70 research outputs found
Surface defects and elliptic quantum groups
A brane construction of an integrable lattice model is proposed. The model is
composed of Belavin's R-matrix, Felder's dynamical R-matrix, the
Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining
operators. This construction implies that a family of surface defects act on
supersymmetric indices of four-dimensional supersymmetric
field theories as transfer matrices related to elliptic quantum groups.Comment: 31 pages. v2: minor changes and corrections; v3: minor improvements,
published versio
Poisson vertex algebras in supersymmetric field theories
A large class of supersymmetric quantum field theories, including all
theories with supersymmetry in three dimensions and theories
with supersymmetry in four dimensions, possess
topological-holomorphic sectors. We formulate Poisson vertex algebras in such
topological-holomorphic sectors and discuss some examples. For a
four-dimensional superconformal field theory, the associated
Poisson vertex algebra is the classical limit of a vertex algebra generated by
a subset of local operators of the theory.Comment: 30 pages. v2: references added. v3: references added. v4: various
improvements; section 3.5 on 3d N=2 SCFTs added; references added; published
versio
\Omega-deformation and quantization
We formulate a deformation of Rozansky-Witten theory analogous to the
-deformation. It is applicable when the target space is
hyperk\"ahler and the spacetime is of the form , with
being a Riemann surface. In the case that is a disk, the
-deformed Rozansky-Witten theory quantizes a symplectic submanifold of
, thereby providing a new perspective on quantization. As applications, we
elucidate two phenomena in four-dimensional gauge theory from this point of
view. One is a correspondence between the -deformation and quantization
of integrable systems. The other concerns supersymmetric loop operators and
quantization of the algebra of holomorphic functions on a hyperk\"ahler
manifold.Comment: 24 pages. v2: minor changes, references added; v3: minor changes, a
reference added, published versio
N=2 supersymmetric gauge theories and quantum integrable systems
We study N=2 supersymmetric gauge theories on the product of a two-sphere and
a cylinder. We show that the low-energy dynamics of a BPS sector of such a
theory is described by a quantum integrable system, with the Planck constant
set by the inverse of the radius of the sphere. If the sphere is replaced with
a hemisphere, then our system reduces to an integrable system of the type
studied by Nekrasov and Shatashvili. In this case we establish a correspondence
between the effective prepotential of the gauge theory and the Yang-Yang
function of the integrable system.Comment: 24 pages. v2: references added; v3: minor changes, published versio
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