Lattice regularisation of a noncompact boundary conformal field theory
Abstract
Noncompact 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 noncompact boundary CFTs and the corresponding Dbrane constructions.The present paper follows a series of previous works on a &Z;_{2}staggered XXZ spin chain, whose continuum limit is known to be a noncompact 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 noncompact 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 noncompact boundary conditions to the previously studied compact ones.
 Publication:

Journal of High Energy Physics
 Pub Date:
 February 2021
 DOI:
 10.1007/JHEP02(2021)180
 arXiv:
 arXiv:2012.07757
 Bibcode:
 2021JHEP...02..180R
 Keywords:

 Bethe Ansatz;
 Boundary Quantum Field Theory;
 Conformal Field Theory;
 Black Holes in String Theory;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 doi:10.1007/JHEP02(2021)180