T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve

Abstract

We propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of $gl(K_1,K_2|M)$ superalgebra. The formalism is inspired by the quantum fusion procedure known from the integrable spin chains and is based on exterior forms of Baxter-like Q-functions. We find a few new interesting relations among the exterior forms of Q-functions and reproduce, using our new formalism, the Wronskian determinant solutions of Hirota equations known in the literature. Then we generalize this construction to the twisted Q-functions and demonstrate the subtleties of untwisting procedure on the examples of rational quantum spin chains with twisted boundary conditions. Using these observations, we generalize the recently discovered, in our paper with N. Gromov, AdS/CFT Quantum Spectral Curve for exact planar spectrum of AdS/CFT duality to the case of arbitrary Cartan twisting of AdS${}_5\times$S${}^5$ string sigma model. Finally, we successfully probe this formalism by reproducing the energy of gamma-twisted BMN vacuum at single-wrapping orders of weak coupling expansion.

122 pages, 14 figures

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• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
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• Geometric aspects of the ODE/IM correspondence
• Hexagons and Correlators in the Fishnet Theory
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Geometric Algebra and Algebraic Geometry of Loop and Potts Models
• Inflation from periodic extra dimensions
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• Colour-Twist Operators I: Spectrum and Wave Functions
• 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
• $(SL(N),q)$-opers, the $q$-Langlands correspondence, and quantum/classical duality
• The Loom for General Fishnet CFTs
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Gravitational Waves from Axion Monodromy
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Chaotic spin chains in AdS/CFT
• Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
• ABJM quantum spectral curve and Mellin transform
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Toroidal q-Opers
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• Extended systems of Baxter Q-functions and fused flags I: simply-laced case
• Integrability treatment of AdS/CFT orbifolds
• N=4 SYM Quantum Spectral Curve in BFKL regime
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• Evaluation of the operatorial Q-system for non-compact super spin chains
• Quantum groups and functional relations for arbitrary rank
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
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• The full spectrum of AdS${}_5$/CFT${}_4$ II: Weak coupling expansion via the quantum spectral curve
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• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• Finite-size Effect for Dyonic Giant Magnons in $C{P}_{\beta }^3$
• Comments on the slope function
• Spin-$s$ $Q$-systems: Twist and Open Boundaries
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve