Spinor construction of the c = 1/2 minimal model
Abstract
The usual spinor construction from one fermion yields four irreducible representations of the Virasoro algebra with central charge $c = 1/2$. The NeveuSchwarz (NS) sector is the direct sum of an $h = 0$ and an $h = 1/2$ module, and the Ramond (R) sector is the direct sum of two copies of an $h = 1/16$ module. In addition to the fundamental fermions, which represent a Clifford algebra, and the Virasoro operators, there are infinitely many other vertex operators, in onetoone correspondence with the vectors (states) in the NS sector. These give the NS sector the structure of a Vertex Operator SuperAlgebra, and the R sector the structure of a ${\bold Z}_2$twisted module for that VOSA. Keeping both copies of the $h = 1/16$ modules in the R sector, we can define intertwining operators in onetoone correspondence with the states in the R sector such that the usual Ising fusion rules for just three modules are replaced by a rule given by the group ${\bold Z}_4$. The main objective is to find a generalization of the VOSA JacobiCauchy identity which is satisfied by these intertwining operators. There are several novel features of this new ``Matrix'' JacobiCauchy Identity (MJCI), most of which come from the fact that correlation functions made from two intertwiners are hypergeometric functions. In order to relate and rationalize the correlation functions we use the Kummer quadratic transformation formulas, lifting the functions to a foursheeted covering, branched over the usual three poles, where the Cauchy residue theorem can be applied. The six possible poles on the cover give six terms in the MJCI. Furthermore, we organize those functions into $2\times 4$ matrices and find the $2\times 2$ (fusion and braiding) matrices which relate them at the six poles. These results for intertwiners
 Publication:

arXiv eprints
 Pub Date:
 January 1995
 arXiv:
 arXiv:hepth/9501114
 Bibcode:
 1995hep.th....1114F
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 48 pages, amstex, v2.1, uses fonts msam, msbm, no figures, tables constructed using standard TeX, so no special macros required. Final version based on referee's comments, a few technical changes. Style changed from preprint to Contemporary Math Proceedings (conmp.sty). A compressed dvi file is available via anonymous ftp as follows: ftp://math.binghamton.edu/pub/alex/minimal.dvi.Z A compressed postscript file is also available via anonymous ftp as: ftp://math.binghamton.edu/pub/alex/minimal.ps.Z