Spin(7) duality for N $$ \mathcal{N} $$ = 1 CS-matter theories

Abstract

In this paper we propose a duality for non-holomorphic N = 1 CS-matter theories living on M2 branes probing Spin(7) cones. We call this duality Spin(7) duality. Two theories are named Spin(7) dual if they have the same moduli space: a real Spin(7) cone with base a weak G 2 manifold, and they are hence holographic dual to the same AdS 4 × G 2 M theory solution. We provide a systematic way to generate these dualities, derived by combining toric duality for N = 2 CS-matter theories and generalized non-holomorphic orientifold projections to N = 1. Brane construction, AdS/CFT correspondence, and the computation of the moduli space support our proposal at the classical level and provide some arguments at the quantum strong coupling regime. The relation with Seiberg-like duality is also analyzed.

$$ \mathcal{N} $$ = 1 dualities in 2+1 dimensions

“…On the other hand if we have an N = 1 duality and we know the mapping of a supermultiplet, we can, in principle, deform the N = 1 duality to an N = 0 duality. See [32][33][34][35][36][37][38][39][40] for earlier work on 3d N = 1 gauge theories and dualities.…”

Phases of $$ \mathcal{N} $$ = 1 quivers in 2 + 1 dimensions

“…19 Consistency requires that k2 = k3 + 1 mod 2, such that the resulting IR TQFTs satisfy the condition stated after (2.1). 20 In the case of U(N ) k 2 ,k 3 the Witten index reads…”

“…Given that we do not have neither non-renormalization theorems, nor localization techniques at our disposal, it may appear that N = 1 supersymmetry does not give any advantage compared to cases without supersymmetry. Nevertheless, in the recent years our understanding of these theories has overcome a new twist [1][2][3][4][5][6][7][8][9] (see also [10][11][12][13][14][15][16][17][18][19][20] for earlier considerations).…”

“…[23][24][25][26][27][28][29][30][31][32][33][34][35][36] and references therein) and also some results regarding non-supersymmetric quiver theories [37][38][39]. For prior studies of N = 1 quivers instead see [20].…”

2d $\mathcal{N}=(0,1)$ Gauge Theories and Spin(7) Orientifolds

“…With these motivations in mind, in this paper we introduce Spin (7) orientifolds, a new class of backgrounds that combine Joyce's construction of Spin (7) manifolds via the quotient of CY 4-folds by anti-holomorphic involutions with worldsheet parity, and construct 2d N = (0, 1) gauge theories on D1-branes probing them. Closely related ideas were presented in the insightful paper [20,21], whose goal was to engineer 3d N = 1 theories on M2-branes. 2 This paper is organized as follows.…”