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Spin-2 spectrum of six-dimensional field theories

Achilleas Passias, Alessandro Tomasiello

TL;DR

The paper analyzes the spin-2 spectrum around $AdS_7$ gravity duals of six-dimensional ${ m N}=(1,0)$ linear-quiver SCFTs, deriving a universal lower bound on graviton masses that translates into a unitarity bound on dual operators. By formulating the mass operator as a Sturm–Liouville problem and performing explicit KK reductions for select backgrounds, it obtains complete or near-complete spectra (e.g., zero Romans mass and $\mathbb{R}^3$--D6) and provides a numerical strategy for more intricate cases like D8-brane configurations. The results yield concrete operator-dimension predictions for dual 6d SCFTs, including universal short spin-2 multiplets with $\Delta=4\ell+6$ and scalar primaries with $\Delta_{\rm pr}=4\ell+4$, while offering field-theory pictures in terms of hypermultiplets, tensor multiplets and stress-energy multiplets. These findings reinforce holographic expectations for non-Lagrangian 6d theories and furnish actionable data on the operator content and multiplet structure in these theories.

Abstract

We analyze the mass spectrum of spin-2 excitations around the gravity duals of "linear quiver" supersymmetric conformal field theories (SCFT's) in six dimensions. We show that for the entire family of gravity solutions it satisfies a bound which corresponds to a unitarity bound for the scaling dimension of the dual field theory operators. We determine the masses of excitations which belong to short multiplets, and for certain gravity solutions we obtain the Kaluza-Klein modes and the corresponding mass spectrum, fully and explicitly. Finally, we discuss an intuitive picture of the dual operators in terms of the effective descriptions of the SCFT's.

Spin-2 spectrum of six-dimensional field theories

TL;DR

The paper analyzes the spin-2 spectrum around gravity duals of six-dimensional linear-quiver SCFTs, deriving a universal lower bound on graviton masses that translates into a unitarity bound on dual operators. By formulating the mass operator as a Sturm–Liouville problem and performing explicit KK reductions for select backgrounds, it obtains complete or near-complete spectra (e.g., zero Romans mass and --D6) and provides a numerical strategy for more intricate cases like D8-brane configurations. The results yield concrete operator-dimension predictions for dual 6d SCFTs, including universal short spin-2 multiplets with and scalar primaries with , while offering field-theory pictures in terms of hypermultiplets, tensor multiplets and stress-energy multiplets. These findings reinforce holographic expectations for non-Lagrangian 6d theories and furnish actionable data on the operator content and multiplet structure in these theories.

Abstract

We analyze the mass spectrum of spin-2 excitations around the gravity duals of "linear quiver" supersymmetric conformal field theories (SCFT's) in six dimensions. We show that for the entire family of gravity solutions it satisfies a bound which corresponds to a unitarity bound for the scaling dimension of the dual field theory operators. We determine the masses of excitations which belong to short multiplets, and for certain gravity solutions we obtain the Kaluza-Klein modes and the corresponding mass spectrum, fully and explicitly. Finally, we discuss an intuitive picture of the dual operators in terms of the effective descriptions of the SCFT's.

Paper Structure

This paper contains 14 sections, 67 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. The AdS(7) solutions
  3. The graviton spectrum
  4. The mass operator
  5. Normalizability, and a bound on the spectrum
  6. Boundary conditions
  7. Examples
  8. The zero Romans mass solution
  9. The $\mathbb{R}^3$--D6 solution
  10. Solutions with D8-branes
  11. Field theory interpretation
  12. $\mathfrak{osp}$($6,2|1$) multiplets
  13. Non-supersymmetric AdS(7) solutions
  14. Hypergeometric function and Jacobi polynomials

Figures (1)

  • Figure 1: Some examples of linear quivers. Round nodes denote gauge symmetries and square nodes denote flavor symmetries. Links correspond to (bi)fundamental hypermultiplets, with tensor multiplets on horizontal ones. \ref{['fig:massless']} corresponds to the massless solution of section \ref{['zeroRomansmass']}; \ref{['fig:R3-D6']} to the $\mathbb{R}^3$--D6 solution of section \ref{['sub:R3D6']}; \ref{['fig:1D8']} to the solution with one D8-brane stack in section \ref{['sub:d8']}. In particular, for the latter one, $k=n_0(N- \mu)=n_0' \mu$, where $n_0=2\pi F_0$, $n_0'=-2\pi F_0'$.