Lattice regularisation of a non-compact boundary conformal field theory

Abstract

Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such CFTs have been identified as the continuum limits of lattice models with a finite number of degrees of freedom per site. However, results have so far been restricted to the case of periodic boundary conditions, precluding the exploration via lattice models of aspects of non-compact boundary CFTs and the corresponding D-brane constructions. The present paper follows a series of previous works on a ${\mathbb{Z}}_2$-staggered XXZ spin chain, whose continuum limit is known to be a non-compact CFT related with the Euclidian black hole sigma model. By using the relationship of this spin chain with an integrable $D_2^2$ vertex model, we here identify integrable boundary conditions that lead to a continuous spectrum of boundary exponents, and thus correspond to non-compact branes. In the context of the Potts model on a square lattice, they correspond to wired boundary conditions at the physical antiferromagnetic critical point. The relations with the boundary parafermion theories are discussed as well. We are also able to identify a boundary renormalisation group flow from the non-compact boundary conditions to the previously studied compact ones.

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Cited by in corpus (13)

• 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
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• $OSp(n|2m)$ quantum chains with free boundaries
• Spin chains with boundary inhomogeneities
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• Exact solution of the quantum integrable model associated with the twisted $D_3^{(2)}$ algebra
• Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries
• Factorization identities and algebraic Bethe ansatz for $D_2^{(2)}$ models