New checks and subtleties for AdS/CFT and a-maximization

TL;DR

This paper cross-checks AdS/CFT correspondence and a-maximization for a specific 4D N=1 SCFT with irrational R-charges, revealing subtle issues and making new predictions for dual theories, with results matching supergravity backgrounds.

Contribution

It uncovers subtle issues in a-maximization and AdS/CFT for irrational R-charges, providing the first consistent match with supergravity duals and predicting duals for second del Pezzo surfaces.

Findings

The theory has irrational central charge and R-charges.

Results match supergravity dual backgrounds.

Predictions for duals of second del Pezzo surface.

Abstract

We provide a cross-check of AdS/CFT and a-charge maximization for a four dimensional $N$=1 SCFT with irrational R-charges. The gauge theory is the low energy effective theory of N D3-branes at the tip of the complex cone over the first del Pezzo surface. By carefully taking into account the subtle issue of flavor symmetry breaking at the fixed point, we show, using a-maximization, that this theory has in fact irrational central charge and R-charges. Our results perfectly match with those inherited from the recently discovered supergravity dual background. Along analogous lines, we make novel predictions for the still unknown AdS dual of the quiver theory for the second del Pezzo surface. This should flow to a SCFT with irrational charges, too. All of our results differ from previous findings in the literature and outline interesting subtleties in a-maximization and AdS/CFT techniques overlooked in the past.