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Register a new userNew 3d $mathcal{N}=2$ SCFTs with $N^{3/2}$ scaling
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We construct several novel examples of 3d $mathcal{N}=2$ models whose free energy scales as $N^{3/2}$ at large $N$. This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d parents of the 3d models, matching the volume extracted from the $a$ conformal anomaly to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.
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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.
S-folds are a non-perturbative generalization of orientifold 3-planes which figure prominently in the construction of 4D $mathcal{N} = 3$ SCFTs and have also recently been used to realize examples of 4D $mathcal{N} = 2$ SCFTs. In this paper we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an S-fold. We develop an S-fold generalization of orientifold projection which applies to non-perturbative string junctions. This procedure leads to a different 4D flavor symmetry algebra depending on whether the S-fold supports discrete torsion. We also show that this same procedure allows us to read off admissible representations of the flavor symmetry in the associated 4D $mathcal{N} = 2$ SCFTs. Furthermore this provides a prescription for how to define F-theory in the presence of S-folds with discrete torsion.
We study a set of four-dimensional $mathcal{N}=2$ superconformal field theories (SCFTs) $widehat{Gamma}(G)$ labeled by a pair of simply-laced Lie groups $Gamma$ and $G$. They are constructed out of gauging a number of $mathcal{D}_p(G)$ and $(G, G)$ conformal matter SCFTs; therefore they do not have Lagrangian descriptions in general. For $Gamma = D_4, E_6, E_7, E_8$ and some special choices of $G$, the resulting theories have identical central charges $(a=c)$ without taking any large $N$ limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of $mathcal{N}=4$ super Yang-Mills theory upon rescaling fugacities. Especially, we find that the Schur index of $widehat{D}_4(SU(N))$ theory for $N$ odd is written in terms of MacMahons generalized sum-of-divisor function, which is quasi-modular. For generic choices of $Gamma$ and $G$, it can be regarded as a generalization of the affine quiver gauge theory obtained from $D3$-branes probing an ALE singularity of type $Gamma$. We also comment on a tantalizing connection regarding the theories labeled by $Gamma$ in the Deligne-Cvitanovic exceptional series.
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.
We study 3d $mathcal{N}=2$ supersymmetric gauge theories on closed oriented Seifert manifold---circle bundles over an orbifold Riemann surface---, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. Our main result is an exact formula for the supersymmetric partition function on any Seifert manifold, generalizing previous results on lens spaces. We explain how the result for an arbitrary Seifert geometry can be obtained by combining simple building blocks, the fibering operators. These operators are half-BPS line defects, whose insertion along the $S^1$ fiber has the effect of changing the topology of the Seifert fibration. We also point out that most supersymmetric partition functions on Seifert manifolds admit a discrete refinement, corresponding to the freedom in choosing a three-dimensional spin structure. As a strong consistency check on our result, we show that the Seifert partition functions match exactly across infrared dualities. The duality relations are given by intricate (and seemingly new) mathematical identities, which we tested numerically. Finally, we discuss in detail the supersymmetric partition function on the lens space $L(p,q)_b$ with rational squashing parameter $b^2 in mathbb{Q}$, comparing our formalism to previous results, and explaining the relationship between the fibering operators and the three-dimensional holomorphic blocks.
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