相关论文: Fermionic field theory for trees and forests

We suggest a conformally invariant generalization of string theory to higher-dimensional objects. As such a model, we consider a conformally invariant $\sigma$ model. For this theory, the Hamiltonian formalism is constructed, and the full…

Using the method of spectral decimation and a modified version of Kirchhoffs Matrix-Tree Theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely…

For an indifference graph $G$ we define a symmetric function of increasing spanning forests of $G$. We prove that this symmetric function satisfies certain linear relations, which are also satisfied by the chromatic quasisymmetric function…

We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave…

The standard perturbation theory in QFT and lattice models leads to asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the…

We revisit a propagating torsion gravity theory obtained by introducing a field coupled to the Holst term in the first-order Einstein-Cartan action. The resulting theory has second order field equations, no adjustable coupling constants,…

Let $A$ be a commutative $k$-algebra over a field of $k$ and $\Xi$ a linear operator defined on $A$. We define a family of $A$-valued invariants $\Psi$ for finite rooted forests by a recurrent algorithm using the operator $\Xi$ and show…

We discuss the relationship between the phase diagram of the Q=0 state Potts model, the arboreal gas model, and the supersphere sigma model S^{0,2} = OSP(1/2) / OSP(0/2). We identify the Potts antiferromagnetic critical point with the…

We give combinatorial criteria for predicting the transcendental weight of Feynman integrals of certain graphs in $\phi^4$ theory. By studying spanning forest polynomials, we obtain operations on graphs which are weight-preserving, and a…

We study large $N$ 2+1 dimensional fermions in the fundamental representation of an $SU(N)_k$ Chern Simons gauge group in the presence of a uniform background magnetic field for the $U(1)$ global symmetry of this theory. The magnetic field…

We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1 dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of…

We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a…

Let $(M,g^{TM})$ be a noncompact (not necessarily complete) enlargeable Riemannian manifold in the sense of Gromov-Lawson and $F$ an integrable subbundle of $T M$ . Let $k^F$ be the leafwise scalar curvature associated to $g^F=g^{TM}|_F$.…

We show that the continuum limit of one-dimensional N=2 supersymmetric matrix models can be described by a two-dimensional interacting field theory of a massless boson and two chiral fermions. We interpret this field theory as a…

A graph-theoretic method is introduced for analyzing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as…

Some spontaneously broken gauge theories with left couplings to fermions, like the abelian model that we propose here, can be endowed with a composite scalar sector and Wess-Zumino field ; their quantization in the functionnal integral…

In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed…

We present the extension to 4 dimensions of an euclidean 2-dimensional model that exhibits spontaneous generation of a metric. In this model gravitons emerge as Goldstone bosons of a global SO(D) X GL(D) symmetry broken down to SO(D). The…

A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix…

Boij-S\"oderberg theory characterizes syzygies of graded modules and sheaves on projective space. This paper continues earlier work with S. Sam, extending the theory to the setting of $GL_k$-equivariant modules and sheaves on Grassmannians.…