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Free Large N Supersymmetric Yang-Mills Theory as a String Theory

Parviz Haggi-Mani, Bo Sundborg

TL;DR

The authors investigate the conjectured AdS/CFT duality in the zero-tension limit by analyzing the spectrum and correlation structure of free N=4 SYM, treating single- and multi-trace operators as string bits. They show that operator dimensions remain N-independent at $\lambda=0$, while 1/N effects mix states and yield a nontrivial interacting theory with features resembling string interactions, including a CFT realization of crossing symmetry and a duality structure among amplitudes. The work reveals a rich set of marginal/relevant primaries and unexpectedly massless spin-2 candidates, suggesting a complex landscape of backgrounds even in the tensionless regime. Overall, the paper provides indirect but concrete evidence that free gauge theory data can define a consistent, interacting string theory in AdS5×S5, via OPE-driven vertices and duality relations.

Abstract

The strong version of Maldacena's AdS/CFT conjecture implies that the large N expansion of free N=4 super-YM theory describes an interacting string theory in the extreme limit of high spacetime curvature relative to the string length. String states may then be understood as composed of SYM string bits. We investigate part of the low-lying spectrum of the tensionless (zero-coupling) limit and find a large number of states that are not present in the infinite tension (strong-coupling) limit, notably several massless spin two particles. We observe that all conformal dimensions are N-independent in the free SYM theory, implying that masses in the corresponding string theory are unchanged by string interactions. Degenerate string states do however mix in the interacting string theory because of the complicated N-dependence of general CFT two-point functions. Finally we verify the CFT crossing symmetry, which corresponds to the dual properties of string scattering amplitudes. This means that the SYM operator correlation functions define AdS dual models analogous to the Minkowski dual models that gave rise to string theory.

Free Large N Supersymmetric Yang-Mills Theory as a String Theory

TL;DR

The authors investigate the conjectured AdS/CFT duality in the zero-tension limit by analyzing the spectrum and correlation structure of free N=4 SYM, treating single- and multi-trace operators as string bits. They show that operator dimensions remain N-independent at , while 1/N effects mix states and yield a nontrivial interacting theory with features resembling string interactions, including a CFT realization of crossing symmetry and a duality structure among amplitudes. The work reveals a rich set of marginal/relevant primaries and unexpectedly massless spin-2 candidates, suggesting a complex landscape of backgrounds even in the tensionless regime. Overall, the paper provides indirect but concrete evidence that free gauge theory data can define a consistent, interacting string theory in AdS5×S5, via OPE-driven vertices and duality relations.

Abstract

The strong version of Maldacena's AdS/CFT conjecture implies that the large N expansion of free N=4 super-YM theory describes an interacting string theory in the extreme limit of high spacetime curvature relative to the string length. String states may then be understood as composed of SYM string bits. We investigate part of the low-lying spectrum of the tensionless (zero-coupling) limit and find a large number of states that are not present in the infinite tension (strong-coupling) limit, notably several massless spin two particles. We observe that all conformal dimensions are N-independent in the free SYM theory, implying that masses in the corresponding string theory are unchanged by string interactions. Degenerate string states do however mix in the interacting string theory because of the complicated N-dependence of general CFT two-point functions. Finally we verify the CFT crossing symmetry, which corresponds to the dual properties of string scattering amplitudes. This means that the SYM operator correlation functions define AdS dual models analogous to the Minkowski dual models that gave rise to string theory.

Paper Structure

This paper contains 5 sections, 21 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. States and propagators
  3. Operator products and string vertices
  4. CFT crossing symmetry and string amplitude duality
  5. Discussion

Figures (3)

  • Figure 1: A schematic description of a four-point function as a tetrahedron. To resolve the $N$-dependence the order of the fields in each operator also has to be taken into account.
  • Figure 2: Leading diagrams contributing to the correlator (\ref{['eq:non-trivial']}).
  • Figure 3: Diagrams showing two possible expansions of a six-point functoion given in eq. \ref{['eq:six-point']}.