Related papers: Miura operators as R-matrices from M-brane interse…
Monopole operators in Abelian N=4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of…
In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of…
The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition.…
A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane…
For a quasi-split Satake diagram, we define a modified $q$-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding $\imath$quantum group. In other words, we provide a differential operator approach to…
We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkaehler…
We first construct an action of the extended double affine braid group $\mathcal{\ddot{B}}$ on the quantum toroidal algebra $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in untwisted and twisted types. As a crucial step in the proof, we obtain a…
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set of basic operations (universal gates). A natural choice,…
R7-branes are a class of recently discovered non-supersymmetric real codimension-two duality defects in type IIB string theory predicted by the Swampland Cobordism Conjecture. For type IIB realizations of 6D SCFTs with $\mathcal{N} = (2,0)$…
A manifestly gauge invariant formulation of 5-dimensional supersymmetric Yang-Mills theories in terms of 4d superfields is derived. It relies on a supersymmetry and gauge-covariant derivative operator in the $x^5$ direction. This…
We study intersecting surface operators in 6d holomorphic field theories with the aim of unraveling associated quantum integrable structures. We first study the intersections of surface operators in 6d holomorphic Chern-Simons theory on…
We study supersymmetric indices of the 6d $(2,0)$ theory of $N$ M5-branes on toric Sasaki-Einstein five-manifolds. Embedding the background into a local toric Calabi-Yau four-fold and equivariantly integrating the anomaly polynomial yields…
A dormant generic Miura $\mathfrak{sl}_2$-oper is a flat $\mathrm{PGL}_2$-bundle over an algebraic curve in positive characteristic equipped with some additional data. In the present paper, we give a combinatorial description of dormant…
In this paper we discuss representations of the Birman-Wenzl-Murakami algebra as well as of its dilute extension containing several free parameters. These representations are based on superalgebras and their baxterizations permit us to…
We constructed a multi-parametric deformation of the Brauer algebra representation related with the symplectic Lie algebras. The notion of Manin matrix of type C was generalised to the case of the multi-parametric deformation by using this…
In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete…
A study of the relation between topology change, energy and Lie algebra representations for fuzzy geometry in connection to $M$-theory is presented. We encounter two different types of topology change, related to the different features of…
We relate Miura type transformations (MTs) over an evolution system to its zero-curvature representations with values in Lie algebras g. We prove that certain homogeneous spaces of g produce MTs and show how to distinguish these spaces. For…
Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of three dimensional manifolds. We show that the model contains…
We derive 4-dimensional N=4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group U(N)^{2n}. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling…