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Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus inExpand
Knot Invariants and Topological Strings
We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of aExpand
Large N Field Theories, String Theory and Gravity
We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal fieldExpand
Wilson loops and minimal surfaces
The AdS-CFT correspondence suggests that the Wilson loop of the large N gauge theory with $\mathcal{N}=4$ supersymmetry in four dimensions is described by a minimal surface inExpand
Black hole attractors and the topological string
A simple relationship of the form ZBH = |Ztop|2 is conjectured, where ZBH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type IIExpand
Notes on the K3 Surface and the Mathieu Group M 24
We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M 24. The reason remains aExpand
Holomorphic anomalies in topological field theories
We study the stringy genus-one partition function of N = 2 SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limitExpand
Holography and defect conformal field theories
We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5Expand
On the Geometry of the String Landscape and the Swampland
We make a number of conjectures about the geometry of continuous moduli parameterizing the string landscape. In particular we conjecture that such moduli are always given by expectation value ofExpand
Two-dimensional black hole and singularities of CY manifolds
We study the degenerating limits of superconformal theories for compactifications on singular K3 and Calabi-Yau threefolds. We find that in both cases the degeneration involves creating an EuclideanExpand