L.B. Drissi

N = 2 Supersymmetric Black Attractors in Six and Seven Dimensions

Using a quaternionic formulation of the moduli space M (IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume V 0, we study extremal N = 2 black attractors in 6D space-time and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D N = 1 hypermultiplets and the Z m central charges isotriplet of the 6D N = 2 superalgebra. We construct explicitly the special hyperKahler geometry of M (IIA/K3) and show that the SO(4)×SO(20)

RG Cascades in Hyperbolic Quiver Gauge Theories

Abstract In this paper, we provide a general classification of supersymmatric QFT 4 s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super- QFT 4 s. This includes, amongst others, its embedding in type II string on local Calabi–Yau threefolds. We give realizations of these supersymmetric QFT 4 s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non-zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made.

Black holes in type IIA string on Calabi–Yau threefolds with affine ADE geometries and q-deformed 2d quiver gauge theories

Abstract Motivated by studies on 4d black holes and q-deformed 2d Yang–Mills theory, and borrowing ideas from compact geometry of the blowing up of affine ADE singularities, we build a class of local Calabi–Yau threefolds (CY 3 ) extending the local 2-torus model O ( m ) ⊕ O ( − m ) → T 2 considered in [C. Gomez, S. Montanez, A comment on quantum distribution functions and the OSV conjecture, hep-th/0608162 ] to test OSV conjecture. We first study toric realizations of T 2 and then build a toric representation of X 3 using intersections of local Calabi–Yau threefolds O ( m ) ⊕ O ( − m − 2 ) → P 1 . We develop the 2d N = 2 linear σ -model for this class of toric CY 3 s. Then we use these local backgrounds to study partition function of 4d black holes in type IIA string theory and the underlying q-deformed 2d quiver gauge theories. We also make comments on 4d black holes obtained from D-branes wrapping cycles in O ( m ) ⊕ O ( − m − 2 ) → B k with m = ( m 1 , … , m k ) a k -dim integer vector and B k a compact complex one dimension base consisting of the intersection of k 2-spheres S i 2 with generic intersection matrix I i j . We give as well the explicit expression of the q-deformed path integral measure of the partition function of the 2d quiver gauge theory in terms of I i j . A comment on the link between our analysis and the construction of [N. Caporaso, M. Cirafici, L. Griguolo, S. Pasquetti, D. Seminara, R.J. Szabo, Topological strings, two-dimensional Yang–Mills theory and Chern–Simons theory on torus bundles, hep-th/0609129 ] is also given.

On local Calabi?Yau supermanifolds and their mirrors

We use local mirror symmetry to study a class of local Calabi?Yau supermanifolds with bosonic sub-variety Vb having a vanishing first Chern class. Solving the usual super-CY condition, requiring the equality of the total U(1) gauge charges of bosons ?b and the ghost-like fields ?f one ?bqb = ?fQf, as ?bqb = 0 and ?fQf = 0, several examples are studied and explicit results are given for local Ar supergeometries. A comment on purely fermionic super-CY manifolds corresponding to the special case where qb = 0, ?b and ?fQf = 0 is also made.

D-string fluid in conifold: II. Matrix model for D-droplets on S3and S2

Abstract Motivated by similarities between Fractional Quantum Hall (FQH) systems and aspects of topological string theory on conifold, we continue in the present paper our previous study [R. Ahl Laamara, L.B. Drissi, E.H. Saidi, D-string fluid in conifold, I: Topological gauge model, Nucl. Phys. B 743 (2006) 333–353; E.H. Saidi, Topological SL ( 2 ) gauge theory on conifold, hep-th/0601020] concerning FQH droplets on conifold. Here we focus our attention on the conifold sub-varieties S 3 and S 2 and study the non-commutative quantum dynamics of D1 branes wrapped on a circle. We give a matrix model proposal for FQH droplets of N point like particles on S 3 and S 2 with filling fraction ν = 1 k . We show that the ground state of droplets on S 3 carries an isospin j = k N ( N − 1 ) 2 and gives remarkably rise to 2 j + 1 droplets on S 2 with Cartan–Weyl charge | j z | ⩽ j .

D-string fluid in conifold, I: Topological gauge model

Abstract Motivated by similarities between quantum Hall systems a la Susskind and aspects of topological string theory on conifold as well as results obtained in [E.H. Saidi, Topological SL ( 2 ) gauge theory on conifold and noncommutative geometry, hep-th/0601020 ], we study the dynamics of D-string fluids running in deformed conifold in presence of a strong and constant RR background B-field. We first introduce the basis of D-string system in fluid approximation and then derive the holomorphic noncommutative gauge invariant field action describing its dynamics in conifold. This study may be also viewed as embedding Susskind description for Laughlin liquid in type IIB string theory. FQH systems on real manifolds R × S 2 and S 3 are shown to be recovered by restricting conifold to its Lagrangian sub-manifolds. Aspects of quantum behaviour of the string fluid are discussed.

Intersecting Black Attractors in 8D N= 1 Supergravity

Abstract We study intersecting extremal black attractors in non-chiral 8D N = 1 supergravity with moduli space SO ( 2 , N ) SO ( 2 ) × SO ( N ) × SO ( 1 , 1 ) and work out explicitly the attractor mechanism for various black p-brane configurations with the typical near horizon geometries AdS p + 2 × S m × T 6 − p − m . We also give the classification of the solutions of the attractor equations in terms of the SO ( N − k ) subgroups of SO ( 2 ) × SO ( N ) symmetry of the moduli space as well as their interpretations in terms of both heterotic string on 2-torus and its type IIA dual. Other features such as non-trivial SO ( 1 , 7 ) central charges Z μ 1 … μ p in 8D N = 1 supergravity and their connections to p-form gauge fields are also given.