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Massless S matrices for AdS3/CFT2

Sergey Frolov, Alessandro Sfondrini

TL;DR

<3-5 sentence high-level summary>Massless excitations in AdS$_3$/CFT$_2$ within the lightcone gauge are non-relativistic and split into distinct chiral and antichiral representations, a split that crucially impacts the analytic structure of the two-particle S matrix. The work develops a detailed Hopf-algebraic framework for one- and two-particle representations, identifies the four massless-massless S-matrix blocks, and derives their dressing-factor constraints from physical unitarity, braiding, parity, time reversal, and crossing symmetry, all while carefully treating the non-analyticities at $p=0$ via a dual chiral/antichiral parametrisation. It further analyzes the implications for mixed-mass sectors and establishes the necessary foundation for a consistent Bethe-Yang treatment, including the mirror model, where the same chiral split governs the kinematics and representations. The results provide a robust, symmetry-driven structure for massless AdS$_3$/CFT$_2$ scattering and set the stage for refined proposals of the dressing factors and finite-volume spectra.

Abstract

The AdS3/CFT2 correspondence features massless non-relativistic modes on the string worldsheet in lightcone gauge. We study in detail these excitations and highlight how they naturally split between chiral (left-moving) and anti-chiral (right-moving) representations. In light of this split we discuss the constraints on the two-particle worldsheet S matrix imposed by braiding and physical unitarity, parity, time-reversal, and crossing invariance. We also comment on the implication of this split in the mirror kinematics.

Massless S matrices for AdS3/CFT2

TL;DR

<3-5 sentence high-level summary>Massless excitations in AdS/CFT within the lightcone gauge are non-relativistic and split into distinct chiral and antichiral representations, a split that crucially impacts the analytic structure of the two-particle S matrix. The work develops a detailed Hopf-algebraic framework for one- and two-particle representations, identifies the four massless-massless S-matrix blocks, and derives their dressing-factor constraints from physical unitarity, braiding, parity, time reversal, and crossing symmetry, all while carefully treating the non-analyticities at via a dual chiral/antichiral parametrisation. It further analyzes the implications for mixed-mass sectors and establishes the necessary foundation for a consistent Bethe-Yang treatment, including the mirror model, where the same chiral split governs the kinematics and representations. The results provide a robust, symmetry-driven structure for massless AdS/CFT scattering and set the stage for refined proposals of the dressing factors and finite-volume spectra.

Abstract

The AdS3/CFT2 correspondence features massless non-relativistic modes on the string worldsheet in lightcone gauge. We study in detail these excitations and highlight how they naturally split between chiral (left-moving) and anti-chiral (right-moving) representations. In light of this split we discuss the constraints on the two-particle worldsheet S matrix imposed by braiding and physical unitarity, parity, time-reversal, and crossing invariance. We also comment on the implication of this split in the mirror kinematics.
Paper Structure (43 sections, 129 equations, 1 figure)

This paper contains 43 sections, 129 equations, 1 figure.

Table of Contents

  1. Introduction and main results
  2. The symmetry algebra and its representations
  3. One-particle (short) representations
  4. Physical value of representation parameters
  5. Two-particle representation
  6. Momentum periodicity of the two-particle representation
  7. Chiral and antichiral particles
  8. Fundamental domain
  9. Rapidity parametrisation
  10. Massless representation, one particle
  11. Antichiral case
  12. Chiral case
  13. Automorphism.
  14. Matrix representation and change of basis.
  15. Two-particle representation
  16. ...and 28 more sections

Figures (1)

  • Figure 1: kinematics of massive and massless modes in $AdS_3\times S^3\times T^4$. On the left, we plot the dispersion relation $E(p)$ for massive particles (blue dashed line) and for massless ones (red solid line); the latter dispersion has cusps at $p=0\,$mod$\,2\pi$. On the right, we do the same for the group velocity $v(p)$, which form for massless particles is discontinuous $p=0\,$mod $2\pi$.