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Multi-Spin Giants

S. Arapoglu, N. S. Deger, A. Kaya, E. Sezgin, P. Sundell

TL;DR

The paper investigates multi spin giant gravitons in AdS_m x S^n by constructing a 1/2 BPS two spin giant wrapped on S^{n-2} and spinning in both AdS_m and S^n. It analyzes stability and spectrum via a 0+1 dimensional sigma model, showing the vibration frequencies are real, curvature determined, and evenly spaced, consistent with a large N Fock space picture. General spherical giants are then treated through a KK reduction yielding integrable dynamics with separable variables and Pöschl-Teller type potentials for the point particle sector, along with a Bohr-Sommerfeld quantization of breathing modes. The work connects bulk giant energies and spins to dual CFT operators, highlighting holographic interpretations and suggesting directions for supersymmetric completions and higher mode Generalizations. These results illuminate the holographic role of semi classical p-brane giants in AdS/CFT and provide a framework for exact quantization and operator mapping in large charge sectors.

Abstract

We examine spherical p-branes in AdS_m x S^n, that wrap an S^p in either AdS_m (p=m-2) or S^n (p=n-2). We first construct a two-spin giant solution expanding in S^n and has spins both in AdS_m and S^n. For (m,n)={(5,5),(4,7),(7,4)}, it is 1/2 supersymmetric, and it reduces to the single-spin giant graviton when the AdS spin vanishes. We study some of its basic properties such as instantons, non-commutativity, zero-modes, and the perturbative spectrum. All vibration modes have real and positive frequencies determined uniquely by the spacetime curvature, and evenly spaced. We next consider the (0+1)-dimensional sigma-models obtained by keeping generally time-dependent transverse coordinates, describing warped product of a breathing-mode and a point-particle on S^n or AdS_m x S^1. The BPS bounds show that the only spherical supersymmetric solutions are the single and the two-spin giants. Moreover, we integrate the sigma-model and separate the canonical variables. We quantize exactly the point-particle part of the motion, which in local coordinates gives Poschl-Teller type potentials, and calculate its contribution to the anomalous dimension.

Multi-Spin Giants

TL;DR

The paper investigates multi spin giant gravitons in AdS_m x S^n by constructing a 1/2 BPS two spin giant wrapped on S^{n-2} and spinning in both AdS_m and S^n. It analyzes stability and spectrum via a 0+1 dimensional sigma model, showing the vibration frequencies are real, curvature determined, and evenly spaced, consistent with a large N Fock space picture. General spherical giants are then treated through a KK reduction yielding integrable dynamics with separable variables and Pöschl-Teller type potentials for the point particle sector, along with a Bohr-Sommerfeld quantization of breathing modes. The work connects bulk giant energies and spins to dual CFT operators, highlighting holographic interpretations and suggesting directions for supersymmetric completions and higher mode Generalizations. These results illuminate the holographic role of semi classical p-brane giants in AdS/CFT and provide a framework for exact quantization and operator mapping in large charge sectors.

Abstract

We examine spherical p-branes in AdS_m x S^n, that wrap an S^p in either AdS_m (p=m-2) or S^n (p=n-2). We first construct a two-spin giant solution expanding in S^n and has spins both in AdS_m and S^n. For (m,n)={(5,5),(4,7),(7,4)}, it is 1/2 supersymmetric, and it reduces to the single-spin giant graviton when the AdS spin vanishes. We study some of its basic properties such as instantons, non-commutativity, zero-modes, and the perturbative spectrum. All vibration modes have real and positive frequencies determined uniquely by the spacetime curvature, and evenly spaced. We next consider the (0+1)-dimensional sigma-models obtained by keeping generally time-dependent transverse coordinates, describing warped product of a breathing-mode and a point-particle on S^n or AdS_m x S^1. The BPS bounds show that the only spherical supersymmetric solutions are the single and the two-spin giants. Moreover, we integrate the sigma-model and separate the canonical variables. We quantize exactly the point-particle part of the motion, which in local coordinates gives Poschl-Teller type potentials, and calculate its contribution to the anomalous dimension.

Paper Structure

This paper contains 24 sections, 179 equations, 3 figures.

Table of Contents

  1. Introduction
  2. 1/2 Supersymmetric Two-Spin Giants
  3. BPS Bound
  4. Supersymmetry
  5. Instantons
  6. Non-commutativity
  7. Validity of the Solution
  8. The Algebra of Unbroken Symmetries
  9. Vibration Spectrum
  10. Bosonic Oscillations
  11. Bosonic Zero Modes and Spectrum
  12. Fermionic Oscillations of $M2$-Brane (Two-spin)
  13. Fermionic Oscillations of $M2$-Brane (Single-spin)
  14. Fermionic Zero Modes and Spectrum
  15. Comments on the Supermultiplet Structure
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Different descriptions of the states in $AdS_5\times S^5$.
  • Figure 2: The potential $V(r)$ in (\ref{['p1']}) for $k>q_1$ (on the left) and for $k=q_1$ (on the right).
  • Figure 3: The potential $V(\theta)$ in (\ref{['pot2']}) for $q<kp$ (on the left) and for $q=kp$ (on the right).