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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, A Marrani, E Orazi, A Shcherbakov
- 2008

We consider the Attractor Equations of particular N = 2, d = 4 supergravity models whose vector multiplets' scalar manifold is endowed with homogeneous symmetric cubic special Kähler geometry, namely of the so-called st 2 and stu models. In this framework, we derive explicit expressions for the critical moduli corresponding to non-BPS attractors with… (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
- 2009

Proceeding from nonlinear realizations of (super)conformal symmetries, we explicitly demonstrate that adding the harmonic oscillator potential to the action of conformal mechanics does not break these symmetries but modifies the transformation properties of the (super)fields. We also analyze the possibility to introduce potentials in N = 4 supersymmetric… (More)

- Stefano Bellucci, Sergio Ferrara, Murat Günaydin, Alessio Marrani
- 2006

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)