Related papers: Null octagon from Deift-Zhou steepest descent

The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of…

We study a class of observables in four-dimensional superconformal Yang--Mills theories which, in the planar limit at finite 't Hooft coupling, can be expressed as determinants of semi-infinite matrices built from Bessel functions. This…

We give a physical interpretation for the analytic continuation of the partition function of superconformal SU$(2)$ $\mathcal{N}=2$ gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d…

We study the quantum mechanical motion in the $x^2y^2$ potentials with $n=2,3$, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. These systems show strong stochasticity in the classical limit ($\hbar = 0$)…

This is a survey of recent studies of singularity formation in solutions of spherically symmetric Yang-Mills equations in higher dimensions. The main attention is focused on five space dimensions because this case exhibits interesting…

We present an analytic derivation of the full four-loop cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory from the Sudakov form factor. To extract the cusp anomalous dimension, we calculate the $\epsilon^{-2}$…

A Yang-Mills theory linear in the scalar curvature for 2d gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As…

We study the compatiblity between the higher dimension dualities and the Yang-Mills equation of motion. Taking a 't Hooft solution as a starting point, we come to the conclusion that for only 4 dimensions the self duality implies the…

Applying the AdS/CFT correspondence, the expansion of the heavy-quark potential of the ${\cal N}$ supersymmetric Yang-Mills theory at large $N_c$ is carried out to the sub-leading term in the large 't Hooft coupling at nonzero temperatures.…

We consider a gauge-invariant Ginzburg-Landau functional (also known as Abelian Yang-Mills-Higgs model) on Hermitian line bundles over closed Riemannian manifolds of dimension $n \geq 3$. Assuming a logarithmic energy bound in the coupling…

Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. {\bf 137}(1993), 295-368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane…

A system of gravity coupled to a 2-form gauge field, a dilaton and Yang-Mills fields in $2n$ dimensions arises from the (2,1) sigma model or string. The field equations imply that the curvature with torsion and Yang-Mills field strength are…

We discuss a new approach to putting supersymmetric theories on the lattice. The basic idea is to start from a {\it twisted} formulation of the underlying supersymmetric theory in which the fermions are represented as grassmann valued…

We consider the light-cone (LC) gauge and LC quantization of the dimensional reduction of super Yang Mills theory from four to two dimensions. After integrating out all unphysical degrees of freedom, the non-local LC Hamiltonian exhibits an…

We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and…

We analyze a beta function with the analytic form of Novikov-Shifman-Vainshtein-Zakharov result in the five dimensional gravity-dilaton environment. We show how dilaton inherits poles and fixed points of such beta function through the zeros…

The conditions leading to a nontrivial renormalization of the topological charge in four--dimensional Yang--Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological…

We consider the normal matrix model with a cubic potential. The model is ill-defined, and in order to reguralize it, Elbau and Felder introduced a model with a cut-off and corresponding system of orthogonal polynomials with respect to a…

The fermionic gyromagnetic ratio g= 2 of the Kerr-Newman spacetime cannot be a computational "coincidence". This naturally immerges in a four dimensional generally covariant modified Yang-Mills action, which depends on the lorentzian…

We study the four-point function of the lowest-lying half-BPS operators in the ${\cal N} =4$ $SU(N)$ super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-$N$…