18 research outputs found
AGT on the S-duality Wall
Three-dimensional gauge theory T[G] arises on a domain wall between
four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L.
We argue that the N=2^* mass deformation of the bulk theory induces a
mass-deformation of the theory T[G] on the wall. The partition functions of the
theory T[SU(2)] and its mass-deformation on the three-sphere are shown to
coincide with the transformation coefficient of Liouville one-point conformal
block on torus under the S-duality.Comment: 14 pages, 3 figures. v2: Revised the analysis in sections 3.3 and 4.
Notes and references added. Version to appear in JHE
A 5d/3d duality from relativistic integrable system
We propose and prove a new exact duality between the F-terms of
supersymmetric gauge theories in five and three dimensions with adjoint matter
fields. The theories are compactified on a circle and are subject to the Omega
deformation. In the limit proposed by Nekrasov and Shatashvili, the
supersymmetric vacua become isolated and are identified with the eigenstates of
a quantum integrable system. The effective twisted superpotentials are the
Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show
that they match on-shell by deriving the Bethe ansatz equation from the saddle
point of the five-dimensional partition function. We also show that the
Chern-Simons terms match and extend our proposal to the elliptic quiver
generalizations.Comment: 30 pages, 4 figures. v2: typo corrected, references adde
S^3/Z_n partition function and dualities
We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge
theories. A gauge theory on the orbifold has degenerate vacua specified by the
holonomy. The partition function is obtained by summing up the contributions of
saddle points with different holonomies. An appropriate choice of the phase of
each contribution is essential to obtain the partition function. We determine
the relative phases in the holonomy sum in a few examples by using duality to
non-gauge theories. In the case of odd n the phase factors can be absorbed by
modifying a single function appearing in the partition function.Comment: 30 pages, 2 figures, added reference
Higgs branch localization in three dimensions
We show that the supersymmetric partition function of three-dimensional N =2 R-symmetric Chern-Simons-matter theories on the squashed S 3 and on S 2
7 S 1 can be computed with the so-called Higgs branch localization method, alternative to the more standard Coulomb branch localization. For theories that could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is dominated by BPS vortex strings sitting at two circles in the geometry. In this way, the partition function directly takes the form of a sum, over a finite number of points on the classical Coulomb branch, of a vortex-string times an antivortex-string partition functions. \ua9 2014 The Author(s)