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Giant Gravitons in Conformal Field Theory

Vijay Balasubramanian, Micha Berkooz, Asad Naqvi, Matthew J. Strassler

TL;DR

The paper challenges the standard AdS/CFT identification of giant gravitons with single-trace chiral primaries, showing that for large R-charge the planar/trace-based description breaks down. It provides evidence across multiple settings that maximal giants are dual to determinants (and near-maximal giants to subdeterminants) of scalar fields, with precise counts and overlaps supporting orthogonality and angular-momentum bounds. The authors give a three-pronged set of demonstrations: topological/orbifold arguments, protected correlators in free field theory, and a Matrix-model analysis of giants on AdS7×S4 via fuzzy S4 geometry, culminating in explicit computations where giant-graviton expectation values reduce to subdeterminants of Higgs vevs. This determinant/subdeterminant framework offers a robust, nonperturbative description of giant gravitons and suggests a broader, noncommutative generalization of geometry in AdS/CFT landscapes, with potential extensions to other backgrounds and fixed points.

Abstract

Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

Giant Gravitons in Conformal Field Theory

TL;DR

The paper challenges the standard AdS/CFT identification of giant gravitons with single-trace chiral primaries, showing that for large R-charge the planar/trace-based description breaks down. It provides evidence across multiple settings that maximal giants are dual to determinants (and near-maximal giants to subdeterminants) of scalar fields, with precise counts and overlaps supporting orthogonality and angular-momentum bounds. The authors give a three-pronged set of demonstrations: topological/orbifold arguments, protected correlators in free field theory, and a Matrix-model analysis of giants on AdS7×S4 via fuzzy S4 geometry, culminating in explicit computations where giant-graviton expectation values reduce to subdeterminants of Higgs vevs. This determinant/subdeterminant framework offers a robust, nonperturbative description of giant gravitons and suggests a broader, noncommutative generalization of geometry in AdS/CFT landscapes, with potential extensions to other backgrounds and fixed points.

Abstract

Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

Paper Structure

This paper contains 40 sections, 73 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Giant gravitons are not traces
  3. Some basic tools
  4. ${\cal N}=4$ theories:
  5. Fixed points of ${\cal N}=1$ theories:
  6. Small angular momenta
  7. Failure of planarity and orthogonality of traces
  8. Scales in gravity, gauge theory and giants
  9. The Puzzle:
  10. Biggest giants should be determinants
  11. The $Z_{3}$ orbifold
  12. Gravity:
  13. Field Theory:
  14. Other examples
  15. SO(2N):
  16. ...and 25 more sections

Figures (1)

  • Figure 1: Planar diagrams for :(A) $\langle {\cal O}_1 {\cal O}_1 \rangle$ (there are $l$ such diagrams from cyclic permutations inside the Trace), (B) $\langle {\cal O}_2 {\cal O}_2 \rangle$ (there are $l_1\, l_2$ such diagrams), (C) $\langle {\cal O}_1 {\cal O}_2 \rangle$ (there are $l_1\, l_2\, l$ such diagrams).