New N=1 dualities from orientifold transitions. Part I. Field Theory

Garcia-Etxebarria, Inaki; Wrase, Timm; Heidenreich, Ben

doi:10.1007/JHEP10(2013)007

Article
Report number	arXiv:1210.7799 ; CERN-PH-TH-2012-293 ; SU-ITP-12-33
Title	New N=1 dualities from orientifold transitions. Part I. Field Theory
Author(s)	Garcia-Etxebarria, Inaki (CERN) ; Heidenreich, Ben (Cornell U., Phys. Dept.) ; Wrase, Timm (Stanford U., ITP)
Publication	2013
Imprint	31 Oct 2012
Number of pages	58
Note	Comments: 58 pages plus appendices, 11 figures; v2: minor changes, added references, published version 58 pages plus appendices, 11 figures; v2: minor changes, added references, published version
In:	JHEP 10 (2013) 007
DOI	10.1007/JHEP10(2013)007
Subject category	Particle Physics - Theory
Abstract	We report on a broad new class of N=1 gauge theory dualities which relate the worldvolume gauge theories of D3 branes probing different orientifolds of the same Calabi-Yau singularity. In this paper, we focus on the simplest example of these new dualities, arising from the orbifold singularity C^3/Z_3. We present extensive checks of the duality, including anomaly matching, partial moduli space matching, matching of discrete symmetries, and matching of the superconformal indices between the proposed duals. We then present a related duality for the dP_1 singularity, as well as dualities for the F_0 and Y^{4,0} singularities, illustrating the breadth of this new class of dualities. In a companion paper, we show that certain infinite classes of geometries which include C^3/Z_3 and dP_1 all exhibit such dualities, and argue that their ten-dimensional origin is the SL(2,Z) self-duality of type IIB string theory.
Copyright/License	Preprint: © 2012-2025 CERN (License: CC-BY-3.0)

$The modular invariant $|j(\tau)|$ plotted across the upper half plane $\bH$, where $\bH$ is conformally mapped to the unit disk via $w = \frac{1+i \tau}{i+\tau}$, so that $\tau = +i \infty$ (weak coupling) lies at the top edge of the disk, $\tau = i$ (intermediate coupling) in the center and $\tau = 0$ (strong coupling) at the bottom, whereas the left and right edges correspond to $\tau = -1$ and $\tau = +1$ respectively, and the $\mathrm{Im\ } \tau = 0$ axis spans the perimeter. The black regions, corresponding to $|j(\tau)| < 12^3$, serve to divide the plane into an infinite number of disjoint colored regions, each containing a subregion with a weakly coupled dual description ($|j(\tau)| \to \infty$), colored blue/purple. The superimposed curved grey lines illustrate the boundary of the region $|\mathrm{Re\ } \tau| < 1/2$, a fundamental domain under the identification $\tau \to \tau + 1$. The transformation $\tau \to -1/\tau$ is equivalent to inversion through the center of the disk, and the shaded triangular region is the canonical fundamental domain for $\SL(2,\bZ)$.$