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Boundary bound states and integrable Wilson loops in ABJM

Diego H. Correa, Maximiliano G. Ferro, Victor I. Giraldo-Rivera, Nicolas A. Ivanovich

TL;DR

The paper addresses the problem of determining integrable boundary scattering in ABJM with a boundary degree of freedom. It combines the residual $SU(1|2)$ symmetry with a boundary Yangian remnant to construct a family of integrable reflection matrices, and shows that a concrete ABJM Wilson loop realization yields a boundary bound-state interpretation for the boundary degree of freedom. A two-parameter family constrained by the twisted boundary Yangian collapses to a physical parameter $ kappa$, with the ABJM specialization $ kappa=1+ frac{i}{x_B}$ reproducing the expected boundary bound-state energy; this is confirmed by perturbative weak-coupling computations in open spin chains. The results unify symmetry-based bootstrap and boundary bound-state approaches, provide explicit all-loop reflection matrices, and offer a route to explore holographic duals and finite-size effects in ABJM line defects.

Abstract

We derive an integrable reflection matrix for the scattering of excitations from a boundary with a degree of freedom when the reflection process preserves an $SU(1|2)$ symmetry. As this residual symmetry is not sufficient to fully determine the reflection matrix, we use the boundary remnant of the Yangian symmetry invariance and obtain a family of integrable solutions. A concrete realization of this setup is found when studying insertions in the 1/2 BPS Wilson loop in ABJM theory. The boundary degree of freedom appears as a boundary bound state due to poles in the dressing phase of the reflection matrix. We also compare our results with those obtained from the boundary bound state bootstrap procedure. The ABJM Wilson loop example enables us to perform perturbative verifications of our results.

Boundary bound states and integrable Wilson loops in ABJM

TL;DR

The paper addresses the problem of determining integrable boundary scattering in ABJM with a boundary degree of freedom. It combines the residual symmetry with a boundary Yangian remnant to construct a family of integrable reflection matrices, and shows that a concrete ABJM Wilson loop realization yields a boundary bound-state interpretation for the boundary degree of freedom. A two-parameter family constrained by the twisted boundary Yangian collapses to a physical parameter , with the ABJM specialization reproducing the expected boundary bound-state energy; this is confirmed by perturbative weak-coupling computations in open spin chains. The results unify symmetry-based bootstrap and boundary bound-state approaches, provide explicit all-loop reflection matrices, and offer a route to explore holographic duals and finite-size effects in ABJM line defects.

Abstract

We derive an integrable reflection matrix for the scattering of excitations from a boundary with a degree of freedom when the reflection process preserves an symmetry. As this residual symmetry is not sufficient to fully determine the reflection matrix, we use the boundary remnant of the Yangian symmetry invariance and obtain a family of integrable solutions. A concrete realization of this setup is found when studying insertions in the 1/2 BPS Wilson loop in ABJM theory. The boundary degree of freedom appears as a boundary bound state due to poles in the dressing phase of the reflection matrix. We also compare our results with those obtained from the boundary bound state bootstrap procedure. The ABJM Wilson loop example enables us to perform perturbative verifications of our results.
Paper Structure (11 sections, 101 equations, 3 figures)

This paper contains 11 sections, 101 equations, 3 figures.

Table of Contents

  1. Introduction
  2. $SU(1|2)$ integrable boundaries
  3. Reflection from a singlet boundary
  4. Reflection from a boundary with a degree of freedom
  5. Boundary Yangian symmetry
  6. Weak coupling verifications
  7. Discussion
  8. ABJM conventions
  9. Supersymmetric Wilson loops in ABJM
  10. Scattering matrix
  11. Functions in the reflection matrix solution

Figures (3)

  • Figure 1: Boundary bound state bootstrap condition.
  • Figure 2: Insertion of two constant primary operators. They work as DCOs, transforming the connection from $\mathcal{L}$ to $\tilde{\mathcal{L}}$ and back, where the change is simply a sign in the off-diagonal fermions.
  • Figure 3: Boundary bound state bootstrap with higher rank representations.