The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system

Abstract

With the formulation of the quantum spectral curve for the AdS5/CFT4 integrable system, it became potentially possible to compute its full spectrum with high efficiency. This is the first paper in a series devoted to the explicit design of such computations, with no restrictions to particular subsectors being imposed. We revisit the representation theoretical classification of possible states in the spectrum and map the symmetry multiplets to solutions of the quantum spectral curve at zero coupling. To this end it is practical to introduce a generalisation of Young diagrams to the case of non-compact representations and define algebraic Q-systems directly on these diagrams. Furthermore, we propose an algorithm to explicitly solve such Q-systems that circumvents the traditional usage of Bethe equations and simplifies the computation effort. For example, our algorithm quickly obtains explicit analytic results for all 495 multiplets that accommodate single-trace operators in N=4 SYM with classical conformal dimension up to 13/2. We plan to use these results as the seed for solving the quantum spectral curve perturbatively to high loop orders in the next paper of the series.

53 pages; v2: minor improvements; v3: published version, details added

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Cited by in corpus (19)

• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame
• Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• A review of the AdS/CFT Quantum Spectral Curve
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Q-systems with boundary parameters
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• ABJM quantum spectral curve and Mellin transform
• Regge spectroscopy of higher twist states in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• The $A_m^{(1)}$ Q-system
• Integrability treatment of AdS/CFT orbifolds
• Oscillator approach to quantization of $Ad{S}_5\times S^5$ superparticle in twistor formulation
• On analytical perturbative solution of ABJM quantum spectral curve
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Spin-$s$ $Q$-systems: Twist and Open Boundaries