Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension

Abstract

We study the integrability properties of Wilson loops in the $\mathcal{N}=6$ three-dimensional Chern-Simons-matter (ABJM) theory. We begin with the construction of an open spin chain that describes the anomalous dimensions of operators inserted along the contour of a 1/2 BPS Wilson loop. Moreover, we compute the all-loop reflection matrices that govern the interaction of spin-chain excitations with the boundary, including their dressing factors, and we check them against weak- and strong-coupling results. Furthermore, we propose a $Y$-system of equations for the cusped Wilson line of ABJM, and we use it to reproduce the one-loop cusp anomalous dimension of ABJM from a leading-order finite-size correction. Finally, we write a set of BTBA equations consistent with the $Y$-system proposal.

42 pages, 1 figure; v3: simplified derivation of Y functions, appendix removed

References in corpus (21)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Giant Magnons
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• The Bethe ansatz for superconformal Chern-Simons
• On String S-matrix, Bound States and TBA
• The all loop AdS4/CFT3 Bethe ansatz
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Small deformations of supersymmetric Wilson loops and open spin-chains
• The AdS4/CFT3 algebraic curve
• The S-matrix of String Bound States
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Towards the exact Bremsstrahlung function of ABJM theory
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Twisted Bethe equations from a twisted S-matrix
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Integrated negative geometries in ABJM
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory

Cited by in corpus (6)

• Wilson-loop One-point Functions in ABJM Theory
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Interpolating Bremsstrahlung function in ABJM
• More Fermionic Supersymmetric Wilson loops in Four Dimensions
• Boundary bound states and integrable Wilson loops in ABJM
• Holographic Wilson Loop One-point Functions in ABJM Theory