Related papers: Lattice path combinatorics in superconformal Yang-…
Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant…
We give the {\it spectral decomposition} of the path space of the $U_q(\hatsl)$ vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the $\hatsl$ level $l$ integrable modules,…
Consideration of a question of E. R. Berlekamp led Carlitz, Roselle, and Scoville to give a combinatorial interpretation of the entries of certain matrices of determinant~1 in terms of lattice paths. Here we generalize this result by…
We introduce and study a new class of power-counting non-renormalisable gauge theories in four space-time dimensions. The Lagrangian is an arbitrary function of the self-dual part of the field strength. The resulting perturbation theory has…
The planar Yang-Mills theory in three spatial dimensions is examined in a particular representation which explicitly embodies factorization. The effective planar Yang-Mills theory Hamiltonian is constructed in this representation.
We study expectation values related to the dynamical lattice spacing that occurs in the recent supersymmetric 2d lattice Yang-Mills constructions of Cohen et al. [hep-lat/0307012]. For the purposes of this preliminary analysis, we restrict…
We present a new lattice super Yang-Mills theory and its SUSY transformation. After our formulation of the model in a fundamental lattice, it is extended to the whole lattice with a substructure of modulo 2.
We review recent results on the derivation of a global path integral density for Yang-Mills theory. Based on a generalization of the stochastic quantization scheme and its geometrical interpretation we first recall how locally a modified…
The construction of a consistent measure for Yang-Mills is a precondition for an accurate formulation of non-perturbative approaches to QCD, both analytical and numerical. Using projective limits as subsets of Cartesian products of…
Numerical simulations of supersymmetric theories on the lattice are intricate and challenging with respect to their theoretical foundations and algorithmic realisation. Nevertheless, the simulations of a four-dimensional supersymmetric…
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…
A method is proposed for latticizing a class of supersymmetric gauge theories, including N=4 super Yang-Mills. The technique is inspired by recent work on ``deconstruction''. Part of the target theory's supersymmetry is realized exactly on…
A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six…
We describe discrete symmetries of two-dimensional Yang-Mills theory with gauge group $G$ associated to outer automorphisms of $G$, and their corresponding defects. We show that the gauge theory partition function with defects can be…
For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum…
We present an entirely new approach towards a realization of the supersymmetric Yang-Mills theory on the lattice. The action consists of the staggered fermion and the plaquette variables distributed in the Euclidean space with a particular…
We employ the analytic Bethe Anzats to construct eigenvalues of transfer matrices with finite-dimensional atypical representations in the auxiliary space for the putative long-range spin chain encoding anomalous dimensions of all composite…
We formulate ${\cal N} = 2^*$ supersymmetric Yang-Mills theory on a Euclidean spacetime lattice using the method of topological twisting. The lattice formulation preserves one scalar supersymmetry charge at finite lattice spacing. The…
We study our Schwinger-Dyson equation as well as the large $N_{c}$ loop equation for supersymmetric Yang-Mills theory in four dimensions by the N=1 superspace Wilson-loop variable. We are successful in deriving a new manifestly…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…