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

M. Bertolini, F. Bigazzi, A. L. Cotrone

TL;DR

The authors validate AdS/CFT against $a$-maximization for a 4d ${ m N}=1$ SCFT arising from D3-branes at the cone over $dP_1$, showing that proper accounting of IR flavor-symmetry breaking yields irrational central charge and $R$-charges that agree with the gravity dual (Y^{2,1}). They demonstrate that neglecting flavor-breaking patterns leads to incorrect rational values, and they provide a robust cross-check via holographic three-cycle volumes and baryonic charges. Extending the method to the second del Pezzo, $dP_2$, they predict irrational IR $R$-charges and a corresponding irrational central charge, and supply explicit R-charges (Tables 2–3) along with predictions for the yet-unknown AdS dual geometry $X_{dP_2}$, including its volume. Overall, the work highlights subtle but crucial aspects of a-maximization and AdS/CFT in non-regular Sasaki–Einstein backgrounds and delivers the first known CFT with irrational R-charges having a known holographic dual.

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.

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

TL;DR

The authors validate AdS/CFT against -maximization for a 4d SCFT arising from D3-branes at the cone over , showing that proper accounting of IR flavor-symmetry breaking yields irrational central charge and -charges that agree with the gravity dual (Y^{2,1}). They demonstrate that neglecting flavor-breaking patterns leads to incorrect rational values, and they provide a robust cross-check via holographic three-cycle volumes and baryonic charges. Extending the method to the second del Pezzo, , they predict irrational IR -charges and a corresponding irrational central charge, and supply explicit R-charges (Tables 2–3) along with predictions for the yet-unknown AdS dual geometry , including its volume. Overall, the work highlights subtle but crucial aspects of a-maximization and AdS/CFT in non-regular Sasaki–Einstein backgrounds and delivers the first known CFT with irrational R-charges having a known holographic dual.

Abstract

We provide a cross-check of AdS/CFT and a-charge maximization for a four dimensional =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.

Paper Structure

This paper contains 6 sections, 25 equations, 2 figures, 3 tables.

Table of Contents

  1. Overview
  2. The quiver gauge theory for the first del Pezzo
  3. Calculating the central charge via $a$-maximization
  4. The $R$-charges
  5. A check for AdS/CFT
  6. The SCFT for the second del Pezzo surface and a prediction for its AdS dual

Figures (2)

  • Figure 1: The quiver associated to the first del Pezzo surface. Each dot represents a $SU(N)$ factor while each arrow represents a bi-fundamental chiral multiplet.
  • Figure 2: The quivers associated to the second del Pezzo surface.