Related papers: Simplicial Chiral Models
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from…
We present results from numerical simulations of three different 3d four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral symmetries, respectively. We performed the simulations by using the hybrid Monte Carlo algorithm. We…
In these lectures I cover various aspects of Chiral Symmetry in the hadronic world from a pre-QCD perspective. I also discuss the absence of spontaneous symmetry breaking in d=4 large N O(N) models.
A brief overview of the authors' work on lattice chirality and its application to the numerical study of planar QCD is presented.
We suggest how versions of Schramm's SLE can be used to describe the scaling limit of some off-critical 2D lattice models. Many open questions remain.
Following a recent proposal for integrable theories in higher dimensions based on zero curvature, new Lorentz invariant submodels of the principal chiral model in 2+1 dimensions are found. They have infinite local conserved currents, which…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
We report the explicit solution for the vacuum state of the two-dimensional $SU(N)$ Principal Chiral Model at large-$N$ for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an…
We discuss some algebraic setting of chiral $SU(N)_{k}$ models in terms of the statistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral $SU(N)_{k}$ models are calculated from their…
We formulate and solve a class of two-dimensional matrix gauge models describing ensembles of non-folding surfaces covering an oriented, discretized, two-dimensional manifold. We interpret the models as string theories characterized by a…
We investigate simplicial complexes deterministically growing from a single vertex. In the first step, a vertex and an edge connecting it to the primordial vertex are added. The resulting simplicial complex has a 1-dimensional simplex and…
We study d=2, N=(2,2) non-linear sigma-models in (2,2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted…
We introduce a new duality for $\mathcal{N}=1$ supersymmetric gauged matrix models. This $0d$ duality is an order 4 symmetry, namely an equivalence between four different theories, hence we call it Quadrality. Our proposal is motivated by…
Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…
We study 2D non-linear sigma models on a group manifold with a special form of the metric. We address the question of integrability for this special class of sigma models. We derive two algebraic conditions for the metric on the group…
On the basis of previous work on chiral gauged fermions on a lattice, we discuss the lattice-regularization of the standard model by introducing two Weyl fields interacting with quarks and leptons. These interactions form massive bound…
Two-dimensional N=1,2 supersymmetric chiral models and their dual extensions are introduced and canonically quantized. Working within a superspace formalism, the non-manifest invariance under 2D-superPoincare' transformations is proven. The…
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…
We present results for the large-$N$ limit of the (1+1)-dimensional principal chiral sigma model. This is an asymptotically-free $N\times N$ matrix-valued field with massive excitations. All the form factors and the exact correlation…
Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…