New $ \mathcal{N} $ =1 dualities

Abstract

We show that the N =1 supersymmetric SU (N ) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the so-called T N theory. This is a natural generalization to N > 2 of a dual description of SU (2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other N =1 SCFTs involving copies of T N theories. Our duality is the basic operation from which a recently-found web of N =1 dualities obtained by compactifying M5-branes on Riemann surfaces can be derived field-theoretically.

N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

“…This higgsing looks similar to our deformation procedure, but a crucial difference is that the latter has an additional adjoint chiral multiplet M and M is given a nilpotent vev rather than µ. This difference can be understood once we consider the N = 1 version of the class S theories [28,33,61,62].…”

“…2 Indeed, the same deformation has been already studied in [28][29][30][31] in the framework of class S theories [25,32,33]. We take the principal embeddings of all the SU(N ) 3 flavor symmetry of T N theory.…”

“…Even though the superpotential (2.1) makes the theory N = 1 supersymmetric, this term turns out to be irrelevant and the deformed theory in the IR simply decouples into the original T and the free chiral multiplets M we added in the beginning. A nontrivial N = 1 fixed point can be produced by giving a nilpotent vev to M , as in [28][29][30][31]34]. From the Jacobson-Morozov theorem, any nilpotent element of a semisimple Lie algebra f is given via embedding ρ : su(2) → f as ρ(σ + ).…”

Mass-deformed T N as a linear quiver

“…As T N theories have the flavor symmetry SU(N ) A × SU(N ) B × SU(N ) C , the mass terms take values in three traceless complex-valued N × N matrices m A,B,C , that are hermitian in the case of 5d version. The effect of the mass terms when they are nilpotent was studied in [12,13], and therefore our aim here is the case when they are diagonalizable.…”

Linear quivers and N $$ \mathcal{N} $$ = 1 SCFTs from M5-branes

“…Moreover it opens the way for an N = 1 generalization of the large class of N = 2 SCFTs constructed from M5-branes on Riemann surfaces [8,10,11]. Many examples of such 4D N = 1 theories have already been discussed in the literature, see for instance [4][5][6][12][13][14][15]. However we believe that the efforts so far only scratch the surface of a large structure underlying the space of 4D N = 1 SCFT's arising from M5-branes.…”