Related papers: QCD Instantons and 2D Surfaces

We consider U(n+1) Yang-Mills instantons on the space \Sigma\times S^2, where \Sigma is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n+1) instanton equations on \Sigma\times S^2…

Two-dimensional SU(N) Yang-Mills theory is endowed with a non-trivial vacuum structure (k-sectors). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content, the (Euclidean) space-time being…

We explore the correspondence between Yang-Mills instantons and algebraic curves. The curve is defined by Higgs zero locus of dyonic instantons in 1+4 dimensional Yang-Mills-Higgs theory, and it is identified in string theory with the…

We introduce the description of a Wilson surface as a 2-dimensional topological quantum field theory with a 1-dimensional Hilbert space. On a closed surface, the Wilson surface theory defines a topological invariant of the principal…

The existence of K-instantons on a cylinder M^7 = R_tau x K/H over a homogeneous nearly K"ahler 6-manifold K/H requires a conformally parallel or a cocalibrated G_2-structure on M^7. The generalized anti-self-duality on M^7 implies a…

Large $N$ two-dimensional QCD on a cylinder and on a vertex manifold (a sphere with three holes) is investigated. The relation between the saddle-point description and the collective field theory of QCD$_2$ is established. Using this…

It is usually assumed that $4D$ instantons can only arise in non-Abelian theories. In this paper we re-examine this conventional wisdom by explicitly constructing instantons in an Abelian gauge theory: ${\rm QED}_4$ with $N_f$ flavors of…

We study a natural contact instanton (CI) equation on gauge fields over 7-dimensional Sasakian manifolds, which is closely related both to the transverse Hermitian Yang-Mills (tHYM) condition and the G_2-instanton equation. We obtain, by…

We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a…

We consider the $SU(N)$ Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of $p$. We can formulate such a quantum field theory maintaining locality and unitarity, and the model…

On an oriented, compact, connected, real four-dimensional manifold, $M$, we introduce a topological Lagrangian gauge field theory with a Bogomol'nyi structure that leads to non-singular, finite-Action, stable solutions to the variational…

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, RxG/H and R^2xG/H, where G/H is a compact nearly Kaehler six-dimensional homogeneous space, and the manifolds RxG/H and R^2xG/H carry G_2- and Spin(7)-structures,…

The correlation between instantons and QCD-monopoles is studied both in the lattice gauge theory and in the continuum theory. From a simple topological consideration, instantons are expected to live only around the QCD-monopole trajectory…

Yang-Mills theory and QCD are well-defined for any Lie group as gauge group. The choice G2 is of great interest, as it is the smallest group with trivial center and being at the same time accessible to simulations. This theory has been…

We study self-dual instantons of topological charge $Q=r/N$, for any natural $r$, in $SU(N)$ Yang-Mills theory on a four torus with 't Hooft twists, by embedding them into worldvolume theories of $D$-branes. To study their moduli, we…

In both Yang-Mills theories and sigma models, instantons are endowed with degrees of freedom associated to their scale size and orientation. It has long been conjectured that these degrees of freedom have a dual interpretation as the…

We consider the six-sphere S^6=G_2/SU(3) and its twistor space Z=G_2/U(2) associated with the SU(3)-structure on S^6. It is shown that a Hermitian Yang-Mills connection (instanton) on a smooth vector bundle over S^6 is equivalent to a flat…

We review the theory and phenomenology of instantons in QCD. After a general overview, we provide a pedagogical introduction to semi-classical methods in quantum mechanics and field theory. The main part of the review summarizes our…

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R^{2n}_\theta x S^2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S^2, we reduce…

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this…