Generating string solutions in BTZ

Integrability of classical strings in the BTZ black hole enables the construction and study of classical string propagation in this background. We first apply the dressing method to obtain classical string solutions in the BTZ black hole. We dress time like geodesics in the BTZ black hole and obtain open string solutions which are pinned on the boundary at a single point and whose end points move on time like geodesics. These strings upon regularising their charge and spins have a dispersion relation similar to that of giant magnons. We then dress space like geodesics which start and end on the boundary of the BTZ black hole and obtain minimal surfaces which can penetrate the horizon of the black hole while being pinned at the boundary. Finally we embed the giant gluon solutions in the BTZ background in two different ways. They can be embedded as a spiral which contracts and expands touching the horizon or a spike which originates from the boundary and touches the horizon. © 2013 SISSA, Trieste, Italy.

Harmonic superspace from the AdS5 × S5 pure spinor formalism

On-shell supergravity vertex operators in an AdS 5 × S 5 background are described in the pure spinor formalism by the zero mode cohomology of a BRST operator. After expanding the pure spinor BRST operator in terms of the AdS 5 radius variable, this cohomology is computed using $ \mathcal{N}=4 $ harmonic superspace variables and explicit super-field expressions are obtained for the behavior of supergravity vertex operators near the boundary of AdS 5. © 2013 SISSA, Trieste, Italy.

Eliminating ambiguities for quantum corrections to strings moving in AdS4×CP3

We apply a physical principle, previously used to eliminate ambiguities in quantum corrections to the two-dimensional kink, to the case of spinning strings moving in AdS4×CP3, thought of as another kind of two-dimensional soliton. We find that this eliminates the ambiguities and selects the result compatible with AdS/CFT, providing a solid foundation for one of the previous calculations, which found agreement. The method can be applied to other classical string «solitons.» © 2013 World Scientific Publishing Company.

De supergravidade em Ad'S IND. 5' X 'S POT. 5' a N = 4 SYM via superespaço harmônico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Anti-de Sitter holography in di?erent coordinates

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The structure of non-abelian kinks

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comments on the T-dual of the gravity dual of D5-branes on S-3

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Integrable deformations of strings on symmetric spaces

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Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

Flat currents in the classical AdS(5) x S-5 pure spinor superstring

It is proven that the classical pure spinor superstring in an AdS(5) X S-5 background has a flat current depending on a continuous parameter. This generalizes the recent result of Bena, et at. for the classical Green-Schwarz superstring.

Some aspects of abelian and nonabelian T-duality and the gauge/gravity correspondence

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Buraco negros, correspondência AdS/BCFT e fluido/gravidade

Einstein’s equations with negative cosmological constant possess the so-called anti de Sitter space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk". The holographic principle states that quantum gravity in the AdSd+1 space can be encoded by a d−dimensional quantum field theory on the boundary of AdSd+1 space, invariant under conformal transformations, a CFTd. In the most famous example, the precise statement is the duality of the type IIB string theory in the space AdS5 × S 5 and the 4−dimensional N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation between Einstein’s equations in the bulk and hydrodynamic equations describing the effective theory on the boundary, the so-called fluid/gravity correspondence. An extension of the "AdS/CFT duality"for the CFT’s with boundary was proposed by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed on the extension of the boundary yield a dynamic equation that determines the shape of the extension. From the perspective of fluid/gravity correspondence, the shape of the Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum tensor Tµν of a fluid residing on this boundary. Clarifying the relation of the Takayanagi’s proposal to the fluid/gravity correspondence, we will study the consistence of the AdS/BCFT with finite temperature CFT’s, or equivalently black hole geometries in the bulk.

Notes on beta-deformations of the pure spinor superstring in AdS(5) x S(5)

We study the properties of the vertex operator for the beta-deformation of the superstring in AdS(5) x S(5) in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal beta-deformation, the application of the homological perturbation theory, and the relation between the worldsheet description and the spacetime supergravity description. (C) 2011 Elsevier B.V. All rights reserved.

Notes on beta-deformations of the pure spinor superstring in AdS(5) x S-5

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