Related papers: Nahm transformation on the lattice
This work concerns the study of certain finite-energy solutions of the anti-self-dual Yang-Mills equations on Euclidean 4-dimensional space which are periodic in two directions, so-called doubly-periodic instantons. We establish a circle of…
We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from…
We propose a discretization of two dimensional Euclidean Yang-Mills theories with N=2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum…
In this talk, we give the lattice regularized formulation of the mixed 't Hooft anomaly between the $\mathbb{Z}_N$ $1$-form symmetry and the $\theta$ periodicity for $4$d pure Yang-Mills theory, which was originally discussed by Gaiotto…
We investigate plane vortices with color structure. The topological charge and gauge action of such colorful plane vortices are studied in the continuum and on the lattice. These configurations are vacuum to vacuum transitions changing the…
We discuss the quantum mechanics of a particle in a magnetic field when its position x^{\mu} is restricted to a periodic lattice, while its momentum p^{\mu} is restricted to a periodic dual lattice. Through these considerations we define…
Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this…
We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a…
We present the first implementation of the Cho--Faddeev--Niemi ecomposition of the SU(2) Yang-Mills field on a lattice. Our construction retains the color symmetry (global SU(2) gauge invariance) even after a new type of Maximally Abelian…
A generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit. At low temperatures string theory describes black holes, whose…
We analyze the Hamiltonian time evolution of classical SU(2) Yang-Mills-Higgs theory with a fundamental Higgs doublet on a spacial lattice. In particular, we study energy transfer and equilibration processes among the gauge and Higgs…
The discrete Nahm equation is an integrable nonlinear difference equation for complex $N\times N$ matrices defined on a one-dimensional lattice, with rank and symmetry boundary conditions at the ends of the lattice. Solutions of this system…
We present the latest results from our ongoing lattice field theory investigations of maximally supersymmetric Yang--Mills theory in three space-time dimensions, focusing on its non-perturbative phase diagram. Exploiting a lattice…
We study the gauge/gravity duality for supersymmetric SU(N) Yang-Mills theory in 1+0 dimension with sixteen supercharges using lattice simulations. The conjectured duality states that the gravity side is described by N D0-branes in type IIA…
Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang--Mills (SYM) theories in such a way that they are compatible with the discretization…
Dual form of 3+1 dimensional Yang-Mills theory is obtained as another SO(3) gauge theory. Duality transformation is realized as a canonical transformation. The The non-abelian Gauss law implies the corresponding Gauss law for the dual…
Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact…
We perform lattice simulations of two-dimensional supersymmetric Yang-Mills theory with sixteen supercharges with a lattice action which has two exact supercharges (Sugino lattice action). According to the gauge/gravity duality, the theory…
We present the Nahm transform of the doubly-periodic instantons introduced in math.DG/9909069, converting them into certain meromorphic solutions of Hitchin's equations over an elliptic curve.
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…