Related papers: Dimensional reduction in QCD: Lessons from lower d…
A 3D-2D dimension reduction for $-\Delta_1$ is obtained. A power law approximation from $-\Delta_p$ as $p \to 1$ in terms of $\Gamma$- convergence, duality and asymptotics for least gradient functions has also been provided.
We consider the dimensional reduction of N=1 {SYM}_{2+1} to 1+1 dimensions. The gauge groups we consider are U(N) and SU(N), where N is finite. We formulate the continuum bound state problem in the light-cone formalism, and show that any…
Analytic variational techniques for lattice gauge theories based on the Rayleigh-Ritz(RR) method were previously developed for euclidean SU(2) gauge theories in 3 and 4 dimensions. Their extensions to SU(3) gauge theory including…
We study the interface between two different Z(3) vacua in the deconfined phase of SU(3) pure gauge theory in 2+1 dimensions just above the critical temperature. In simulations of the Euclidean lattice gauge theory formulation of the system…
This paper discusses the relationships between gauge theories defined by gauge groups with finite trivially-acting centers, and theories with restrictions on nonperturbative sectors, in two and four dimensions. In two dimensions, these…
In models inspired by non-commutative geometry, patterns of gauge symmetry breaking are analyzed, and SU(5) models are found to naturally favor a vacuum preserving SU(3) X SU(2) X U(1). A more realistic model is presented, and the…
It is argued that dimensional reduction of Seiberg-Witten map for a gauge field induces Seiberg-Witten maps for the other noncommutative fields of a gauge invariant theory. We demonstrate this observation by dimensionally reducing the…
We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate the $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$ lattices. The Creutz ratios of the Wilson loops agree with the exact results for $U(1)$…
A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the…
We consider the dimensional reductions of N=4 Supersymmetric Yang-Mills theory on R x S^3 to the three-dimensional theory on R x S^2, the orbifolded theory on R x S^3/Z_k, and the plane-wave matrix model. With explicit emphasis on the…
Performing lattice simulations of the four dimensional SU(2)gluodynamics we find evidence for existence of three-dimensional domains whose total volume scales in physical units. Technically, the domains are defined in terms of the minimal…
Screening masses in the equilibrium thermodynamics of gauge theories were measured. The spectroscopy of these screening masses gives strong evidence for dimensional reduction at $T\ge2T_c$. A perturbative explanation of these masses is…
We present our preliminary results of SO(2N) gauge theories, approaching the large-N limit. SO(2N) theories may help us to understand QCD at finite chemical potential since there is an orbifold equivalence between SO(2N) and SU(N) gauge…
We show how 3-dimensional, N=2 supersymmetric theories, including super QCD with matter fields, can be put on the lattice with existing techniques, in a way which will recover supersymmetry in the small lattice spacing limit. Residual…
The simplest nontrivial toy model of a classical SU(3) lattice gauge theory is studied in the Hamiltonian approach. By means of singular symplectic reduction, the reduced phase space is constructed. Two equivalent descriptions of this space…
We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We consider a bound state problem for a family of supersymmetric gauge theories with fundamental matter. These theories can be obtained by a dimensional reduction of supersymmetric QCD from three dimensions to 1+1 and subsequent truncation…
We have applied a new noncompact, gauge-invariant, Monte Carlo method to simulate the U(1), SU(2), and SU(3) gauge theories on 8^4 and 12^4 lattices. For U(1) the Creutz ratios of the Wilson loops agree with the exact results for beta > 0.5…
We find that a big gap between indicators for the breaking strengths of the global chiral SU(2) and U(1) axial symmetries in QCD of the Standard Model (SM) can be interpreted as a new fine-tuning problem. This may thus imply calling for a…