New results on superconformal quivers

Abstract

All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting a new superconformal quiver from a known one. This procedure is termed "shrinking" and, in the 3 block case, leads to the discovery of two new models. Thus, the number of superconformal 3 block quivers is 16 rather than the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk" del Pezzo models exist.

The toric phases of theYp,qquivers

“…The conclusion is that for any toric phase all the relative number of flavors are integer numbers satisfying n F ≥ 2. This is precisely the condition [15] for a model to be a root of the Duality Tree, i.e. a (local) minimum for the sum of the ranks of the gauge groups.…”

“…However, our experience with a number of examples leads us to believe that this is in fact impossible. For instance, in the case of 3-block and 4-block chiral quivers, the classification of [15] implies that all the toric phases are indeed connected. It will be interesting to find a proof of this.…”

“…The quiver structure of the gauge theory automatically implies that the linear 't Hooft anomaly trR vanishes, since it is given by a weighted sum of the gauge coupling beta functions trR = N i β i [15]. The cubic 't Hooft anomaly trR 3 , proportional to the gravitational central charges c = a [18,19], is given by:…”

The gravity dual of supersymmetric gauge theories on a squashed S 1 × S 3

“…After subtracting the first term, which is divergent in the β → 0 limit (in any case for superconformal quivers this term vanishes [63]), one obtains …”

Superconformal block quivers, duality trees and Diophantine equations

“…e.g., [1][2][3][4][5]), and in theoretical physics, especially in the AdS/CFT correspondence and in the phenomenology of Standard-like models (cf. e.g., [6][7][8][9][10]). One salient feature is that gauge theories arising as worldvolume quantum field theories living on stacks of branes probing Calabi-Yau singularities naturally have a product structure for the gauge group as well as bi-fundamental and adjoint fields realized by open-strings; such generically supersymmetric gauge theories are thus encoded by quivers.…”