On the Exact Interpolating Function in ABJ Theory

Abstract

Based on the recent indications of integrability in the planar ABJ model, we conjecture an exact expression for the interpolating function h(λ_1,λ_2) in this theory. Our conjecture is based on the observation that the integrability structure of the ABJM theory given by its Quantum Spectral Curve is very rigid and does not allow for a simple consistent modification. Under this assumption, we revised the previous comparison of localization results and exact all loop integrability calculations done for the ABJM theory by one of the authors and Grigory Sizov, fixing h(λ_1,λ_2). We checked our conjecture against various weak coupling expansions, at strong coupling and also demonstrated its invariance under the Seiberg-like duality. This match also gives further support to the integrability of the model. If our conjecture is correct, it extends all the available integrability results in the ABJM model to the ABJ model.

13 pages, 1 figure

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Algebraic structures on parallel M2-branes
• Fractional M2-branes
• The Bethe ansatz for superconformal Chern-Simons
• The all loop AdS4/CFT3 Bethe ansatz
• The Quantum Spectral Curve of the ABJM theory
• Two loop integrability for Chern-Simons theories with N=6 supersymmetry
• Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories
• Exact Bremsstrahlung and Effective Couplings
• Two-loop cusp anomaly in ABJM at strong coupling

Cited by in corpus (19)

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• Towards the exact Bremsstrahlung function of ABJM theory
• Exact Bremsstrahlung functions in ABJM theory
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• A review of the AdS/CFT Quantum Spectral Curve
• Integrated negative geometries in ABJM
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• Penrose limits and spin chains in the GJV/CS-SYM duality
• ABJM quantum spectral curve and Mellin transform
• ABJM $\theta$-Bremsstrahlung at four loops and beyond
• Y-system for $\gamma$-deformed ABJM Theory
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Analytic continuation of harmonic sums with purely imaginary indices near the integer values
• Subleading Corrections in N=3 Gaiotto-Tomasiello Theory