Related papers: On Painlev\'e/gauge theory correspondence
We discuss the relation between the cluster integrable systems and $q$-difference Painlev\'e equations. The Newton polygons corresponding to these integrable systems are all 16 convex polygons with a single interior point. The Painlev\'e…
This paper concerns the discrete version of the Painlev\'e identification problem, i.e., how to recognize a certain recurrence relation as a discrete Painlev\'e equation. Often some clues can be seen from the setting of the problem, e.g.,…
Given a 4d N=2 SUSY gauge theory, one can construct the Seiberg-Witten prepotentional, which involves a sum over instantons. Integrals over instanton moduli spaces require regularisation. For UV-finite theories the AGT conjecture favours…
Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal…
We provide evidence for the existence of a new strongly-coupled four dimensional $\mathcal{N}=2$ superconformal field theory arising as a non-trivial IR fixed point on the Coulomb branch of the mass-deformed superconformal Lagrangian theory…
We study the Riemann-Hilbert problem associated to flat sections of oper connections of arbitrary rank on the twice-punctured Riemann sphere with irregular singularities of the mildest type. We construct the solutions in terms of the…
We study four dimensional N=2 supersymmetric gauge theory in the Omega-background with the two dimensional N=2 super-Poincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system…
Bender-Canfield showed that a plethora of graph counting problems in oriented/unoriented surfaces involve two constants $t_g$ and $p_g$ for the oriented and the unoriented case respectively. T.T.Q. Le and the authors recently discovered a…
We consider the first order connection formulation of 4D general relativity in the "orthogonal" gauge. We show how the partial gauge fixing of the phase space canonical coordinates leads to the appearance of second class constraints in the…
The first, second and fourth Painlev\'{e} equations are studied by means of dynamical systems theory and three dimensional weighted projective spaces $\C P^3(p,q,r,s)$ with suitable weights $(p,q,r,s)$ determined by the Newton diagrams of…
Poincar\'{e}-Sobolev-type inequalities involving rearrangement-invariant norms on the entire $\mathbb{R}^n$ are provided. Namely, inequalities of the type $\|u-P\|_{Y(\mathbb{R}^n)}\leq C\|\nabla^m u\|_{X(\mathbb{R}^n)}$, where $X$ and $Y$…
Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric…
A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace-Dunkl operator associated to the $\mathbb{Z}_2^n$ root system. This algebra is also the invariance algebra of the generic…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
We formulate gauge theories on noncompact Lorentzian manifolds. For definiteness we choose an SO(1,4) gauge theory -- the isometry group of the five dimensional Minkowski space. We make use of the natural inner product to construct the…
The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lam'e equations, respectively. This correspondence is usually expressed via an…
In this manuscript we make major progress classifying algebraic relations between solutions of Painlev\'e equations. Our main contribution is to establish the algebraic independence of solutions of various pairs of equations in the…
The extension of the Painlev\'e-Calogero coorespondence for n-particle Inozemtsev systems raises to the multi-particle generalisations of the Painlev\'e equations which may be obtained by the procedure of Hamiltonian reduction applied to…
The two-loop anomalous dimension of the chiral matter superfields is calculated for a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of…
The consistent description of unstable particles, renormalons, or other Schwinger--Dyson-type of solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green's functions,…