Michela Petrini

Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics

We nd new, local, non-supersymmetric conformal eld theories ob- tained by relevant deformations of the N=4 super Yang Mills theory in the large N limit. We contruct interpolating supergravity solutions that naturally represent theflowfromtheN=4super YangMills UVtheorytothese non-supersymmetric IR xed points. We also study the linearization around the N=4 superconformal point ofN=1supersymmetric, marginaldeformations. WeshowthattheygiverisetoN=1 superconformalxed points, as expected from eld-theoretical arguments.

Generalized structures of N=1 vacua

We characterize = 1 vacua of type-II theories in terms of generalized complex structure on the internal manifold M. The structure group of T(M)⊕T*(M) being SU(3) × SU(3) implies the existence of two pure spinors Φ1 and Φ2. The conditions for preserving = 1 supersymmetry turn out to be simple generalizations of equations that have appeared in the context of = 2 and topological strings. They are (d+H∧)Φ1 = 0 and (d+H∧)Φ2 = FRR. The equation for the first pure spinor implies that the internal space is a twisted generalized Calabi-Yau manifold of a hybrid complex-symplectic type, while the RR-fields serve as an integrability defect for the second.

Supersymmetric backgrounds from generalized Calabi-Yau manifolds

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form eiJ and the holomorphic form Ω. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: eiJ is closed under the action of the twisted exterior derivative in IIA theory, and similarly Ω is closed in IIB. Modulo a different action of the B–field, this means that supersymmetric SU(3)-structure manifolds are all generalized Calabi-Yau manifolds, as defined by Hitchin. An equivalent, and somewhat more conventional, description is given as a set of relations between the components of intrinsic torsions modified by the NS flux and the Clifford products of RR fluxes with pure spinors, allowing for a classification of type II supersymmetric vacua on six-manifolds. We find in particular that supersymmetric six-manifolds are always complex for IIB backgrounds while they are twisted symplectic for IIA.

The supergravity dual of N=1 super Yang–Mills theory

Abstract We find an exact, N =1 supersymmetric kink solution of 5d gauged supergravity. We associate this solution with the RG flow from N =4 super Yang–Mills theory, deformed by a relevant operator, to pure N =1 super Yang–Mills in the IR. We test this identification by computing various QFT quantities using the supergravity dual: the tension of electric and magnetic strings and the gaugino condensate. As demanded by our identification, our kink solution is a true deformation of N =4, that exhibits confinement of quarks, magnetic screening, and spontaneous chiral symmetry breaking.

T-duality, generalized geometry and non-geometric backgrounds

We discuss the action of O(d,d), and in particular T-duality, in the context of generalized geometry, focusing on the description of so-called non-geometric backgrounds. We derive local expressions for the pure spinors descibing the generalized geometry dual to an SU(3) structure background, and show that the equations for N=1 vacua are invariant under T-duality. We also propose a local generalized geometrical definition of the charges f, H, Q and R appearing in effective four-dimensional theories, using the Courant bracket. We then address certain global aspects, in particular whether the local non-geometric charges can be gauged away in, for instance, backgrounds admitting a torus action, as well as the structure of generalized parallelizable backgrounds.

A scan for new N = 1 vacua on twisted tori

We perform a systematic search for N = 1 Minkowski vacua of type II string theories on compact six–dimensional parallelizable nil– and solvmanifolds (quotients of six–dimensional nilpotent and solvable groups, respectively). Some of these manifolds have appeared in the construction of string backgrounds and are typically called twisted tori. We look for vacua directly in ten dimensions, using the a reformulation of the supersymmetry condition in the framework of generalized complex geometry. Certain algebraic criteria to establish compactness of the manifolds involved are also needed. Although the conditions for preserved N = 1 supersymmetry fit nicely in the framework of generalized complex geometry, they are notoriously hard to solve when coupled to the Bianchi identities. We find solutions in a large–volume, constant–dilaton limit. Among these, we identify those that are T–dual to backgrounds of IIB on a conformal T 6 with self–dual three–form flux, and hence conceptually not new. For all backgrounds of this type fully localized solutions can be obtained. The other new solutions need multiple intersecting sources (either orientifold planes or combinations of O–planes and D–branes) to satisfy the Bianchi identities; the full list of such new solution is given. These are so far only smeared solutions, and their localization is yet unknown. Although valid in a large–volume limit, they are the first examples of Minkowski vacua in supergravity which are not connected by any duality to a Calabi–Yau. Finally, we discuss a class of flat solvmanifolds that may lead to AdS4 vacua of type IIA strings.

The baryonic branch of Klebanov-Strassler solution: a supersymmetric family of SU(3) structure backgrounds

We exhibit a one-parameter family of regular supersymmetric solutions of type IIB theory that describes the baryonic branch of the Klebanov-Strassler (KS) theory. The solution is obtained by applying the supersymmetry conditions for SU(3)-structure manifolds to an interpolating ansatz proposed by Papadopoulos and Tseytlin. Other than at the KS point, the family does not have a conformally-Ricci-flat metric, neither it has self-dual three-form flux. By varying also the string coupling, our solution smoothly interpolates between Klebanov-Strassler and Maldacena-Nu?ez (MN). The asymptotic IR and UV are that of KS throughout the interpolating flow, except for the extremal value of the parameter where the UV solution drastically changes to MN.

Gravity duals to deformed SYM theories and generalized complex geometry

We analyze the supersymmetry conditions for a class of SU(2) structure backgrounds of Type IIB supergravity, corresponding to a specific ansatz for the supersymmetry parameters. These backgrounds are relevant for the AdS/CFT correspondence since they are suitable to describe mass deformations or beta-deformations of four-dimensional superconformal gauge theories. Using Generalized Complex Geometry we show that these geometries are characterized by a closed nowhere-vanishing vector field and a modified fundamental form which is also closed. The vector field encodes the information about the superpotential and the type of deformation - mass or beta respectively. We also show that the Pilch-Warner solution dual to a mass-deformation of = 4 Super Yang-Mills and the Lunin-Maldacena beta-deformation of the same background fall in our class of solutions.

Non-relativistic solutions of \mathcal{N} = 2 gauged supergravity

We find infinite families of supersymmetric solutions of four dimensional,

A note on string interaction on the pp-wave background

\mathcal{N} = 2