Related papers: Yang-Mills measure on compact surfaces
Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action…
The large-N limit of the two-dimensional U$(N)$ Yang-Mills theory on an arbitrary orientable compact surface with boundaries is studied. It is shown that if the holonomies of the gauge field on boundaries are near the identity, then the…
We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength and its…
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 consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parametrized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom.…
We prove that Yang-Mills connections on a surface are characterized as those with the property that the holonomy around homotopic closed paths only depends on the oriented area between the paths. Using this we have an alternative proof for…
We study a gauge-invariant variational framework for the Yang-Mills vacuum wave functional. Our approach is built on gauge-averaged Gaussian trial functionals which substantially extend previously used trial bases in the infrared by…
Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics,…
$F$-Yang-Mills connections are critical points of $F$-Yang Mills functional on the space of connections of a principal fiber bundle, which is a generalization of Yang-Mills connections, $p$-Yang-Mills connections and exponential Yang-Mills…
Refinements of the Yang-Mills stratifications of spaces of connections over a compact Riemann surface are investigated. The motivation for this study was the search for a complete set of relations between the standard generators for the…
New collective coordinates, related to the field at the `center' of the monopoles, are proposed. A systematic computation of the infrared properties of 2+1- and 3+1- dimensional Yang-Mills theory is now possible and is related to solutions…
We study the massive Yang-Mills theory in which the mass term is added by hand. The standard perturbative approach suggests that the massless limit of this theory is not smooth. We confirm that this issue is related to the existence of…
Yang-Mills theory is growing at the interface between high energy physics and mathematics. It is well known that Yang-Mills theory and Gauge theory in general had a profound impact on the development of modern differential and algebraic…
In this paper we study the relationship between three compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the…
We study a smooth analogue of jumping curves of a holomorphic vector bundle, and use Yang-Mills theory over $ S ^{2} $ to show that any non-trivial, smooth Hermitian vector bundle $E $ over a smooth simply connected manifold, must have such…
This work is a step towards merging the ideas that arise from semi-classical methods in continuum QFT with analytic/numerical lattice field theory. In this context, we consider Yang-Mills theories coupled to fermions in the adjoint…
We consider Yang-Mills theory in a general class of Abelian gauges. Exploiting the residual Abelian symmetry on a quantum level, we derive a set of Ward identities in functional form, valid to all orders in perturbation theory. As a…
Non-commutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum…
Spatial compactification on $\mathbb R^{3} \times \mathbb S^1_L$ at small $\mathbb S^1$-size $L$ often leads to a calculable vacuum structure, where various "topological molecules" are responsible for confinement and the realization of the…
We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically…