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An efficient method of computing power expansions of algebraic functions is the method of Kung and Traub and is based on exact arithmetic. This paper shows a numeric approach is both feasible and accurate while also introducing a…
Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions $d \geq 2$. While the ferro- and antiferromagnetic models are essentially equivalent, the…
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa…
The multiplicative structure of the trivial symplectic groupoid over $\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function…
The Bollob\'as-Riordan polynomial [Math. Ann. 323, 81 (2002)] is a universal polynomial invariant for ribbon graphs. We find an extension of this polynomial for a particular family of combinatorial objects, called rank 3 weakly-colored…
The coefficients appearing at leading and subleading order in the $1/m$ expansion of bilinear heavy quark currents are related to each other by imposing reparametrization invariance on both the effective current operators and the…
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…
We study the growth of the values of binary quadratic forms $Q$ on a binary planar tree as it was described by Conway. We show that the corresponding Lyapunov exponents $\Lambda_Q(x)$ as a function of the path determined by $x\in \mathbb…
We consider the count of subgraphs with an arbitrary configuration of endpoints in the random-connection model based on a Poisson point process on ${\Bbb R}^d$. We present combinatorial expressions for the computation of the cumulants and…
We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums. In 1997 Murakami and Ohtsuki [MO] first constructed such…
We study the $n$-point differentials corresponding to Kadomtsev-Petviashvili tau functions of hypergeometric type (also known as Orlov-Scherbin partition functions), with an emphasis on their $\hbar^2$-deformations and expansions. Under the…
We investigate the scalar sector of linear cosmological perturbations in quadratic gravity. Working in the Einstein frame, we derive the equations of motion in a gauge-independent manner and express them in terms of three sets of…
We study the large $N$ expansion of twisted partition functions of 3d $\mathcal{N}=2$ superconformal field theories arising from $N$ M5-branes wrapped on a hyperbolic 3-manifold, $M_3$. Via the 3d-3d correspondence, the partition functions…
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method,…
The important parameter \mu_G^2 of the heavy quark expansion is analyzed including perturbative and power corrections. It is found that \mu_G^2(2GeV) is known with a few percent accuracy. The perturbative corrections are computed and found…
We continue the development of the topological membrane approach to open and unoriented string theories. We study orbifolds of topologically massive gauge theory defined on the geometry $[0,1]\times\Sigma$, where $\Sigma$ is a generic…
We discuss kinematical features of conformal Carroll field theories in three dimensions (3d). Conformal extension of Carroll algebra is infinite dimensional even in 3d unlike its relativistic counterpart, and hence 3d Carroll CFTs share…
We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using…
A generalized version of Groeneveld's convergence criterion for the virial expansion and generating functionals for weighted $2$-connected graphs is proven. The criterion works for inhomogeneous systems and yields bounds for the density…
We give a simple, multiplicative-weight update algorithm for learning undirected graphical models or Markov random fields (MRFs). The approach is new, and for the well-studied case of Ising models or Boltzmann machines, we obtain an…