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These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N = 2 supergravity and N = 1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and… (More)

- S Bellucci, P.-Y Casteill, J F Morales, C Sochichiu
- 2008

We derive the coherent state representation of the integrable spin chain Hamil-tonian with symmetry group SL(2,R). By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL(2,R)/U(1). The same sigma model is found by considering strings rotating with large angular momentum in AdS 5 × S 5. The… (More)

- S Bellucci, P.-Y Casteill, J F Morales, C Sochichiu
- 2008

We study spin models underlying the non-planar dynamics of N = 4 SYM gauge theory. In particular, we derive the non-local spin chain Hamiltonian generating dilatations in the gauge theory at leading order in g 2 YM N but exact in 1 N. States in the spin chain are characterized by a spin-configuration and a linking variable describing how sites in the chain… (More)

- S Bellucci, P Y Casteill, J F Morales, C Sochichiu
- 2008

We review the spin bit model describing anomalous dimensions of the operators of Super Yang–Mills theory. We concentrate here on the scalar sector. In the limit of large N this model coincides with integrable spin chain while at finite N it has nontrivial chain splitting and joining interaction.

- Stefano Bellucci, Sergey Krivonos
- 2008

We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to n V vector multiplets, in an asymptotically flat extremal black hole background described by a 2 (n V + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold. For the case of homogeneous… (More)

We discuss the Attractor Equations of N = 2, d = 4 supergravity in an extremal black hole background with arbitrary electric and magnetic fluxes (charges) for field-strength two-forms. The effective one-dimensional Lagrangian in the radial (evolution) variable exhibits features of a spontaneously broken supergravity theory. Indeed, non-BPS Attractor… (More)

We report on recent advances in the study of critical points of the " black hole effective potential " V BH (usually named attractors) of N = 2, d = 4 supergravity coupled to n V Abelian vector multiplets, in an asymptotically flat extremal black hole background described by 2n V + 2 dyonic charges and (complex) scalar fields which are coordinates of an n… (More)

We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY 3 s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the moduli space of such 4-dimensional compactifications, we always find two species of extremal black hole attractors,… (More)

We study the attractor equations for a quantum corrected prepotential F = t 3 + iλ, with λ ∈ R,which is the only correction which preserves the axion shift symmetry and modifies the geometry. By performing computations in the " magnetic " charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing λ). For a… (More)