Related papers: WKB expansion of Yang-Yang generating function and…

We apply exact WKB methods to the study of the partition function of pure N=2 epsilon_i-deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in…

We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional…

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…

Form factors in planar $\mathcal{N}=4$ super-Yang-Mills theory have a dual description in terms of periodic Wilson loops. This duality maps the multi-collinear expansion of the former to an operator product expansion of the latter. The…

We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of…

For every family of orthogonal polynomials, we define a new realization of the Yangian of ${\mathfrak{gl}}_n$. Except in the case of Dickson polynomials, the new realizations do not satisfy the RTT relation. We obtain an analogue of the…

We derive two multivariate generating functions for three-dimensional Young diagrams (also called plane partitions). The variables correspond to a colouring of the boxes according to a finite Abelian subgroup G of SO(3). We use the vertex…

We study the path integral of a twisted $N=2$ supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the $SU(2)$ theory on a compact oriented simply…

In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. We generalize their study to all closed, compact, connected, possibly…

We introduce the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton-Jacobi equation for field…

After the work of Seiberg and Witten, it has been seen that the dynamics of N=2 Yang-Mills theory is governed by a Riemann surface $\Sigma$. In particular, the integral of a special differential $\lambda_{SW}$ over (a subset of) the periods…

Let $M$ be an exact symplectic manifold with $c_1(M)=0$. Denote by $\mathrm{Fuk}(M)$ the Fukaya category of $M$. We show that the dual space of the bar construction of $\mathrm{Fuk}(M)$ has a differential graded noncommutative Poisson…

We relate the semiclassical limit of the quantum Yang-Mills partition function on a compact oriented surface to the symplectic volume of the moduli space of flat connections, by using an explicit expression for the symplectic form. This…

The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…

For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of…

In this paper we give a concrete recipe how to construct triples of algebra-valued meromorphic functions on a complex vector space $\mathfrak{a}$ satisfying three coupled classical dynamical Yang-Baxter equations and an associated classical…

On a Poisson manifold endowed with a Riemannian metric we will construct a vector field that generalizes the double bracket vector field defined on semi-simple Lie algebras. On a regular symplectic leaf we will construct a generalization of…

Recently M. Kontsevich found a combinatorial formula defining a star-product of deformation quantization for any Poisson manifold. Kontsevich's formula has been reinterpreted physically as quantum correlation functions of a topological…

Yang-Mills gauge theory on Minkowski space supports a Batalin-Vilkovisky-infinity algebra structure, all whose operations are local. To make this work, the axioms for a BV-infinity algebra are deformed by a quadratic element, here the…