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Giant Graviton Correlators from Dual SU(N) super Yang-Mills Theory

Robert de Mello Koch, Rhiannon Gwyn

TL;DR

This work extends the Schur-polynomial approach to exact correlators from U(N) to SU(N) N=4 SYM at zero coupling, constructing a linearly independent basis of half-BPS operators built from the traceless field $\Psi=\phi_1+i\phi_2$ and establishing a finite-N dictionary with giant gravitons in AdS5×S5. By introducing a ghost-field subtraction and a differential operator $D$ that removes a box from Young diagrams, the authors map SU(N) correlators to the known U(N) results and identify the null space of $D$ as the space of independent SU(N) BPS operators, with explicit reduction rules and a constructive algorithm. They analyze large-N and finite-N limits, showing that at large $N$ the totally symmetric and antisymmetric sectors remain approximately orthogonal for heavy giant gravitons, while for finite N significant mixing persists and Gram–Schmidt or other bases are needed. The work also provides a framework to disentangle bulk and boundary degrees of freedom, showing that for heavy (giant) probes the boundary contributions are exponentially suppressed, thereby validating Schur-polynomial operators as localized probes of the dual geometry in the SU(N) theory.

Abstract

Certain correlation functions are computed exactly in the zero coupling limit of N=4 super Yang-Mills theory with gauge group SU(N). A set of linearly independent operators that are in one-to-one correspondence with the half-BPS representations of the SU(N) gauge theory is given. These results are used to study giant gravitons in the dual AdS5xS5 string theory. In addition, for the U(N) gauge theory, we explain how to systematically identify contributions coming from the boundary degrees of freedom.

Giant Graviton Correlators from Dual SU(N) super Yang-Mills Theory

TL;DR

This work extends the Schur-polynomial approach to exact correlators from U(N) to SU(N) N=4 SYM at zero coupling, constructing a linearly independent basis of half-BPS operators built from the traceless field and establishing a finite-N dictionary with giant gravitons in AdS5×S5. By introducing a ghost-field subtraction and a differential operator that removes a box from Young diagrams, the authors map SU(N) correlators to the known U(N) results and identify the null space of as the space of independent SU(N) BPS operators, with explicit reduction rules and a constructive algorithm. They analyze large-N and finite-N limits, showing that at large the totally symmetric and antisymmetric sectors remain approximately orthogonal for heavy giant gravitons, while for finite N significant mixing persists and Gram–Schmidt or other bases are needed. The work also provides a framework to disentangle bulk and boundary degrees of freedom, showing that for heavy (giant) probes the boundary contributions are exponentially suppressed, thereby validating Schur-polynomial operators as localized probes of the dual geometry in the SU(N) theory.

Abstract

Certain correlation functions are computed exactly in the zero coupling limit of N=4 super Yang-Mills theory with gauge group SU(N). A set of linearly independent operators that are in one-to-one correspondence with the half-BPS representations of the SU(N) gauge theory is given. These results are used to study giant gravitons in the dual AdS5xS5 string theory. In addition, for the U(N) gauge theory, we explain how to systematically identify contributions coming from the boundary degrees of freedom.

Paper Structure

This paper contains 17 sections, 53 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review of $U(N)$ Technology
  3. Exact Correlators
  4. Giant Gravitons
  5. The Schur Polynomial/D-brane Correspondence
  6. Technology for $SU(N)$
  7. A First Look
  8. Recycling $U(N)$ Results
  9. Constraints
  10. A Linearly Independent Basis of $SU(N)$ BPS Operators
  11. Correlators of traces in the $SU(N)$ theory
  12. Giant Gravitons
  13. Large $N$
  14. Finite $N$
  15. Giant Gravitons as probes of the Dual Geometry
  16. ...and 2 more sections

Figures (3)

  • Figure 1: A plot showing $\log\left|{{\cal O}\over {\cal N}_S{\cal N}_A}\right|$ as a function of the number of boxes $n$, for $N=20$.
  • Figure 2: This plot shows the components in the operator dual to a sphere giant. $\log\left|\alpha_i\right|$ is plotted as a function of $i$, for $N=20$ and $n=20$.
  • Figure 3: This plot shows the components in the operator dual to an AdS giant. $\log\left|\alpha_i\right|$ is plotted as a function of $i$, for $N=20$ and $n=20$.