Related papers: Supersymmetric matrix models and branched polymers
In this note we give various characterizations of random walks with possibly different steps that have relatively large discrepancy from the uniform distribution modulo a prime p, and use these results to study the distribution of the rank…
We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size $N$ infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models…
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…
The primes or prime polynomials (over finite fields) are supposed to be distributed `irregularly' , despite nice asymptotic or average behavior. We provide some conjectures/guesses/hypotheses with `evidence' of surprising symmetries in…
Transfer-matrix methods on finite-width strips with free boundary conditions are applied to lattice site animals, which provide a model for randomly branched polymers in a good solvent. By assigning a distinct fugacity to sites along the…
We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models on a circle with two point interactions…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the…
Theories with gauge-mediated supersymmetry breaking provide an interesting alternative to the scenario in which the soft terms of the low-energy fields are induced by gravity. These theories allow for a natural suppression of flavour…
A hermitian one-matrix model with an even quartic potential exhibits a third-order phase transition when the cuts of the matrix model curve coalesce. We use the known solutions of this matrix model to compute effective superpotentials of an…
We demonstrate how the fundamental supersymmetric theory at high energy scales can be reconstructed using precision data expected at future high energy collider experiments. We have studied a set of representative examples in this context:…
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General asymptotic formulae describing deformations of a conical…
We consider supersymmetric theories where the standard-model quark and lepton fields are localized on a "3-brane" in extra dimensions, while the gauge and Higgs fields propagate in the bulk. If supersymmetry is broken on another 3-brane,…
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
In supersymmetric models a tree-level neutrino mass could originate from the (weak-scale) superpotential. We propose and examine a realization of that idea, which arises naturally in the framework of a spontaneously broken U(1) R-symmetry.…
The generic supersymmetric version of the Standard Model would have the minimal list of superfields incorporating the Standard Model particles, and a Lagrangian dictated by the Standard Model gauge symmetries. To be phenomenologically…
I provide a brief summary of the status of supersymmetric models with parameters defined at either the unification or weak scale, based on global fits using the GAMBIT framework.