58 research outputs found
Cluster Structure on Generalized Weyl Algebras
We introduce a class of non-commutative algebras that carry a non-commutative
(geometric) cluster structure which are generated by identical copies of
generalized Weyl algebras. Equivalent conditions for the finiteness of the set
of the cluster variables of these cluster structures are provided. Some
combinatorial data, called \textit{cluster strands,} arising from the cluster
structure are used to construct irreducible representations of generalized Weyl
algebras.Comment: in Algebras and Representation Theory, Volume 19, No1, Feb. 201
Integrability on the Master Space
It has been recently shown that every SCFT living on D3 branes at a toric
Calabi-Yau singularity surprisingly also describes a complete integrable
system. In this paper we use the Master Space as a bridge between the
integrable system and the underlying field theory and we reinterpret the
Poisson manifold of the integrable system in term of the geometry of the field
theory moduli space.Comment: 47 pages, 20 figures, using jheppub.st
Network and Seiberg Duality
We define and study a new class of 4d N=1 superconformal quiver gauge
theories associated with a planar bipartite network. While UV description is
not unique due to Seiberg duality, we can classify the IR fixed points of the
theory by a permutation, or equivalently a cell of the totally non-negative
Grassmannian. The story is similar to a bipartite network on the torus
classified by a Newton polygon. We then generalize the network to a general
bordered Riemann surface and define IR SCFT from the geometric data of a
Riemann surface. We also comment on IR R-charges and superconformal indices of
our theories.Comment: 28 pages, 28 figures; v2: minor correction
The Omega Deformation, Branes, Integrability, and Liouville Theory
We reformulate the Omega-deformation of four-dimensional gauge theory in a
way that is valid away from fixed points of the associated group action. We use
this reformulation together with the theory of coisotropic A-branes to explain
recent results linking the Omega-deformation to integrable Hamiltonian systems
in one direction and Liouville theory of two-dimensional conformal field theory
in another direction.Comment: 96 p
On Arnold's 14 `exceptional' N=2 superconformal gauge theories
We study the four-dimensional superconformal N=2 gauge theories engineered by
the Type IIB superstring on Arnold's 14 exceptional unimodal singularities
(a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435
to singularities which are not the direct sum of minimal ones. In particular,
we compute their BPS spectra in several `strongly coupled' chambers.
From the TBA side, we construct ten new periodic Y-systems, providing
additional evidence for the existence of a periodic Y-system for each isolated
quasi-homogeneous singularity with (more generally, for each N=2
superconformal theory with a finite BPS chamber whose chiral primaries have
dimensions of the form N/l).Comment: 73 pages, 7 figure
Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
In this work we investigate the canonical quantization of 2+1 gravity with
cosmological constant in the canonical framework of loop quantum
gravity. The unconstrained phase space of gravity in 2+1 dimensions is
coordinatized by an SU(2) connection and the canonically conjugate triad
field . A natural regularization of the constraints of 2+1 gravity can be
defined in terms of the holonomies of . As a first step
towards the quantization of these constraints we study the canonical
quantization of the holonomy of the connection on the
kinematical Hilbert space of loop quantum gravity. The holonomy operator
associated to a given path acts non trivially on spin network links that are
transversal to the path (a crossing). We provide an explicit construction of
the quantum holonomy operator. In particular, we exhibit a close relationship
between the action of the quantum holonomy at a crossing and Kauffman's
q-deformed crossing identity. The crucial difference is that (being an operator
acting on the kinematical Hilbert space of LQG) the result is completely
described in terms of standard SU(2) spin network states (in contrast to
q-deformed spin networks in Kauffman's identity). We discuss the possible
implications of our result.Comment: 19 pages, references added. Published versio
Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
We define a theory of Galilean gravity in 2+1 dimensions with cosmological
constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke
group, extending our previous study of classical and quantum gravity in 2+1
dimensions in the Galilean limit. We exhibit an r-matrix which is compatible
with our Chern-Simons action (in a sense to be defined) and show that the
associated bi-algebra structure of the Newton-Hooke Lie algebra is that of the
classical double of the extended Heisenberg algebra. We deduce that, in the
quantisation of the theory according to the combinatorial quantisation
programme, much of the quantum theory is determined by the quantum double of
the extended q-deformed Heisenberg algebra.Comment: 22 page
General Argyres-Douglas Theory
We construct a large class of Argyres-Douglas type theories by compactifying
six dimensional (2,0) A_N theory on a Riemann surface with irregular
singularities. We give a complete classification for the choices of Riemann
surface and the singularities. The Seiberg-Witten curve and scaling dimensions
of the operator spectrum are worked out. Three dimensional mirror theory and
the central charges a and c are also calculated for some subsets, etc. Our
results greatly enlarge the landscape of N=2 superconformal field theory and in
fact also include previous theories constructed using regular singularity on
the sphere.Comment: 55 pages, 20 figures, minor revision and typos correcte
Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
We study classical open string solutions with a null polygonal boundary in
AdS_3 in relation to gluon scattering amplitudes in N=4 super Yang-Mills at
strong coupling. We derive in full detail the set of integral equations
governing the decagonal and the dodecagonal solutions and identify them with
the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon models.
By evaluating the free energy in the conformal limit we compute the central
charges, from which we observe general correspondence between the polygonal
solutions in AdS_n and generalized parafermions.Comment: 25 pages, 4 figures, v2: a figure and references added, minor
corrections, v3: references added, minor corrections, to appear in JHE
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