Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains

Abstract

We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one can expand the analytic continuation of energies in the scaling limit around another 'pseudo-vacuum' sitting at a negative number of Bethe roots, in the same way as around the usual pseudo-vacuum. We show that this method can be used to compute the energy levels of some states of the $SL(2,\mathbb{C})$ integrable spin chain in the infinite-volume limit, and as a proof of principle recover the ground-state value previously obtained in [1] (for the case of spins $s=0,\bar{s}=-1$) by extrapolating results in small sizes. These results represent, as far as we know, the first (partial) description of the spectrum of $SL(2,\mathbb{C})$ non-compact spin chains in the thermodynamic limit.

arXiv comment50 pages

References in corpus (42)

• Quantum Inverse Scattering Method and Correlation Functions
• High energy QCD as a completely integrable model
• Baryon Distribution Amplitudes in QCD
• Integrability of three-particle evolution equations in QCD
• Precision Spectroscopy of AdS/CFT
• Logarithmic scaling in gauge/string correspondence
• Integrability in QCD and beyond
• Renormalization of twist-three operators and integrable lattice models
• High Energy Asymptotics of Multi--Colour QCD and Exactly Solvable Lattice Models
• Fine structure of spectrum of twist-three operators in QCD
• Solution of the Odderon Problem
• Integrability and WKB solution of twist-three evolution equations
• Bethe Ansatz for QCD Pomeron,
• Baxter's Q-operator for the homogeneous XXX spin chain
• Quasiclassical QCD Pomeron
• Integrability of Conformal Fishnet Theory
• Review of AdS/CFT Integrability, Chapter VI.1: Superconformal Symmetry
• Separation of variables for the quantum SL(2,R) spin chain
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum
• QCD Pomeron from AdS/CFT Quantum Spectral Curve
• Solution of the odderon problem for arbitrary conformal weights
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Integrable structures and duality in high-energy QCD
• Finite-size scaling and the toroidal partition function of the critical asymmetric six-vertex model
• High Energy QCD: Stringy Picture from Hidden Integrability
• Non-compact quantum spin chains as integrable stochastic particle processes
• On zero-remainder conditions in the Bethe ansatz
• Noncompact SL(2,R) spin chain
• Inhomogeneous Gaussian Free Field inside the interacting arctic curve
• An integrable modification of the critical Chalker-Coddington network model
• On the scaling behaviour of the alternating spin chain
• Integrable boundary conditions in the antiferromagnetic Potts model
• Noncompact Heisenberg spin magnets from high-energy QCD: III. Quasiclassical approach
• Spectral flow of non-hermitian Heisenberg spin chain with complex twist
• Algebraic Bethe ansatz
• Analytical results on the Heisenberg spin chain in a magnetic field
• Non compact continuum limit of two coupled Potts models
• Bethe Ansatz for XXX chain with negative spin
• On truncations of the Chalker-Coddington model

Cited by in corpus (1)

• KPZ fluctuations in finite volume