Related papers: Einstein and Yang-Mills implies conformal Yang-Mil…

We discuss the moduli space of flat connections of Yang-Mills theories formulated on T^3 x R, with periodic boundary conditions. When the gauge group is SO(N>=7), G_2, F_4, E_6, E_7 or E_8, the moduli space consists of more than one…

In this paper we consider the classification problem of extensions of Yang-Mills-type (YMT) theories. For us, a YMT theory differs from the classical Yang-Mills theories by allowing an arbitrary pairing on the curvature. The space of YMT…

We formulate notions of subadditivity and additivity of the Yang-Mills action functional in noncommutative geometry. We identify a suitable hypothesis on spectral triples which proves that the Yang-Mills functional is always subadditive, as…

There is the notion of action Lie algebroids, containing information about Lie algebras and their actions, which is why it is natural to generalise gauge theories to a formulation using Lie algebroids; these allow structure functions in…

I summarize some recent developments in the issue of planar equivalence between supersymmetric Yang-Mills theory and its orbifold/orientifold daughters. This talk is based on works carried out in collaboration with Adi Armoni, Sasha Gorsky…

We prove that the renormalized Yang-Mills energy on six dimensional Poincar\'e-Einstein spaces can be expressed as the bulk integral of a local, pointwise conformally invariant integrand. We show that the latter agrees with the…

We consider the Hermitian-Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle E over an almost complex manifold X^6 which is the twistor space of an oriented Riemannian manifold M^4. Each solution of the HYM equations…

Topological Yang-Mills theory with the Belavin-Polyakov-Schwarz-Tyupkin $SU(2)$ instanton is solved completely, revealing an underlying multi-link intersection theory. Link invariants are also shown to survive the coupling to a certain kind…

Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large $N$. We calculate entanglement entropy in the $1/N$ expansion by mapping the theory to a system of $N$ fermions…

We introduce the covariant forms for the non-Abelian anomaly counterparts in topological Yang-Mills theory, which satisfies the topological descent equation modulo terms that vanish at the space of BRST fixed points. We use the covariant…

The compatibility conditions for generalised continua are studied in the framework of differential geometry, in particular Riemann-Cartan geometry. We show that Vall\'{e}e's compatibility condition in linear elasticity theory is equivalent…

We discuss bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. We begin by finding convergence conditions for the partition and correlation functions. Moving on, we specialise to the SU(N) models with…

If X is a full, finitely generated, projective module over a non-commutative torus, the Yang-Mills functional attains its minimum exactly on the flat connections on X. We classify the flat connections on modules admitting integrable…

In the following article we study the limiting properties of the Yang-Mills flow associated to a holomorphic vector bundle E over an arbitrary compact K\"ahler manifold (X,{\omega}). In particular we show that the flow is determined at…

Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in…

We give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some complete non-compact K\"ahler manifolds $(X,\omega)$, where $X$ is the complement of a divisor in a…

We embed the perturbative Fock state of the Yang-Mills BV-multiplet in the vertex operator algebra of the path-integral for the $\mathcal{N}=2$ supersymmetric world line and evaluate the pull-back of the latter to an integral form on…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

In this article we present some probably unexpected (in our opinion) properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ym(n) on n…

By employing the higher dimensional version of the Wu-Yang Ansatz we obtain black hole solutions in the spherically symmetric Einstein-Yang-Mills (EYM) theory. Although these solutions were found recently by other means, our method provides…