Related papers: Loop measures and the Gaussian free field
We demonstrate that the large-N expansion of Wilson loop expectation values in SO(N) and Sp(N) Yang-Mills theory on orientable and nonorientable surfaces has a natural description as a weighted sum over covers of the given surface. The sum…
We test the unified-gauge formalism by computing a Wilson loop in Yang-Mills theory to one-loop order. The unified-gauge formalism is characterized by the abritrary, but fixed, four-vector $N_\mu$, which collectively represents the…
When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…
N=2* gauge theory in four space-time dimensions arises as a deformation of the parent N=4 supersymmetric Yang-Mill theory under which its hypermultiplet acquires a mass. This theory, on the one hand, has a known supergravity dual and on the…
We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation, from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter eps.…
The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be…
We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators. The…
Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theory that can yields results in positive characteristic, and…
This paper analyzes the performance of sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. Precise bounds on the number of samples required to yield an accurate estimate are derived.…
We study the thickness of the confining flux tube generated by a pair of sources in higher representations of the gauge group. Using a simple geometric picture we argue that the area of the cross-section of the flux tube, as measured by a…
We consider the topological theories of cond-mat/0404617 and cond-mat/0610583 and study ground state amplitudes of string net configurations which consist of large chunks $G$ of (trivalent) regular lattice. We evaluate these amplitudes in…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
As an illustration of the formalism of the master field we consider generalised $QCD_2$. We show how Wilson Loop averages for an arbitrary contour can be computed explicitly and with some ease. A generalised Hopf equation is shown to govern…
We use Pesin theory to study possible equilibrium measures for piecewise monotone maps of the interval. The maps may have unbounded derivative.
We perform the two loop level renormalization of quantum gravity in $2+\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly…
We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…
We extend the classical Lyapunov inequality on the measurable space with infinite measure and on the so-called Grand Lebesgue spaces (GLS). We find also the exact value for correspondent constant. Possible applications: Functional Analysis…
We derive exact formulas for circular Wilson loops in the $\mathcal{N}=4$ and $\mathcal{N}=2^{* }$ theories with gauge groups $U(N)$ and $SU(N)$ in the $k$-fold symmetrized product representation. The formulas apply in the limit of large…
In the framework of generalized finite element methods for elliptic equations with rough coefficients, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several…
We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of…