Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling

Abstract

The Quantum Spectral Curve (QSC) equations for planar $\mathcal{N}=6$ super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the $\mathfrak{sl}(2|1)$ sector. New weak coupling results for conformal dimensions of operators outside the $\mathfrak{sl}(2)$-like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator $\text{20}$ is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between $\mathcal{N}=6$ SCS and type IIA superstring theory on $Ad{S}_4\times C{P}^3$. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

42 pages, 11 figures, Mathematica notebooks and data files containing numerical results are attached; v2: published version

References in corpus (14)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• The Bethe ansatz for superconformal Chern-Simons
• The all loop AdS4/CFT3 Bethe ansatz
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• The AdS4/CFT3 algebraic curve
• Anomalous radius shift in AdS(4)/CFT(3)
• The Quantum Spectral Curve of the ABJM theory
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Wronskian Solution for AdS/CFT Y-system
• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms

Cited by in corpus (12)

• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• A review of the AdS/CFT Quantum Spectral Curve
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• On analytical perturbative solution of ABJM quantum spectral curve
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal