On modular properties of the AdS3 CFT

WALTER H. BARON; CARMEN NÚÑEZ

PHYSICAL REVIEW D - PARTICLE AND FILDS

American Physical Society

Lugar: New York; Año: 2011 vol. 83 p. 106010 - 106033

0556-2821

We study modular properties of the AdS3 WZNW model. Although the Euclidean  partition  function is modular invariant, the characters on the Euclidean  torus are ill-defined and their  modular transformations are unknown. We reconsider  the characters defined on the Lorentzian  torus, focusing on their structure  as distributions. We find a generalized S matrix, depending on  the  sign of the  real modular parameters, which has two diagonal blocks and one off-diagonal   block, mixing discrete and continuous representations, that we fully determine.  We then explore  the relations among the modular transformations, the fusion  algebra and the boundary states. We  explicitly construct Ishibashi states for  the maximally symmetric D-branes and show that the  generalized S matrix defines  the one-point functions associated to point-like and H2 branes as  well  as  the fusion rules of the degenerate representations of SL(2,R) appearing in the  open string  spectrum of the point-like D-branes, through a generalized Verlinde  theorem.