N=1 gauge superpotentials from supergravity

We review the supergravity derivation of some non-perturbatively generated effective superpotentials for N=1 gauge theories. Specifically, we derive the Veneziano-Yankielowicz superpotential for pure N=1 Super Yang-Mills theory from the warped deformed conifold solution, and the Affleck-Dine-Seiberg superpotential for N=1 SQCD from a solution describing fractional D3-branes on a C^3 / Z_2 x Z_2 orbifold.Comment: LaTeX, iopart class, 8 pages, 3 figures. Contribution to the proceedings of the workshop of the RTN Network "The quantum structure of space-time and the geometric nature of fundamental interactions", Copenhagen, September 2003; v2: published version with minor clarification

Sound Waves in (2+1) Dimensional Holographic Magnetic Fluids

We use the AdS/CFT correspondence to study propagation of sound waves in strongly coupled (2+1) dimensional conformal magnetic fluids. Our computation provides a nontrivial consistency check of the viscous magneto-hydrodynamics of Hartnoll-Kovtun-Muller-Sachdev to leading order in the external field. Depending on the behavior of the magnetic field in the hydrodynamic limit, we show that it can lead to further attenuation of sound waves in the (2+1) dimensional conformal plasma, or reduce the speed of sound. We present both field theory and dual supergravity descriptions of these phenomena. While to the leading order in momenta the dispersion of the sound waves obtained from the dual supergravity description agrees with the one predicted from field theory, we find a discrepancy at higher order. This suggests that further corrections to HKMS magneto-hydrodynamics are necessary.Comment: 32 pages, LaTeX; minor corrections, references added; an error in the boundary conditions fixed, a slight change in the result

Hydrodynamics of R-charged D1-branes

We study the hydrodynamic properties of strongly coupled $SU(N)$ Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to $1/4\pi$. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.Comment: 57 pages, 12 figure

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

Warped Spectroscopy: Localization of Frozen Bulk Modes

We study the 10D equation of motion of dilaton-axion fluctuations in type IIB string compactifications with three-form flux, taking warping into account. Using simplified models with physics comparable to actual compactifications, we argue that the lightest mode localizes in long warped throats and takes a mass of order the warped string scale. Also, Gukov-Vafa-Witten superpotential is valid for the lightest mass mode; however, the mass is similar to the Kaluza-Klein scale, so the dilaton-axion should be integrated out of the effective theory in this long throat regime (leaving a constant superpotential). On the other hand, there is a large hierarchy between flux-induced and KK mass scales for moderate or weak warping. This hierarchy agrees with arguments given for trivial warping. Along the way, we also estimate the effect of the other 10D supergravity equations of motion on the dilaton-axion fluctuation, since these equations act as constraints. We argue that they give negligible corrections to the simplest approximation.Comment: 24pp + appendices, 6 figs, JHEP3 class; v2. corrected reference; v3. added clarifications; v4. corrected typo

Cascading RG Flows from New Sasaki-Einstein Manifolds

In important recent developments, new Sasaki-Einstein spaces $Y^{p,q}$ and conformal gauge theories dual to $AdS_5\times Y^{p,q}$ have been constructed. We consider a stack of N D3-branes and M wrapped D5-branes at the apex of a cone over $Y^{p,q}$. Replacing the D-branes by their fluxes, we construct asymptotic solutions for all p and q in the form of warped products of the cone and $R^{3,1}$. We show that they describe cascading RG flows where N decreases logarithmically with the scale. The warp factor, which we determine explicitly, is a function of the radius of the cone and one of the coordinates on $Y^{p,q}$. We describe the RG cascades in the dual quiver gauge theories, and find an exact agreement between the supergravity and the field theory beta functions. We also discuss certain dibaryon operators and their dual wrapped D3-branes in the conformal case M=0.Comment: 22 pages, 6 figures; v2 minor corrections; v3 refs, orbifold discussion added; v4 more ref

Sum Rules from an Extra Dimension

Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green's functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning their large and small frequency behavior and their pole structure. From these results, it is straightforward to prove the validity of various sum rules on the field theory side of the duality. We introduce a novel contraction mapping we use to study the large frequency behavior of the Green's functions.Comment: v2: 23 pages (plus appendix), revised presentation, discussion of branch cuts moved to appendix, and some minor changes; v1: 24 pages (plus appendix

Green's Functions and Non-Singlet Glueballs on Deformed Conifolds

We study the Laplacian on Stenzel spaces (generalized deformed conifolds), which are tangent bundles of spheres endowed with Ricci flat metrics. The (2d-2)-dimensional Stenzel space has SO(d) symmetry and can be embedded in C^d through the equation \sum_{i = 1}^d {z_i^2} = \epsilon^2. We discuss the Green's function with a source at a point on the S^{d-1} zero section of TS^{d-1}. Its calculation is complicated by mixing between different harmonics with the same SO(d) quantum numbers due to the explicit breaking by the \epsilon-deformation of the U(1) symmetry that rotates z_i by a phase. A similar mixing affects the spectrum of normal modes of warped deformed conifolds that appear in gauge/gravity duality. We solve the mixing problem numerically to determine certain bound state spectra in various representations of SO(d) for the d=4 and d=5 examples.Comment: 52 pages, 3 figure

Nuclear myocardial perfusion imaging with a cadmium-zinc-telluride detector technique: optimized protocol for scan time reduction

We aimed at establishing the optimal scan time for nuclear myocardial perfusion imaging (MPI) on an ultrafast cardiac gamma-camera using a novel cadmium-zinc-telluride (CZT) solid-state detector technology. METHODS: Twenty patients (17 male; BMI range, 21.7-35.5 kg/m(2)) underwent 1-d (99m)Tc-tetrofosmin adenosine stress and rest MPI protocols, each with a 15-min acquisition on a standard dual-detector SPECT camera. All scans were immediately repeated on an ultrafast CZT camera over a 6-min acquisition time and reconstructed from list-mode raw data to obtain scan durations of 1 min, 2 min, etc., up to a maximum of 6 min. For each of the scan durations, the segmental tracer uptake value (percentage of maximum myocardial uptake) from the CZT camera was compared by intraclass correlation with standard SPECT camera data using a 20-segment model, and clinical agreement was assessed per coronary territory. Scan durations above which no further relevant improvement in uptake correlation was found were defined as minimal required scan times, for which Bland-Altman limits of agreement were calculated. RESULTS: Minimal required scan times were 3 min for low dose (r = 0.81; P < 0.001; Bland-Altman, -11.4% to 12.2%) and 2 min for high dose (r = 0.80; P < 0.001; Bland-Altman, -7.6% to 12.9%), yielding a clinical agreement of 95% and 97%, respectively. CONCLUSION: We have established the minimal scan time for a CZT solid-state detector system, which allows 1-d stress/rest MPI with a substantially reduced acquisition time resulting in excellent agreement with regard to uptake and clinical findings, compared with MPI from a standard dual-head SPECT gamma-camera