Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
Abstract
We study twodimensional nonlinear sigma models in which the target spaces are the coset supermanifolds U(n+mn)/[ U(1)× U(n+m1n)]≅ CP^{ n+m1n } (projective superspaces) and OSp(2 n+ m2 n)/OSp(2 n+ m12 n)≅ S^{2 n+ m12 n} (superspheres), n, m integers, 2⩽ m⩽2; these quantum field theories live in Hilbert spaces with indefinite inner products. These theories possess nontrivial conformallyinvariant renormalizationgroup fixed points, or in some cases, lines of fixed points. Some of the conformal fixedpoint theories can also be obtained within LandauGinzburg theories. We obtain the complete spectra (with multiplicities) of exact conformal weights of states (or corresponding local operators) in the isolated fixedpoint conformal field theories, and at one special point on each of the lines of fixed points. Although the conformal weights are rational, the conformal field theories are not, and (with one exception) do not contain the affine versions of their superalgebras in their chiral algebras. The method involves lattice models that represent the strongcoupling region, which can be mapped to loop models, and then to a Coulomb gas with modified boundary conditions. The results apply to percolation, dilute and dense polymers, and other statistical mechanics models, and also to the spin quantum Hall transition in noninteracting fermions with quenched disorder.
 Publication:

Nuclear Physics B
 Pub Date:
 October 2001
 DOI:
 10.1016/S05503213(01)003959
 arXiv:
 arXiv:hepth/0106124
 Bibcode:
 2001NuPhB.613..409R
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 21 pages, no figures, RevTex format