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{s}mathfrak{l}left(2Big|1right) sector.New weak coupling results for conformal dimensions of operators outside the mathfrak{s}mathfrak{l}(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 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 AdS4 × CP3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.
Highlights
The results of this paper are an important test of the Quantum Spectral Curve (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 N = 6 superconformal Chern-Simons (SCS) and type IIA superstring theory on AdS4 × CP 3
Triggered by the works [4, 5], the spectrum of the theory was studied by adopting very powerful integrable model techniques, such as the Bethe Ansatz (BA) [4, 6, 7], the Thermodynamic Bethe Ansatz (TBA) [8–10] and closely related sets of functional relations [11–14] which allowed to recast the spectral problem into a finite dimensional non-linear RiemannHilbert problem, the Quantum Spectral Curve (QSC) [15, 16]
As an attachment to the arXiv submission, we provide a simple Mathematica implementation of the numerical method for the subsector of parity-even operators; more general versions of the code are available upon request
Summary
We review the basics of the QSC formulation presented in [54, 55]. It involves a large number of Q functions, depending on the spectral parameter which we denote as u. Which allow us to write Pab(u) ∼ uNa+Nb , Qij (u) ∼ uNi+Nj , Qa|i(u) ∼ uNa+Ni. upon a specific choice of basis for the solutions of the system (2.14), the Q functions and their analytic continuations fulfil a further set of constraining equations, the so-called gluing conditions, which were derived in [55] for the ABJM model in the case of half-integer spin and real values of h. Upon a specific choice of basis for the solutions of the system (2.14), the Q functions and their analytic continuations fulfil a further set of constraining equations, the so-called gluing conditions, which were derived in [55] for the ABJM model in the case of half-integer spin and real values of h These equations are the main ingredient of the numerical algorithm.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
