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Register a new user3d $mathcal{N}=2$ Brane Webs and Quivers
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Shi Cheng
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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.
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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.
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.
It is widely considered that the classical Higgs branch of 4d $mathcal{N}=2$ SQCD is a well understood object. However there is no satisfactory understanding of its structure. There are two complications: (1) the Higgs branch chiral ring contains nilpotent elements, as can easily be checked in the case of $mathrm{SU}(N)$ with 1 flavour. (2) the Higgs branch as a geometric space can in general be decomposed into two cones with nontrivial intersection, the baryonic and mesonic branches. To study the second point in detail we use the recently developed tool of magnetic quivers for five-brane webs, using the fact that the classical Higgs branch for theories with 8 supercharges does not change through dimensional reduction. We compare this approach with the computation of the hyper-Kahler quotient using Hilbert series techniques, finding perfect agreement if nilpotent operators are eliminated by the computation of a so called radical. We study the nature of the nilpotent operators and give conjectures for the Hilbert series of the full Higgs branch, giving new insights into the vacuum structure of 4d $mathcal{N}=2$ SQCD. In addition we demonstrate the power of the magnetic quiver technique, as it allows us to identify the decomposition into cones, and provides us with the global symmetries of the theory, as a simple alternative to the techniques that were used to date.
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.
Magnetic quivers have led to significant progress in the understanding of gauge theories with 8 supercharges at UV fixed points. For a given low-energy gauge theory realised via a Type II brane construction, there exist magnetic quivers for the Higgs branches at finite and infinite gauge coupling. Comparing these moduli spaces allows to study the non-perturbative effects when transitioning to the fixed point. For 5d $mathcal{N}=1$ SQCD, 5-brane webs have been an important tool for deriving magnetic quivers. In this work, the emphasis is placed on 5-brane webs with orientifold 5-planes which give rise to 5d theories with orthogonal or symplectic gauge groups. For this set-up, the magnetic quiver prescription is derived and contrasted against a unitary magnetic quiver description extracted from an O$7^-$ construction. Further validation is achieved by a derivation of the associated Hasse diagrams. An important class of families considered are the orthogonal exceptional $E_n$ families ($-infty < n leq 8$), realised as infinite coupling Higgs branches of $mathrm{Sp}(k)$ gauge theories with fundamental matter. In particular, the moduli spaces are realised by a novel type of magnetic quivers, called unitary-orthosymplectic quivers.
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