We study giant graviton probes in the framework of the three-parameter deformation of the AdS 5 × S 5 background. We examine both the case when the brane expands in the deformedS 5 part of the geometry and the case when it blows up into AdS 5 . Performing a detailed analysis of small fluctuations around the giants, the configurations turn out to be stable. Our results hold even for the supersymmetric Lunin-Maldacena deformation.

For N = 1 SU(N) SYM theories obtained as marginal deformations of the N = 4 parent theory we study perturbatively some sectors of the chiral ring in the weak coupling regime and for finite N. By exploiting the relation between the definition of chiral ring and the effective superpotential we develop a procedure which allows us to easily determine protected chiral operators up to n loops once the superpotential has been computed up to (n−1) order. In particular, for the Lunin-Maldacena β-deformed theory we determine the quantum structure of a large class of operators up to three loops. We extend our procedure to more general Leigh-Strassler deformations whose chiral ring is not fully understood yet and determine the weight-two and weight-three sectors up to two loops. We use our results to infer general properties of the chiral ring.

Formation evaluation analysis, rock-physics models, and log-facies classification are powerful tools to link the physical properties measured at wells with petrophysical, elastic, and seismic properties. However, this link can be affected by several sources of uncertainty. We proposed a complete statistical workflow for obtaining petrophysical properties at the well location and the corresponding log-facies classification. This methodology is based on traditional formation evaluation models and cluster analysis techniques, but it introduces a full Monte Carlo approach to account for uncertainty evaluation. The workflow includes rock-physics models in log-facies classification to preserve the link between petrophysical properties, elastic properties, and facies. The use of rock-physics model predictions guarantees obtaining a consistent set of well-log data that can be used both to calibrate the usual physical models used in seismic reservoir characterization and to condition reservoir models. The final output is the set of petrophysical curves with the associated uncertainty, the profile of the facies probabilities, and the entropy, or degree of confusion, related to the most probable facies profile. The full statistical approach allows us to propagate the uncertainty from data measured at the well location to the estimated petrophysical curves and facies profiles. We applied the proposed methodology to two different well-log studies to determine its applicability, the advantages of the new integrated approach, and the value of uncertainty analysis.

We review the results of 0710.4292 [hep‐th] where we study the embedding of spacetime filling D7‐branes in β‐deformed backgrounds. This corresponds to flavoring β‐deformed 𝒩 = 4 super Yang–Mills. For the supersymmetric and the more general non‐supersymmetric three parameter deformations, we study quadratic fluctuations of a probe D7‐brane wrapped on a deformed three‐sphere, which correspond to mesonic configurations of the dual field theory. We manage to solve their equations exactly in the presence of a non‐trivial coupling between scalar and vector modes induced by the deformation. We find a mesonic mass spectrum which is discrete, with a mass gap and a Zeeman‐like splitting occurs.

We study the embedding of spacetime filling D7-branes in β-deformed backgrounds which, according to the AdS/CFT dictionary, corresponds to flavoring β-deformed N = 4 super Yang-Mills. We consider supersymmetric and more general non-supersymmetric three parameter deformations. The equations of motion for quadratic fluctuations of a probe D7-brane wrapped on a deformed three-sphere exhibit a non-trivial coupling between scalar and vector modes induced by the deformation. Nevertheless, we manage to solve them analytically and find that the mesonic mass spectrum is discrete, with a mass gap and a Zeeman-like splitting occurs. Finally we propose the action for the dual field theory as obtained by * -product deformation of super Yang-Mills with fundamental matter.