Related papers: Simplicial Chiral Models
A multi-fermion interaction model is investigated in a compact spacetime with non-trivial topology and in a weakly curved spacetime. Evaluating the effective potential in the leading order of the 1/N expansion, we show the phase boundary…
We discuss a method for regularizing chiral gauge theories. The idea is to formulate the gauge fields on the lattice, while the fermion determinant is regularized and computed in the continuum. A simple effective action emerges which lends…
In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This…
The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the potential KP hierarchy, there is a corresponding scaling…
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…
The SU($N$) principal chiral model is asymptotically free and integrable in $1+1$ dimensions. In the large-$N$ limit, there is no scattering, but correlation functions are {\em not} those of a free field theory. We briefly review the…
We study $d$-dimensional simplicial complexes that are PL embeddable in $\mathbb{R}^{d+1}$. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic…
We investigate the spectrum of the principal chiral model (PCM) on odd-dimensional superspheres as a function of the curvature radius R. For volume-filling branes on S^{3|2}, we compute the exact boundary spectrum as a function of R. The…
It is established by numerical means that the continuum large N principal chiral model in two dimensions has a phase transition in a smoothed two point function at a critical distance of the order of the correlation length.
Thermal and chiral critical exponents of the fully frustrated XY model on a square-lattice are obtained from a finite-size scaling analysis of the free energy of chiral domain walls. Data were obtained by extensive Monte Carlo transfer…
We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of…
We carry out a comparative study among five-dimensional formulations of chirally symmetric fermions about the algorithmic performance, chiral symmetry violation and topological tunneling to find a computationally inexpensive formulation…
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…
Previous results on fermion chirality-flipping four-point functions are extended to $SU(N)$ gauge theories. The problem is purely non-perturbative, and it is approached by truncating the Schwinger-Dyson hierarchy. The large-$N$ limit also…
The exact nature of the chiral phase transition in QCD is still under investigation. In $N_f=2$ and $N_f=(2+1)$ lattice simulations with staggered fermions the expected O($N$)-scaling behavior was observed. However, it is still not clear…
We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates…
The Dirac fermion in the random chiral models is studied which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random…
For the case of the single-O($N$)-vector linear sigma models the critical behaviour following from any $A_k$ singularity in the action is worked out in the double scaling limit $N \rightarrow \infty$, $f_r \rightarrow f_r^c$, $2 \leq r \leq…
We perform Monte Carlo calculation of correlation functions in 4d N=4 super Yang-Mills theory on R*S^3 in the planar limit. In order to circumvent the well-known problem of lattice SUSY, we adopt the idea of a novel large-N reduction, which…
We derive the double scaling limit of eigenvalue correlations in the random matrix model at critical points and we relate the limiting correlation functions to a nonlinear hierarchy of ordinary differential equations.