On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories

Recently, it was found that certain 4d $\mathcal{N}=1$ Lagrangians experience supersymmetry enhancement at their IR fixed point, thereby giving a Lagrangian description for a plethora of Argyres-Douglas theories. A generic feature of these Lagrangians is that a number of gauge invariant operators decouple (as free fields) along the RG-flow. These decoupled operators can be naturally taken into account from the beginning itself by introducing additional gauge singlets (sometimes called `flipping fields') that couple to the decoupled operators via appropriate superpotential terms. It has also been checked that upon dimensionally reducing to 3d, the $(A_1,A_{2n-1})$ type Lagrangians only produce the expected behavior when flipping fields are included in the Lagrangian. In this paper we further investigate the role of flipping fields and find an example where the expected necessity of including the flipping fields in the dimensionally reduced Lagrangians seems to get violated. In the process we find two new dual Lagrangians for the so called 3d $T[SU(2)]$ theory.Comment: v1: 26 pages, 7 figures ; v2: Minor typos corrected; v3: Corrected typos and other minor errors, added a discussion section to highlight the subtle but very important role played by accidental symmetries in this set-u

New N=1 Dualities from M5-branes and Outer-automorphism Twists

We generalize recent construction of four-dimensional $\mathcal{N}=1$ SCFT from wrapping six-dimensional $\mathcal{N}=(2,0)$ theory on a Riemann surface to the case of $D$-type with outer-automorphism twists. This construction allows us to build various dual theories for a class of $\mathcal{N}=1$ quiver theories of $SO-USp$ type. In particular, we find there are five dual frames to $SO(2N)/USp(2N-2)/G_2$ gauge theories with $(4N-4)/4N/8$ fundamental flavors, where three of them are non-Lagrangian. We check the dualities by computing the anomaly coefficients and the superconformal indices. In the process we verify that the index of $D_4$ theory on a certain three punctured sphere with $Z_2$ and $Z_3$ twist lines exhibits the expected symmetry enhancement from $G_2 \times USp(6)$ to $E_7$.Comment: 56 pages, 29 colored figures; v2: minor corrections, references adde

BPS states and their reductions

We develop a method to identify the BPS states in the Hilbert space of a supersymmetric field theory on a generic curved space which preserves at least two real supercharges. We also propose a one-to-one map between BPS states in d-dimensional field theories and states that contribute to the supersymmetric partition function of a corresponding (d-1)-dimensional field theory. As an application we obtain the superconformal index on rounded and squashed three spheres, and we show a natural reduction of the respective indices to the three-dimensional exact partition functions. We discuss the validity of the correspondence both at the perturbative and at the non-perturbative level and exploit the idea to uplift the computation of the exact supersymmetric partition function on a general manifold to a higher dimensional index.Comment: 25 pages, 1 figure, typos fixe

Quiver Tails and N=1 SCFTs from M5-branes

We study a class of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify UV descriptions of four-dimensional SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their N=2 counterpart. We find a new type of object that we call the `Fan'. We show how to construct new N=1 superconformal theories using the Fan. Various dual descriptions for these SCFTs can be identified with different colored pair-of-pants decompositions. For example, we find an N=1 analog of Argyres-Seiberg duality for the SU(N) SQCD with 2N flavors. We also compute anomaly coefficients and superconformal indices for these theories and show that they are invariant under dualities.Comment: 40 pages + appendices, 32 figures; v2: minor corrections; v3: more corrections, improved figures and presentation. to appear in JHE