Non-Linear Integral Equations for the SL(2,R)/U(1) black hole sigma model

Abstract

It was previously established that the critical staggered XXZ spin chain provides a lattice regularization of the black hole CFT. We reconsider the continuum limit of this spin chain with the exact method of non-linear integral equations (NLIEs), paying particular attention to the effects of a singular integration kernel. With the help of the NLIEs, we rederive the continuous black hole spectrum, but also numerically match the density of states of the spin chain with that of the CFT, which is a new result. Finally, we briefly discuss the integrable structure of the black hole CFT and the identification of its massive integrable perturbation on the lattice.

36 pages, 12 figures

References in corpus (7)

• The ODE/IM Correspondence
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• Integrability of a family of quantum field theories related to sigma models
• Continuum Limit of gl(M/N) Spin Chains

Cited by in corpus (25)

• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• The Staggered Six-Vertex Model: Conformal Invariance and Corrections to Scaling
• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• On the scaling behaviour of the alternating spin chain
• Lattice regularisation of a non-compact boundary conformal field theory
• The Floquet Baxterisation
• Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions
• Integrable boundary conditions for staggered vertex models
• An Ising-type formulation of the six-vertex model
• Finite-size effects in the spectrum of the $OSp(3|2)$ superspin chain
• Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain
• Spectral flow for an integrable staggered superspin chain
• Non compact continuum limit of two coupled Potts models
• On the scaling behaviour of an integrable spin chain with ${\mathcal{Z}}_r$ symmetry
• On the critical behaviour of the integrable $q$-deformed $OSp(3|2)$ superspin chain
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections
• Spin chains with boundary inhomogeneities
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin-$\frac{1}{2}$ chain
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum