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Dibaryon Spectroscopy

Christopher P. Herzog, James McKernan

TL;DR

The paper establishes a metric-free bridge between dibaryon conformal dimensions in AdS/CFT and holomorphic curves on Kähler–Einstein bases: the dimension Δ of a time-independent dibaryon equals Δ = -3N (K_V · C)/(K_V · K_V), where V is the KE base of the Sasaki–Einstein manifold X and C is a holomorphic curve in V. This formula is validated for AdS_5×S^5, AdS_5×T^{1,1}, and S^5/ℤ_3, and is then extended to smooth del Pezzo bases and generalized conifolds, showing agreement with known gauge-theory dibaryon spectra and providing a unified method to count and predict dibaryon operators without explicit metrics. The work also develops a geometric toolkit (volume relations, push-pull and Riemann–Hurwitz techniques) to compute Δ from intersection data K_V · C and K_V · K_V, enabling predictions across a broad class of geometries and their gauge duals. The results illuminate the deep link between holomorphic curve data and gauge-theory operator spectra, and they raise questions about the precise counting of holomorphic curves versus dibaryons and the role of Seiberg duality in preserving spectra. Overall, the paper broadens checks of AdS/CFT and provides practical geometric formulas for dibaryon spectroscopy in diverse AdS/CFT backgrounds.

Abstract

The AdS/CFT correspondence relates dibaryons in superconformal gauge theories to holomorphic curves in Kaehler-Einstein surfaces. The degree of the holomorphic curves is proportional to the gauge theory conformal dimension of the dibaryons. Moreover, the number of holomorphic curves should match, in an appropriately defined sense, the number of dibaryons. Using AdS/CFT backgrounds built from the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999), we show that the gauge theory prediction for the dimension of dibaryonic operators does indeed match the degree of the corresponding holomorphic curves. For AdS/CFT backgrounds built from cones over del Pezzo surfaces, we are able to match the degree of the curves to the conformal dimension of dibaryons for the n'th del Pezzo surface, n=1,2,...,6. Also, for the del Pezzos and the A_k type generalized conifolds, for the dibaryons of smallest conformal dimension, we are able to match the number of holomorphic curves with the number of possible dibaryon operators from gauge theory.

Dibaryon Spectroscopy

TL;DR

The paper establishes a metric-free bridge between dibaryon conformal dimensions in AdS/CFT and holomorphic curves on Kähler–Einstein bases: the dimension Δ of a time-independent dibaryon equals Δ = -3N (K_V · C)/(K_V · K_V), where V is the KE base of the Sasaki–Einstein manifold X and C is a holomorphic curve in V. This formula is validated for AdS_5×S^5, AdS_5×T^{1,1}, and S^5/ℤ_3, and is then extended to smooth del Pezzo bases and generalized conifolds, showing agreement with known gauge-theory dibaryon spectra and providing a unified method to count and predict dibaryon operators without explicit metrics. The work also develops a geometric toolkit (volume relations, push-pull and Riemann–Hurwitz techniques) to compute Δ from intersection data K_V · C and K_V · K_V, enabling predictions across a broad class of geometries and their gauge duals. The results illuminate the deep link between holomorphic curve data and gauge-theory operator spectra, and they raise questions about the precise counting of holomorphic curves versus dibaryons and the role of Seiberg duality in preserving spectra. Overall, the paper broadens checks of AdS/CFT and provides practical geometric formulas for dibaryon spectroscopy in diverse AdS/CFT backgrounds.

Abstract

The AdS/CFT correspondence relates dibaryons in superconformal gauge theories to holomorphic curves in Kaehler-Einstein surfaces. The degree of the holomorphic curves is proportional to the gauge theory conformal dimension of the dibaryons. Moreover, the number of holomorphic curves should match, in an appropriately defined sense, the number of dibaryons. Using AdS/CFT backgrounds built from the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999), we show that the gauge theory prediction for the dimension of dibaryonic operators does indeed match the degree of the corresponding holomorphic curves. For AdS/CFT backgrounds built from cones over del Pezzo surfaces, we are able to match the degree of the curves to the conformal dimension of dibaryons for the n'th del Pezzo surface, n=1,2,...,6. Also, for the del Pezzos and the A_k type generalized conifolds, for the dibaryons of smallest conformal dimension, we are able to match the number of holomorphic curves with the number of possible dibaryon operators from gauge theory.

Paper Structure

This paper contains 16 sections, 75 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Geometry of the Dibaryon
  3. Dibaryons in $T^{1,1}$ and Giant Gravitons in $\mathbf{S}^5$
  4. $AdS_5 \times \mathbf{S}^5$
  5. $AdS_5 \times T^{1,1}$
  6. Smooth $\mathbf{V}$
  7. The Third del Pezzo
  8. del Pezzos Five and Six
  9. The Fourth del Pezzo
  10. The First and Second del Pezzos
  11. del Pezzos Seven and Eight
  12. The Generalized Conifolds
  13. Gauge Theory Duals for Generalized Conifolds
  14. The Geometry of the Generalized Conifolds
  15. Dibaryons from Gauge Theory
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Quivers of Wijnholt for the (a) fourth, (b) fifth, and (c) sixth del Pezzos. In this condensed notation, each $SU(N)$ represents a node. For example, for the fourth del Pezzo, a pair of bifundamentals $Y$ and $Z$ attaches to each $SU(N)$ node in the lower right hand corner of the quiver.
  • Figure 2: a) The quiver of IW for the first del Pezzo. b) The Model II quiver of Hanetal2 for the second del Pezzo. The nodes correspond to $SU(N)$ gauge groups.
  • Figure 3: The extended Dynkin diagrams of $ADE$ type, including the indices $n_i$ of each vertex.