Related papers: A Comment on Non-Chiral Operators in SQCD and its …
We propose a Seiberg duality for a 3d $\mathcal{N}=2$ $Spin(7)$ gauge theory with $F$ spinor matters. For $F \ge 6$, the theory allows a magnetic dual description with an $SU(F-4)$ gauge group. The matter content on the magnetic side is…
Expanding upon earlier work of Pouliot and Strassler, we construct chiral magnetic duals to nonchiral supersymmetric electric theories based upon SO(7), SO(8) and SO(9) gauge groups with various numbers of vector and spinor matter…
We establish the consistency of duality transformations for generic systems of $N=2$ vector supermultiplets in the presence of a chiral background field. This is relevant, for instance, when dealing with spurion fields or when considering…
Several definitions of differential operators on modules over noncommutative rings are discussed.
We study the connection of the chiral dynamics in QED and QCD in a strong magnetic field with noncommutative field theories (NCFT). It is shown that these dynamics determine complicated nonlocal NCFT. In particular, although the interaction…
Introduction of supersymmetry into the noncommutative geometry is investigated. We propose a new Dirac operator which plays the role of the metric over the extended algebra of chiral and antichiral supermultiplets and is invariant under the…
We study the implications of non-invertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic $SL(2,\mathbb{Z})$ duality. This is done by deriving the Adler-Bell-Jackiw anomaly of…
The structure of S-duality in U(1) gauge theory on a 4-manifold M is examined using the formalism of noncommutative geometry. A noncommutative space is constructed from the algebra of Wilson-'t Hooft line operators which encodes both the…
We consider the quantum theory of a two-form gauge field on a space-time which is a direct product of time and a spatial manifold, taken to be a compact five-manifold with no torsion in its cohomology. We show that the Hilbert space of this…
We examine several aspects of S-duality of four-dimensional noncommutative gauge theory. By making duality transformation explicit, we find that S-dual of noncommutative gauge theory is defined in terms of dual noncommutative deformation.…
We study electric-magnetic duality in the chiral ring of a supersymmetric U(N_c) gauge theory with adjoint and fundamental matter, in presence of a general confining phase superpotential for the adjoint and the mesons. We find the magnetic…
The algebraic notion of a differential operator on a module over a commutative ring is not extended to a module over a noncommutative ring.
We introduce a new model of spin noncommutative space in which noncommutative extension of the coordinate operators are assumed to be chirality dependent. Noncommutative correspondences of classical fields are defined via Weyl ordering, and…
Dimensional deconstruction of 5D SQCD with general n_c, n_f and k_CS gives rise to 4D N=1 gauge theories with large quivers of SU(n_c) gauge factors. We construct the chiral rings of such [SU(n_c)]^N theories, off-shell and on-shell. Our…
We introduce a non-perturbative framework for quantizing chiral solitons in interacting quantum spin chains. This approach provides a direct lattice extension of the well-established $S$-duality between the sine-Gordon and Thirring models,…
The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a two-fold Kramers degeneracy. A non-zero chirality implies that the spins are not coplanar, and is a measure of…
In this short article, we overview a concept of electronic toroidal multipoles, and their ordering with associated physical properties in non-magnetic and magnetic materials. The toroidal multipoles are introduced as microscopic electronic…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
We generalize our picture in [arXiv:0904.1744], and consider a pure abelian gauge theory on a four-manifold with nonlocal operators of every codimension arbitrarily and simultaneously inserted. We explicitly show that (i) the theory enjoys…
The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subject to an appropriate local boundary…