduced and the thermal partition function calculated. We test the…

We construct a free-probability quantum Yang-Mills theory on the two dimensional plane, determine the Wilson loop expectation values, and show that this theory is the $N=\infty$ limit of U(N) quantum Yang-Mills theory on the plane.

We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this…

We show that two-dimensional SO(N) and Sp(N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold M can be…

We give a simple diagrammatic algorithm for writing the chiral large $N$ expansion of intersecting Wilson loops in $2D$ $SU(N)$ and $U(N) $Yang Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for…

In this paper, we study the deformed Hermitian-Yang-Mills equation on compact K\"ahler manifold with non-negative orthogonal bisectional curvature. We prove that the curvatures of deformed Hermitian-Yang-Mills metrics are parallel with…

A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be…