SL(2;R)/U(1) Supercoset and Elliptic Genera of Noncompact CalabiYau Manifolds
Abstract
We first discuss the relationship between the SL(2;Bbb R)/U(1) supercoset and Script N = 2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;Bbb R)/U(1) theory correspond exactly to those massless representations of Script N = 2 Liouville theory which are closed under modular transformations and studied in our previous work [18]. It is known that toroidal partition functions of SL(2;Bbb R)/U(1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the spacetime volume and is divergent in the infinitevolume limit while the part of discrete representations is volumeindependent. In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2;Bbb R)/U(1), we compute elliptic genera for various noncompact spacetimes such as the conifold, ALE spaces, CalabiYau 3folds with A_{n} singularities etc. We find that these elliptic genera in general have a complex modular property and are not Jacobi forms as opposed to the cases of compact CalabiYau manifolds.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2004
 DOI:
 10.1088/11266708/2004/05/014
 arXiv:
 arXiv:hepth/0403193
 Bibcode:
 2004JHEP...05..014E
 Keywords:

 Superstrings and Heterotic Strings Superstring Vacua Conformal Field Models in String Theory Black Holes in String Theory;
 High Energy Physics  Theory
 EPrint:
 39 pages, no figure