Isometry groups of borel randomizations

We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. In particular, we show that if properties such as the Rohklin property, topometric generics, extreme amenability hold for the isometry group of the structure, they also hold in the isometry group of the randomization.UCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA)UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic

Scaling Violations in Yang-Mills Theories and Strings in AdS_5

String solitons in AdS_5 contain information of N=4 SUSY Yang-Mills theories on the boundary. Recent proposals for rotating string solitons reproduce the spectrum for anomalous dimensions of Wilson operators for the boundary theory. There are possible extensions of this duality for lower supersymmetric and even for non-supesymmetric Yang-Mills theories. We explicitly demonstrate that the supersymmetric anomalous dimensions of Wilson operators in N=0,1 Yang-Mills theories behave, for large spin J, at the two-loop level in perturbation theory, like log J. We compile the analytic one- and two-loop results for the N=0 case which is known in the literature, as well as for the N=1 case which seems to be missing.Comment: 16 pages, Appendix included in chapter. Version to appear in Nucl.Phys.

Origin of Logarithmic Operators in Conformal Field Theories

We study logarithmic operators in Coulomb gas models, and show that they occur when the ``puncture'' operator of the Liouville theory is included in the model. We also consider WZNW models for $SL(2,R)$, and for SU(2) at level 0, in which we find logarithmic operators which form Jordan blocks for the current as well as the Virasoro algebra.Comment: 22 pages Latex. Some references adde

Penrose Limits of Orbifolds and Orientifolds

We study the Penrose limit of various AdS_p X S^q orbifolds. The limiting spaces are waves with parallel rays and singular wave fronts. In particular, we consider the orbifolds AdS_3 X S^3/\Gamma, AdS_5 X S^5/\Gamma and AdS_{4,7} X S^{7,4}/\Gamma where \Gamma acts on the sphere and/or the AdS factor. In the pp-wave limit, the wave fronts are the orbifolds C^2/\Gamma, C^4/\Gamma and R XC^4/\Gamma, respectively. When desingularization is possible, we get asymptotically locally pp-wave backgrounds (ALpp). The Penrose limit of orientifolds are also discussed. In the AdS_5 X RP^5 case, the limiting singularity can be resolved by an Eguchi-Hanson gravitational instanton. The pp-wave limit of D3-branes near singularities in F-theory is also presented. Finally, we give the embedding of D-dimensional pp-waves in flat M^{2,D} space.Comment: 20 pages, references adde

A note on the universality of the Hagedorn behavior of pp-wave strings

Following on from recent studies of string theory on a one-parameter family of integrable deformations of $AdS_{5}\times S^{5}$ proposed by Lunin and Maldacena, we carry out a systematic analysis of the high temperature properties of type IIB strings on the associated pp-wave geometries. In particular, through the computation of the thermal partition function and free energy we find that not only does the theory exhibit a Hagedorn transition in both the $(J,0,0)$ and $(J,J,J)$ class of pp-waves, but that the Hagedorn temperature is insensitive to the deformation suggesting an interesting universality in the high temperature behaviour of the pp-wave string theory. We comment also on the implications of this universality on the confinement/deconfinement transition in the dual $\mathcal{N}=1$ Leigh-Strassler deformation of ${\cal N}=4$ Yang-Mills theory.Comment: 25 pages; fixed minor typo; added reference

Lessons from giant gravitons on AdS5×T1,1AdS_{5}\times T^{1,1}

We implement Mikhailov's holomorphic curve construction to explore various properties of giant gravitons in type IIB string theory on $AdS_{5}\times T^{1,1}$. By coloring the D-brane worldvolume, we are able to show how, in the string theory, the giant graviton factorizes at its maximal size into two dibaryons - topologically stable D-branes wrapping non-contractible cycles in the $T^{1,1}$. This is related to the structure of the symmetry group of the emergent Klebanov-Witten gauge theory being a product - $SU(N) \times SU(N)$ instead of the canonical $SU(N)$. Finally, we complete this study with a systematic and detailed construction of the spectrum of small fluctuations about the giant graviton configuration. Curiously, we find that the fluctuation spectrum depends on the size of the giant. The similarity of the operator structures in the Klebanov-Witten and ABJM theories leads us to believe that the D4-brane giant graviton in type IIA string theory on $AdS_{4}\times \mathbb{CP}^{3}$ factorizes into two $\mathbb{CP}^{2}$ dibaryons in a qualitatively similar way.Comment: 39 pages; abstract reworded slightly; additional comments included in subsection 3.3; section 5 revised with the addition of subsection 5.3; added reference

Gauge/string correspondence in curved space

We discuss Gubser-Klebanov-Polyakov proposal for the gauge/string theory correspondence for gauge theories in curved space. Specifically, we consider Klebanov-Tseytlin cascading gauge theory compactified on S^3. We explain regime when this gauge theory is a small deformation of the superconformal N=1 gauge theory on the world volume of regular D3-branes at the tip of the conifold. We study closed string states on the leading Regge trajectory in this background, and attempt to identify the dual gauge theory twist two operators.Comment: 26 pages, v2: refs adde

Viscosity Bound and Causality in Superfluid Plasma

It was argued by Brigante et.al that the lower bound on the ratio of the shear viscosity to the entropy density in strongly coupled plasma is translated into microcausality violation in the dual gravitational description. Since transport properties of the system characterize its infrared dynamics, while the causality of the theory is determined by its ultraviolet behavior, the viscosity bound/microcausality link should not be applicable to theories that undergo low temperature phase transitions. We present an explicit model of AdS/CFT correspondence that confirms this fact.Comment: 27 pages, 5 figures. References added, typos fixe

Giant Graviton Oscillators

We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N=4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.Comment: 72 page