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**1 - 4**of**4**### Abelian Varieties, RCFTs, Attractors, and Hitchin Functional in Two Dimensions

"... We consider a generating function for the number of conformal blocks in rational conformal field theories with an even central charge c on a genus g Riemann surface. It defines an entropy functional on the moduli space of conformal field theories and is captured by the gauged WZW model whose target ..."

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We consider a generating function for the number of conformal blocks in rational conformal field theories with an even central charge c on a genus g Riemann surface. It defines an entropy functional on the moduli space of conformal field theories and is captured by the gauged WZW model whose target space is an abelian variety. We study a special coupling of this theory to two-dimensional gravity. When c = 2g, the coupling is non-trivial due to the gravitational instantons, and the action of the theory can be interpreted as a twodimensional analog of the Hitchin functional for Calabi-Yau manifolds. This gives rise to the effective action on the moduli space of Riemann surfaces, whose critical points are attractive and correspond to Jacobian varieties admitting complex multiplication. The theory that we describe can be viewed as a dimensional reduction of topological M-theory.

### hep-th/0611327 Computing Amplitudes in topological M-theory

, 2006

"... We define a topological quantum membrane theory on a seven dimensional manifold of G2 holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is CY3 ×S 1 quantum amplitudes of non-local obs ..."

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We define a topological quantum membrane theory on a seven dimensional manifold of G2 holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is CY3 ×S 1 quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. In particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in Topological strings on Calabi-Yau (CY) manifolds describe a certain sector of the superstrings. In particular, various BPS quantities in superstrings can be computed using the topological version. There are two different topological string models on CY, A- and B-models, which can be obtained from the physical model through a topological twist [33].

### Black Holes, Entropy Functionals, and Topological Strings

, 2007

"... This thesis is devoted to study of the connection between extremal black holes and topological strings. Important ingredient of this connection is the relation between Hartle-Hawking wave function associated to black holes and topological string partition function. This leads to a natural entropy fu ..."

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This thesis is devoted to study of the connection between extremal black holes and topological strings. Important ingredient of this connection is the relation between Hartle-Hawking wave function associated to black holes and topological string partition function. This leads to a natural entropy functional defined on the moduli space of string compactifications. We discuss several examples of such entropy functionals. We start by proposing a wave function for scalar metric fluctuations on S3 embedded in a Calabi-Yau. This problem maps to a study of non-critical bosonic string propagating on a circle at the self-dual radius. This can be viewed as a stringy toy model for a quantum cosmology. Then we formulate an entropy functional on the moduli space of Calabi-Yau compactifications. We find that the maximization of the entropy is correlated with the appearance of asymptotic freedom in the effective field theory. The points where the entropy is maximized correspond to points on