Related papers: Double quantization of Seiberg-Witten geometry and…
We consider the associativity (or WDVV) equations in the form they appear in Seiberg-Witten theory and prove that they are covariant under generic electric-magnetic duality transformations. We discuss the consequences of this covariance…
We investigate the metric dependence of the partition function of the self-dual p-form gauge field on an arbitrary Riemannian manifold. Using geometric quantization of the space of middle-dimensional forms, we derive a projectively flat…
We develop a geometric approach toward an interplay between a pair of quantum Schur algebras of arbitrary finite type. Then by Beilinson-Lusztig-MacPherson's stabilization procedure in the setting of partial flag varieties of type A (resp.…
We discuss quantum theory of fields \phi defined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which is a bilinear form in \phi defines the Gaussian measure with a covariance (Green function)…
Motivated by affine Schubert calculus, we construct a family of dual graded graphs $(\Gamma_s,\Gamma_w)$ for an arbitrary Kac-Moody algebra $\g(A)$. The graded graphs have the Weyl group $W$ of $\g(A)$ as vertex set and are labeled versions…
Quiver 5D $\mathcal{N}=1$ gauge theories describe the low-energy dynamics on webs of $(p,q)$-branes in type IIB string theory. S-duality exchanges NS5 and D5 branes, mapping $(p,q)$-branes to branes of charge $(-q,p)$, and, in this way,…
We investigate the gauging of conformal algebras with relations between the generators. We treat the $W_{5/2}$--algebra as a specific example. We show that the gauge-algebra is in general reducible with an infinite number of stages. We show…
We give proofs of the PBW and duality theorems for the quantum Kac-Moody algebras and quantum current algebras, relying on Lie bialgebra duality. We also show that the classical limit of the quantum current algebras associated with an…
We investigate the worldline quantum field theory (WQFT) formalism for scalar-QED and observe that a generating function emerges from WQFT, from which the scattering angle ensues. This generating function bears important similarities with…
We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. This approach allows us to analyze the dynamics of…
We explicate relations among the Gelfand--Graev modules for central covers, the Euler--Poincar\'e polynomial of the Arnold--Brieskorn manifold, and the quantum affine Schur--Weyl duality. These three objects and their relations are dictated…
The standard formulation of gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic qunantum theoretical access in the spirit of Wigner's representation theory shows that…
We study new Seiberg-like dualities for 1d $\mathcal{N}=2$ supersymmetric gauge theories -- that is, supersymmetric gauged quantum mechanics -- with unitary gauge group and (anti)fundamental matter in chiral and fermi multiplets, and with…
We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees…
Gauge freedom in quantum particle physics is shown to arise in a natural way from the geometry of two-spinors (Weyl spinors). Various related mathematical notions are reviewed, and a special ansatz of the kind "the system defines the…
In this work we study the quantisation of the Seiberg-Witten curve for the E-string theory compactified on a two-torus. We find that the resulting operator expression belongs to the class of elliptic quantum curves. It can be rephrased as…
In recent years soft factorization theorems in scattering amplitudes have been reinterpreted as conservation laws of asymptotic charges. In gauge, gravity, and higher spin theories the asymptotic charges can be understood as canonical…
In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport)…
We present a physical interpretation of the doubling of the algebra, which is the basic ingredient of the noncommutative spectral geometry, developed by Connes and collaborators as an approach to unification. We discuss its connection to…
We generalize the geometric structures generated by Witten's ground ring. It is shown that these generalized structures involve in a natural way some geometric constructions from Self-dual gravity [1,12]. The formal twistor construction on…