Related papers: Nahm transformation on the lattice
We study a class of twisted 3D $N=4$ supersymmetric Yang-Mills (SYM) theory on particular 3-dimensional lattice denoted as $\mathcal{L}_{3D}^{su_3\times u_1}$ and given by non trivial fibration $\mathcal{L}_{1D}^{u_1}\times…
We consider the S-duality transformation of gauge invariant operators and states in $\mathcal{N}$ $=4$ SYM theory. The transformation is realized through an operator $ S $ which is the $ SL(2,Z) $ canonical transformation in loop space with…
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect…
The three-dimensional integer-valued lattice gauge theory, which is also known as a "frozen superconductor," can be obtained as a certain limit of the Ginzburg-Landau theory of superconductivity, and is believed to be in the same…
We present a nonperturbative lattice formulation of noncommutative Yang-Mills theories in arbitrary even dimension. We show that lattice regularization of a noncommutative field theory requires finite lattice volume which automatically…
We show how to cast an interacting system of M--branes into manifestly gauge-invariant form using an arrangement of higher-dimensional Dirac surfaces. Classical M--theory has a cohomologically nontrivial and noncommutative set of gauge…
We present a procedure to improve the lattice definition of $\mathcal N = 4$ supersymmetric Yang--Mills theory. The lattice construction necessarily involves U(1) flat directions, and we show how these can be lifted without violating the…
Quantization of two-dimensional Yang-Mills theory on a torus in the gauge where the field strength is diagonal leads to twisted sectors that are completely analogous to the ones that originate long string states in Matrix String Theory. If…
The dual of an arbitrary $D$-dimensional nonabelian lattice gauge theory, obtained after character expansion and integration over the gauge group, is shown to be a {\em local} lattice theory in the eigenspace of the Casimir operators. For…
Optical accordion lattices are routinely used in quantum simulation and quantum computation experiments to tune optical lattice spacings. Here, we present a technique for creating tunable optical lattices using binary-phase transmission…
We present a completely unbiased and controlled numerical method to solve quantum impurity problems in d-dimensional lattices. This approach is based on a canonical transformation, of the Lanczos form, where the complete lattice Hamiltonian…
When studied at finite temperature, Yang-Mills theories in $3+1$ dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order -- the $SU(2)$ gauge theory being the exception.…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
Three techniques for performing gauge-invariant, noncompact lattice simulations of nonabelian gauge theories are discussed. In the first method, the action is not itself gauge invariant, but a kind of lattice gauge invariance is restored by…
The evolution of a quantum lattice gas automaton (LGA) for a single charged particle is invariant under multiplication of the wave function by a global phase. Requiring invariance under the corresponding local gauge transformations…
The feasibility of studying, numerically, properties of infinite volume QCD-like theories in the large $N$ limit using coherent state variational methods is reassessed. An entirely new implementation of this approach is described,…
The pure $SU(N)$ gauge theory with a $\theta$ term has the $\mathbb{Z}_N$ $1$-form global symmetry. When this symmetry is gauged, it is formally established that the topological charge becomes fractional. In this talk, we generate gauge…
We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices includes the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with…
A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant…
We show how a scheme of rewriting a divergent momentum integral can conciliate results obtained with the Nambu--Jona-Lasinio model and recent lattice results for the chiral transition in the presence of a chiral imbalance in quark matter.…