相关论文: Polymer Statistics and Fermionic Vector Models
We study the supersymmetric extensions of the $O(3)$ $\sigma$-model in $1+1$ and $2+1$ dimensions. We show that it is possible to construct non-equivalent supersymmetric versions of a given model sharing the same bosonic sector and free…
Let $P: \F \times \F \to \F$ be a polynomial of bounded degree over a finite field $\F$ of large characteristic. In this paper we establish the following dichotomy: either $P$ is a moderate asymmetric expander in the sense that $|P(A,B)|…
General fermionic expressions for the branching functions of the rational coset conformal field theories $\widehat{su}(2)_{M}\times \widehat{su}(2)_N/\widehat{su}(2)_{M+N}$ are given. The equality of the bosonic and fermionic…
Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the…
Boundary integrable models with N=2 supersymmetry are considered. For the simplest boundary N=2 superconformal minimal model with a Chebyshev bulk perturbation we show explicitly how fermionic boundary degrees of freedom arise naturally in…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
The Extended Supersymmetric Standard Model (ESSM), motivated on several grounds, introduces two vector-like families [16+ 16-bar of SO(10)] with masses of order one TeV. In an earlier work, a successful pattern for fermion masses and…
We present calculations of the leading and O(1/N) terms in a large-N expansion of the \beta-functions for various supersymmetric theories: a Wess-Zumino model, supersymmetric QED and a non-abelian supersymmetric gauge theory. In all cases N…
We establish a strong-weak coupling duality between two types of free matrix models. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model. Using the large-N conformal invariant collective field…
The general theory of a massless fermion coupled to a massive vector meson in two dimensions is formulated and solved to obtain the complete set of Green's functions. Both vector and axial vector couplings are included. In addition to the…
We describe a rich family of binary variables statistical mechanics models on a given planar graph which are equivalent to Gaussian Grassmann Graphical models (free fermions) defined on the same graph. Calculation of the partition function…
We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…
The wormlike chain model of stiff polymers is a nonlinear $\sigma$-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only…
The derivation of the full Standard Model from noncommutative geometry has been a promising sign for possible applications of the latter in High Energy Physics. Many believe, however, that the Standard Model cannot be the final answer. We…
We extend the left-right symmetric model with an additional non-abelian $SU(2)$ gauge symmetry. The particle content is augmented by one generation of vector-like fermions transforming under the fundamental representation of this new gauge…
Violations of universality of couplings in a vectorlike extension of the standard model with three heavy mirror fermion families are considered. The recently observed discrepancies between experiments and the standard model in the hadronic…
We prove a non-stationary analog of the Furstenberg Theorem on random matrix products (that can be considered as a matrix version of the law of large numbers). Namely, under a suitable genericity conditions the sequence of norms of random…
We derive the fermion loop formulation for the supersymmetric nonlinear O$(N)$ sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over…
We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the…
We put forward several information-theoretic measures for analyzing the uncertainty of fermionic phase-space distributions using the theory of supernumbers. In contrast to the bosonic case, the anticommuting nature of Grassmann variables…