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Conformal Bootstrap in the Regge Limit

Daliang Li, David Meltzer, David Poland

TL;DR

The paper develops analytic conformal bootstrap methods in the Regge limit for large-N CFTs with a large gap, showing that, in the gravity regime, spin-2 exchanges reproduce AdS bulk phase shifts and that chaos constraints enforce negative anomalous dimensions and OPE corrections. It extends the analysis to current–scalar correlators to recover Einstein–Maxwell–type structures and establishes bounds on three-point functions. Pushing beyond the gravity limit, the authors resum the leading Regge trajectory, derive associated anomalous dimensions and OPE-correction formulas, and argue that crossing symmetry necessitates an infinite tower of new single-trace operators in the crossed channel, consistent with string-like bulk dynamics. The work thus links bulk causality and unitarity to boundary Regge data, providing a concrete framework for understanding universality of Einstein gravity and the onset of stringy behavior in AdS/CFT via the Regge limit.

Abstract

We analytically solve the conformal bootstrap equations in the Regge limit for large N conformal field theories. For theories with a parametrically large gap, the amplitude is dominated by spin-2 exchanges and we show how the crossing equations naturally lead to the construction of AdS exchange Witten diagrams. We also show how this is encoded in the anomalous dimensions of double-trace operators of large spin and large twist. We use the chaos bound to prove that the anomalous dimensions are negative. Extending these results to correlators containing two scalars and two conserved currents, we show how to reproduce the CEMZ constraint that the three-point function between two currents and one stress tensor only contains the structure given by Einstein-Maxwell theory in AdS, up to small corrections. Finally, we consider the case where operators of unbounded spin contribute to the Regge amplitude, whose net effect is captured by summing the leading Regge trajectory. We compute the resulting anomalous dimensions and corrections to OPE coefficients in the crossed channel and use the chaos bound to show that both are negative.

Conformal Bootstrap in the Regge Limit

TL;DR

The paper develops analytic conformal bootstrap methods in the Regge limit for large-N CFTs with a large gap, showing that, in the gravity regime, spin-2 exchanges reproduce AdS bulk phase shifts and that chaos constraints enforce negative anomalous dimensions and OPE corrections. It extends the analysis to current–scalar correlators to recover Einstein–Maxwell–type structures and establishes bounds on three-point functions. Pushing beyond the gravity limit, the authors resum the leading Regge trajectory, derive associated anomalous dimensions and OPE-correction formulas, and argue that crossing symmetry necessitates an infinite tower of new single-trace operators in the crossed channel, consistent with string-like bulk dynamics. The work thus links bulk causality and unitarity to boundary Regge data, providing a concrete framework for understanding universality of Einstein gravity and the onset of stringy behavior in AdS/CFT via the Regge limit.

Abstract

We analytically solve the conformal bootstrap equations in the Regge limit for large N conformal field theories. For theories with a parametrically large gap, the amplitude is dominated by spin-2 exchanges and we show how the crossing equations naturally lead to the construction of AdS exchange Witten diagrams. We also show how this is encoded in the anomalous dimensions of double-trace operators of large spin and large twist. We use the chaos bound to prove that the anomalous dimensions are negative. Extending these results to correlators containing two scalars and two conserved currents, we show how to reproduce the CEMZ constraint that the three-point function between two currents and one stress tensor only contains the structure given by Einstein-Maxwell theory in AdS, up to small corrections. Finally, we consider the case where operators of unbounded spin contribute to the Regge amplitude, whose net effect is captured by summing the leading Regge trajectory. We compute the resulting anomalous dimensions and corrections to OPE coefficients in the crossed channel and use the chaos bound to show that both are negative.

Paper Structure

This paper contains 23 sections, 127 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Summary of Results
  3. Regge Limit in Large N CFTs
  4. Bootstrap in the Gravity Limit
  5. Identity Matching
  6. Single-Trace Matching
  7. Current-Scalar Correlators
  8. Negativity of Anomalous Dimensions
  9. Beyond the Gravity Limit
  10. The Leading Regge Trajectory
  11. Crossing Symmetry
  12. Examples
  13. Chaos Bounds and Eikonalization
  14. New States
  15. Discussion
  16. ...and 8 more sections

Figures (1)

  • Figure 1: The bounds on the coefficient $a_{2}$ of $\langle J_{\mu}J_{\nu}T_{\rho\sigma}\rangle$ derived from the negativity of the anomalous dimensions in the Regge limit $\gamma^{(T)}_{h,\bar{h}}\le0$ as a function of $\bar{h}/h$.