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... of D-brane BPS states on compact and non-compact Calabi-Yau manifolds, and gave new insights on the topological strings and quantum cosmology. For a recent review and references on this subject, see =-=[21]-=-. Define a mixed partition function for a black hole with magnetic charge pI and electric potential φI by ZBH(p I , φI) = ∑ qI Ω(pI , qI) e −φIqI , (1.1) where Ω(pI , qI) represent supersymmetric blac...

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...n Table 2 have previously entered the physics literature through “magic” and extended supergravities [38, 39, 40], and their ranks through the classification of the corresponding black hole solutions =-=[41, 42, 43]-=-. Indeed, although it is logically independent of it, the present work was inspired by the black-hole/qubit correspondence [44, 45, 46, 47, 48, 49, 50, 43, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31]....

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...ges, aimed at the student preparing for research in this area, and building up to a discussion of the OSV conjecture in the last section. For excellent and recent reviews at a more advanced level see =-=[7,8]-=-. We begin in lecture 2 with the basics of Type II Calabi-Yau compactification, BPS black holes, attractors, and their CFT duals. In lecture 3 we give a brief introduction to the topological string. I...

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...roscopic descriptions of black holes in string theory. The program of including R 2 corrections in 4D supergravity has received much attention over the past few years [1,2,3,4,5,6,7] (for reviews see =-=[8,9,10]-=-). By contrast, the relevant 5D supergravity action was constructed only very recently, as the supersymmetric completion of a certain mixed gauge/gravitational Chern-Simons term [11]. The 5D theory ca...

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...ity theories defining effective theories of string theory compactifications on a six-dimensional manifold are of prime importance for the understanding of non-perturbative properties of string theory =-=[1]-=-. In particular, the derivation of BPS multi-black hole solutions within N = 2 supergravity defining bound states of the theory has permitted to explain the mismatch between the enumeration of spheric...

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...can be computed from the special geometry constraint (13). In particular, if we define the dual charges q I through then ℓA = 1 2 Q1/2 with k qI = 1 2 cIJKq J q K , (44) Q 3/2 = 1 6 cIJKq I q J q K . =-=(45)-=- The entropy is S = 2π √ Q 3 . Finding explicit expressions in terms of the charges qI requires that the equation (44) can be inverted to find q I , but this is only possible for special choices of cI...

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... at g = 0, 1 need separate treatment, in particular F0 denotes the prepotential and can be calculated from the geometry of the deformation bundle. 9More details on topological strings can be found in =-=[9, 37, 38, 39, 40, 36, 41]-=-. 10It is assumed that h2,0(Z) = 0 . 14 with αa ∈ H3(Z∗). The appropriate choice of coordinates on the moduli space of complex structures as well as the normalization of Ω̃ is determined by the geomet...

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...mensional supergravities that arise from string and M-theory, such as the N = 2 STU, N = 2 “magic”, N = 4 heterotic and N = 8 M/Type II, may all be described by a Freudenthal triple system (FTS) M(J) =-=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]-=-, where J is a cubic Jordan algebra underlying the corresponding 5D supergravity [3, 11, 12]. The corresponding continuous U-duality is given by the automorphism group Aut(M(J)), e.g. E 7(7) in the ca...