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From Gravitons to Giants

Avinash Dhar, Gautam Mandal, Mikael Smedbäck

TL;DR

Addressing nonperturbative gravity in the half-BPS sector, the paper uses exact bosonization of N fermions into N bosonic oscillators to analyze graviton dynamics in AdS5×S5 via the boundary theory. It shows that three-point graviton correlators grow exponentially with N at high energies, signaling breakdown of a graviton-based description well before reaching the Planck or AdS scales. The authors identify giant gravitons (and their oscillator/Schur-polynomial realizations) as weakly coupled bulk degrees of freedom that restore a tractable description, with single-particle states matching the giant-graviton spectrum. A universal, non-interacting bosonic description with a finite cutoff emerges, while Schur states illuminate the antisymmetric sector and clarify the bulk-boundary correspondence.

Abstract

We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdS$_5 \times $S$^5$ background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number $N$ of fermions in terms of $N$ bosonic oscillators. An exact computation of the three-point correlation function of gravitons for finite $N$ shows that they become strongly coupled at sufficiently high energies, with an interaction that grows exponentially in $N$. We show that even at such high energies a description of the bulk physics in terms of weakly interacting particles can be constructed. The single particle states providing such a description are created by our bosonic oscillators or equivalently these are the multi-graviton states corresponding to the so-called Schur polynomials. Both represent single giant graviton states in the bulk. Multi-particle states corresponding to multi-giant gravitons are, however, different, since interactions among our bosons vanish identically, while the Schur polynomials are weakly interacting at high enough energies.

From Gravitons to Giants

TL;DR

Addressing nonperturbative gravity in the half-BPS sector, the paper uses exact bosonization of N fermions into N bosonic oscillators to analyze graviton dynamics in AdS5×S5 via the boundary theory. It shows that three-point graviton correlators grow exponentially with N at high energies, signaling breakdown of a graviton-based description well before reaching the Planck or AdS scales. The authors identify giant gravitons (and their oscillator/Schur-polynomial realizations) as weakly coupled bulk degrees of freedom that restore a tractable description, with single-particle states matching the giant-graviton spectrum. A universal, non-interacting bosonic description with a finite cutoff emerges, while Schur states illuminate the antisymmetric sector and clarify the bulk-boundary correspondence.

Abstract

We discuss exact quantization of gravitational fluctuations in the half-BPS sector around AdSS background, using the dual super Yang-Mills theory. For this purpose we employ the recently developed techniques for exact bosonization of a finite number of fermions in terms of bosonic oscillators. An exact computation of the three-point correlation function of gravitons for finite shows that they become strongly coupled at sufficiently high energies, with an interaction that grows exponentially in . We show that even at such high energies a description of the bulk physics in terms of weakly interacting particles can be constructed. The single particle states providing such a description are created by our bosonic oscillators or equivalently these are the multi-graviton states corresponding to the so-called Schur polynomials. Both represent single giant graviton states in the bulk. Multi-particle states corresponding to multi-giant gravitons are, however, different, since interactions among our bosons vanish identically, while the Schur polynomials are weakly interacting at high enough energies.

Paper Structure

This paper contains 16 sections, 58 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review of exact bosonization
  3. Graviton interaction
  4. The exact correlators
  5. Graviton interaction at long wavelengths
  6. Chiral ring structure
  7. Four-point function and 'bootstrap'
  8. Cubic gravity theory
  9. Breakdown of the graviton description
  10. The universal bosonic excitations
  11. Bulk interpretation of the states $a^\dagger_{m_1} a^\dagger_{m_2}...| 0 \rangle$
  12. Schurs and the bosonic oscillators
  13. Summary and discussion
  14. Beta's and oscillators
  15. Derivation of Eqn.(3.21)
  16. ...and 1 more sections

Figures (3)

  • Figure 1: The action of $\sigma_{k}^{\dagger}$.
  • Figure 2: Bootstrap: Test for a cubic graviton field theory.
  • Figure 3: Forming the state $\beta_m^{\dagger} \sigma_{k-m}^{\dagger} | 0 \rangle$.