D-brane probes on L^{abc} Superconformal Field Theories

We study supersymmetric embeddings of D-brane probes of different dimensionality in the AdS_5xL^{abc} background of type IIB string theory. In the case of D3-branes, we recover the known three-cycles dual to the dibaryonic operators of the gauge theory and we also find a new family of supersymmetric embeddings. Supersymmetric configurations of D5-branes, representing fractional branes, and of spacetime filling D7-branes (which can be used to add flavor) are also found. Stable non supersymmetric configurations corresponding to fat strings and domain walls are found as well.Comment: 20 pages, LaTeX;v2: minor improvements, references adde

Comments on Anomalies and Charges of Toric-Quiver Duals

We obtain a simple expression for the triangle `t Hooft anomalies in quiver gauge theories that are dual to toric Sasaki-Einstein manifolds. We utilize the result and simplify considerably the proof concerning the equivalence of a-maximization and Z-minimization. We also resolve the ambiguity in defining the flavor charges in quiver gauge theories. We then compare coefficients of the triangle anomalies with coefficients of the current-current correlators and find perfect agreement.Comment: 22 pages, 3 figure

Zonotopes and four-dimensional superconformal field theories

The a-maximization technique proposed by Intriligator and Wecht allows us to determine the exact R-charges and scaling dimensions of the chiral operators of four-dimensional superconformal field theories. The problem of existence and uniqueness of the solution, however, has not been addressed in general setting. In this paper, it is shown that the a-function has always a unique critical point which is also a global maximum for a large class of quiver gauge theories specified by toric diagrams. Our proof is based on the observation that the a-function is given by the volume of a three dimensional polytope called "zonotope", and the uniqueness essentially follows from Brunn-Minkowski inequality for the volume of convex bodies. We also show a universal upper bound for the exact R-charges, and the monotonicity of a-function in the sense that a-function decreases whenever the toric diagram shrinks. The relationship between a-maximization and volume-minimization is also discussed.Comment: 29 pages, 15 figures, reference added, typos corrected, version published in JHE

A brittle fracture criterion for PMMA V-notches tensile specimens based on a length-enriched eXtended Finite Element approach

A criterion for the prediction of the static failure loads in tensile PMMA specimens with sharp notches is presented. The proposed criterion is based on a regularized version of the eXtended Finite Element Method (XFEM), which has been previously applied to concrete-like materials. The main feature of the proposed approach is that the cracking process is not treated as a local process, but it is modeled by assuming that macro-cracks stem from the interaction of micro-cracks within a finite width process zone. The case of a brittle materials with thin process zone is tackled by assuming one layer of enriched finite elements. Preliminary results concerning PMMA specimens subjected to mode-one loading are presented

Non-singlet QCD analysis of F_2(x,Q^2) up to NNLO

The significance of NNLO (3-loop) QCD contributions to the flavor non-singlet sector of F_2^ep and F_2^ed has been studied as compared to uncertainties (different factorization schemes, higher twist and QED contributions) of standard NLO (and LO) QCD analyses. The latter effects turn out to be comparable in size to the NNLO contributions. Therefore the minute NNLO effects are not observable with presently available data on non-singlet structure functions.Comment: 14 pages, 2 figure

From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr

The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories is studied from the perspective of massless BPS geodesics. The recently constructed toric Lpqr geometries are considered: we determine the dual superconformal quivers and the spectrum of BPS mesons. The conformal anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R global symmetry quantum numbers of the mesonic operators are successfully matched with the conserved momenta of the geodesics, providing a test of AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to find new precise relations between the two sides of the duality. In particular the parameters that characterize the geometry are mapped directly to the parameters used for a-maximization in the field theory. The analysis simplifies for the special case of the Lpqq models, which are shown to correspond to the known "generalized conifolds". These geometries can break conformal invariance through toric deformations of the complex structure.Comment: 30 pages, 8 figures, LaTeX. v2: One more figure. References added, typos correcte

Small x Behavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep Inelastic Scattering Cross Section

We fit the reduced cross section for deep-inelastic electron scattering data to a three parameter ln^2 s fit, A + beta ln^2 (s/s_0), where s= [Q^2/x] (1-x) + m^2, and Q^2 is the virtuality of the exchanged photon. Over a wide range in Q^2 (0.11 < Q^2 < 1200 GeV^2) all of the fits satisfy the logarithmic energy dependence of the Froissart bound. We can use these results to extrapolate to very large energies and hence to very small values of Bjorken x -- well beyond the range accessible experimentally. As Q^2 --> infinity, the structure function F_2^p(x, Q^2) exhibits Bjorken scaling, within experimental errors. We obtain new constraints on the behavior of quark and antiquark distribution functions at small x.Comment: 10 pages, 2 figure

Strings on the deformed T^{1,1}: giant magnon and single spike solutions

In this paper we find giant magnon and single spike string solutions in a sector of the gamma-deformed conifold. We examine the dispersion relations and find a behavior analogous to the undeformed case. The transcendental functional relations between the conserved charges are shifted by certain gamma-dependent term. The latter is proportional to the total momentum and thus qualitatively different from known cases.Comment: 35 pages, no figure