Related papers: Nahm transformation on the lattice
Anti-self-dual (ASD) connections for a compact smooth four manifold arise as critical values for the Yang-Mills action functional. Nahm transform is a nice correspondence between a vector bundle with ASD connections and a vector bundle with…
We consider maximally supersymmetric SU(N) Yang--Mills theory in Euclidean signature compactified on a flat two-dimensional torus with anti-periodic (`thermal') fermion boundary conditions imposed on one cycle. At large N, holography…
A generalized gauge invariant Ising model on random surfaces with non-trivial topology is proposed and investigated with the dual transformation. It is proved that the model is self-dual in case of a self-dual lattice. In special cases the…
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological…
We reconsider gauge-transformation properties in chiral gauge theories on the lattice observing all pertinent information and show that these properties are actually determined in a general way for any gauge group and for any value of the…
We extend the definition of L\"uscher's lattice topological charge to the case of $4$d $SU(N)$ gauge fields coupled with $\mathbb{Z}_N$ $2$-form gauge fields. This result is achieved while maintaining the locality, the $SU(N)$ gauge…
Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is dis cussed. First results of the quenched Monte Carlo simulations, for D=4 and with higher g auge groups (3 <= N <= 8), are presented. We confirm an earlier (N=2)…
The two-dimensional supersymmetric Yang-Mills (SYM) theory with sixteen supercharges at large $N$ and strong 't~Hooft coupling is conjectured to be dual to certain supergravity solutions in the decoupling limit. We discretize the gauge…
As a non-perturbative and gauge invariant regularization the lattice provides a tool for deeper understanding of the celebrated Yang-Mills theory, QCD and chiral gauge theories. For illustration, I discuss some analytic developments on the…
Duality relations for the 2D nonhomogeneous Ising model on the finite square lattice wrapped on the torus are obtained. The partition function of the model on the dual lattice with arbitrary combinations of the periodical and antiperiodical…
We study the spectrum of BPS states in N=4 supersymmetric U(N) Yang-Mills theory. This theory has been proposed to describe M-theory on T^3 in the discrete light-cone formalism. We find that the degeneracy of irreducible BPS bound states in…
The equivalence between the Non-Abelian Nambu model (NANM) and Yang Mills theory is proved, after demanding the Gauss laws at some initial time to the first one. Thereby, the Lorentz violation encoded into the constraint that defines the…
I propose a self-dual deformation of the classical phase space of lattice Yang--Mills theory, in which both the electric and magnetic fluxes take value in the gauge Lie group. A local construction of the deformed phase space requires the…
The magnetic switching of ferromagnetic nanotubes is investigated as a function of their geometry. Two independent methods are used: Numerical simulations and analytical calculations. It is found that for long tubes the reversal of…
We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat…
We study a duality transformation from the gauge-invariant subspace of a $\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an $N$-clock model on a single chain. The main feature of this mapping is the emergence of a…
The ${\cal N} = 2^*$ Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric ${\cal N} = 4$ Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence…
%In order to understand how gauge fixing can be affected on the %lattice, we first study a simple model of pure Yang-mills theory on a %cylindrical spacetime [$SU(N)$ on $S^1 \times$ {\bf R}] where the %gauge fixed subspace is explicitly…
We derive an exact duality transformation for pure non-Abelian gauge theory regularized on a lattice. The duality transformation can be applied to gauge theory with an arbitrary compact Lie group G as the gauge group and on Euclidean…
We study abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformulate the theory in terms of new dynamical variables; however, we avoid the use of the dual lattice…