Continuous distributions of D3-branes and gauged supergravity

States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.Comment: 19 pages, two figures, latex. v2: reference added, small corrections. v3: corrected unbounded spectrum erro

Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem

We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N=4 gauged supergravity theory holographically dual to a sector of N=2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For even-dimensional boundaries, the c-function coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.Comment: 56 pages, three figures, harvmac. v2: improved referencing, corrected discussion of energy conditions. v3: one more reference fixe

Extremal Correlators in the AdS/CFT Correspondence

The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t \phi \phi$ and $s \phi \phi$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 \times S^5$.Comment: 26 pages, LateX, no figure

Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random phase approximation

Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous studies and available data. Using the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections, and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on $^{16}$O and $^{208}$Pb target nuclei are analyzed as functions of the temperature and chemical potential.Comment: 28 pages, 8 figures, 2 tables, submitted to Phys. Rev.

Supersymmetry algebra in N = 1 chiral supergravity

We consider the supersymmetry (SUSY) transformations in the chiral Lagrangian for $N = 1$ supergravity (SUGRA) with the complex tetrad following the method used in the usual $N = 1$ SUGRA, and present the explicit form of the SUSY trasformations in the first-order form. The SUSY transformations are generated by two independent Majorana spinor parameters, which are apparently different from the constrained parameters employed in the method of the 2-form gravity. We also calculate the commutator algebra of the SUSY transformations on-shell.Comment: 10 pages, late

From Soft Walls to Infrared Branes

Five dimensional warped spaces with soft walls are generalizations of the standard Randall-Sundrum compactifications, where instead of an infrared brane one has a curvature singularity (with vanishing warp factor) at finite proper distance in the bulk. We project the physics near the singularity onto a hypersurface located a small distance away from it in the bulk. This results in a completely equivalent description of the soft wall in terms of an effective infrared brane, hiding any singular point. We perform explicitly this calculation for two classes of soft wall backgrounds used in the literature. The procedure has several advantages. It separates in a clean way the physics of the soft wall from the physics of the five dimensional bulk, facilitating a more direct comparison with standard two-brane warped compactifications. Moreover, consistent soft walls show a sort of universal behavior near the singularity which is reflected in the effective brane Lagrangian. Thirdly, for many purposes, a good approximation is obtained by assuming the bulk background away from the singularity to be the usual Randall-Sundrum metric, thus making the soft wall backgrounds better analytically tractable. We check the validity of this procedure by calculating the spectrum of bulk fields and comparing it to the exact result, finding very good agreement.Comment: 14 pages, 2 figures, v2: subsection on IR brane potentials and appendix on fermions added, version to appear in PR

Seeing a c-theorem with holography

There is no known model in holography exhibiting a $c$-theorem where the central charges of the dual CFT are distinct. We examine a holographic model of RG flows in a framework where the bulk gravity theory contains higher curvature terms. The latter allows us to distinguish the flow of the central charges $a$ and $c$ in the dual field theories in four dimensions. One finds that the flow of $a$ is naturally monotonic but that of $c$ is not. Extending the analysis of holographic RG flows to higher dimensions, we are led to formulate a novel c-theorem in arbitrary dimensions for a universal coefficient appearing in the entanglement entropy of the fixed point CFT's.Comment: 5 pages, 1 figure, v2: minor change