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Register a new userMulti-cover skeins, quivers, and 3d $mathcal{N}=2$ dualities
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The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of holomorphic disks on a Lagrangian brane are observed to generate dual quiver descriptions of the geometry. Embedding into M-theory, a large class of dualities of 3d $mathcal{N}=2$ theories associated to quivers is obtained. The multi-cover skein relation admits a compact formulation in terms of quantum torus algebras associated to the quiver and in this language the relations are similar to wall-crossing identities of Kontsevich and Soibelman.
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Seiberg-like dualities in $2+1$d quiver gauge theories with $4$ supercharges are investigated. We consider quivers made of various combinations of classical gauge groups $U(N)$, $Sp(N)$, $SO(N)$ and $SU(N)$. Our main focus is the mapping of the supersymmetric monopole operators across the dual theories. There is a simple general rule that encodes the mapping of the monopoles upon dualising a single node. This rule dictates the mapping of all the monopoles which are not dressed by baryonic operators. We also study more general situations involving baryons and baryon-monopoles, focussing on three examples: $SU-Sp$, $SO-SO$ and $SO-Sp$ quivers.
We discuss the effective Chern-Simons levels for 3d $mathcal{N}=2$ gauge theories and their relations to the relative angles between NS5-brane and NS5-brane. We find that turning on real masses for chiral multiplets leads to various equivalent brane webs that are related by flipping the sign of mass parameters. This flip can be interpreted as 3d mirror symmetry for abelian theories. Each of these webs has a corresponding mathematical quiver structure. We check the equivalence of vortex partition functions for these brane webs by implementing topological vertex method. In addition, we compute the vortex partition functions of nonabelian theories with gauge group $U(N)$ and find the associated quiver structures and brane webs. We find that on Higgs branch nonabelian brane webs are broken to abelian brane webs with gauge group $U(1)^{otimes N}$. We also discuss the Ooguri-Vafa invariants for nonabelian theories and the movement of flavor D5-branes that leads to equivalent brane webs.
Aspects of three dimensional $mathcal{N}=2$ gauge theories with monopole superpotentials and their dualities are investigated. The moduli spaces of a number of such theories are studied using Hilbert series. Moreover, we propose new dualities involving quadratic powers for the monopole superpotentials, for unitary, symplectic and orthogonal gauge groups. These dualities are then tested using the three sphere partition function and matching of the Hilbert series. We also provide an argument for the obstruction to the duality for theories with quartic monopole superpotentials.
We study the moduli space of 3d $mathcal{N}=4$ quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $mathcal{N}=1$ superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.
We consider a family of $mathcal{N}=2$ superconformal field theories in four dimensions, defined as $mathbb{Z}_q$ orbifolds of $mathcal{N}=4$ Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $mathcal{N}=1$ superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of $N$, exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $mathcal{N}=4$ only at high orders in perturbation theory.
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