相关论文: Critical dimension of Spectral Triples

A simple proof is given of the necessary and sufficient condition on a triple of positive numbers A,B,C for the existence of a conformal metric of constant positive curvature on the sphere, with three conic singularities of total angles…

In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincar\'e duality pair with aspherical boundary components. We provide a construction which shows that the necessary conditions are…

For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's…

Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing.…

We show that single-valuation exponential kernels, under mild regularity assumptions, converge in the continuum limit to a fourth-order operator with heat asymptotics $\Theta(t)\sim t^{-1/4}$ and hence spectral dimension $d_s=\tfrac12$.…

Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D_1 and the spectral compressibility chi are related by the simple equation…

Consider the indicator function $f$ of a two-dimensional percolation crossing event. In this paper, the Fourier transform of $f$ is studied and sharp bounds are obtained for its lower tail in several situations. Various applications of…

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.

In this paper we will extend the product of spectral triples to a product of semifinite spectral triples. We will prove that finite summability and regularity are preserved under taking products. Connes and Marcolli constructed for each…

We consider nontrivial critical models in $d=6+\epsilon$ spacetime dimensions with anticommuting scalars transforming under the symplectic group $\text{Sp}(N)$. These models are nonunitary, but the couplings are real and all operator…

This survey paper discusses five equivalent ways of defining a ``critical point at infinity'' for a complex polynomial of two variables.

Spectral triples are defined for C*-algebras associated with hyperbolic dynamical systems known as Smale spaces. The spectral dimension of one of these spectral triples is shown to recover the topological entropy of the Smale space.

We determine the pseudo-critical couplings at imaginary chemical potentials by high-statistics Monte Carlo simulations of QCD with four degenerate quarks at non-zero temperature and baryon density by the method of analytic continuationan.…

The critical point degree of a periodic graph operator is the number of critical points of its complex Bloch variety. Determining it is a step towards the spectral edges conjecture and more generally understanding Bloch varieties. Previous…

We study the spectral dimensions and spectral asymptotics of Krein-Feller operators for arbitrary finite Borel measures on $\left(0,1\right).$ Connections between the spectral dimension, the $L^{q}$-spectrum, the partition entropy and the…

In this paper we study dynamical chiral symmetry breaking in dimensionally regularized quenched QED within the context of Dyson-Schwinger equations. In D < 4 dimensions the theory has solutions which exhibit chiral symmetry breaking for all…

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical…

We derive an analytic formula at three loops for the cusp anomalous dimension Gamma_cusp(phi) in N=4 super Yang-Mills. This is done by exploiting the relation of the latter to the Regge limit of massive amplitudes. We comment on the…

We study the minimal number of existential quantifiers needed to define a diophantine set over a field and relate this number to the essential dimension of the functor of points associated to such a definition.

We study the dependence on the number of colors of the leading pi pi scattering amplitude in chiral dynamics. We demonstrate the existence of a critical number of colors for and above which the low energy pi pi scattering amplitude computed…