Triangle Seminars

Abstract:
Recently, Ooguri, Strominger and Vafa have proposed to
identify the macroscopic Bekenstein-Hawking-Wald entropy of extremal
charged Black Holes in type II string compactified on a Calabi-Yau
threefold, with the all order microscopic entropy in a specific
statistical ensemble. We present a test of this conjecture in the
case of 'small' black holes (which have zero Bekenstein-Hawking entropy
at tree level, but obtain a non-zero entropy after quantum corrections)
using heterotic / type II duality. We find a remarkable agreement to all
orders in a class of N=2 and N=4 compactifications. Nevertheless, the
OSV proposal misses non-perturbative corrections which are computable
on the heterotic side. We comment on possible improvements of this
proposal.

Abstract:
We analyze the continuum limit of the integrable 3 3 times bar(3) times 3 times bar(3)... sl(2/1) superspin chain. We discover profoundly new
features, including a continuous spectrum of conformal weights, whose
numerical evidence is infinite degeneracies of the scaled gaps in the
thermodynamic limit. This indicates that the corresponding conformal field
theory has a non compact target space (even though our lattice model
involves only finite dimensional representations). We argue that our
results are compatible with this theory being the level k=3D1, SU(2/1) WZW
model (whose precise definition requires some care). In doing so, we
establish several new results for this model. With regard to potential
applications to the spin quantum Hall effect, we conclude that the
continuum limit of the 3 times bar (3) times 3 times bar(3)... sl(2,1)
integrable superspin chain is not the same as (and is in fact very
different from) the continuum limit of the corresponding chain with
two-superspin interactions only, which is known to be a model for the spin
quantum Hall effect. The study of possible RG flows between the two
theories is left for further study.