Supersymmetric AdS_3 solutions of type IIB supergravity

For every positively curved Kahler-Einstein manifold in four dimensions we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS_3 with a compact seven-dimensional manifold and have non-vanishing five-form flux. Via the AdS/CFT correspondence, the solutions are dual to two-dimensional conformal field theories with (2,0) supersymmetry. The corresponding central charges are rational numbers.Comment: Dedicated to Rafael Sorkin in celebration of his 60th birthday; 5 pages, latex. v2, typos corrected, to appear in PR

Bernoulli potential in type-I and weak type-II superconductors: III. Electrostatic potential above the vortex lattice

The electrostatic potential above the Abrikosov vortex lattice, discussed earlier by Blatter {\em et al.} {[}PRL {\bf 77}, 566 (1996){]}, is evaluated within the Ginzburg-Landau theory. Unlike previous studies we include the surface dipole. Close to the critical temperature, the surface dipole reduces the electrostatic potential to values below a sensitivity of recent sensors. At low temperatures the surface dipole is less effective and the electrostatic potential remains observable as predicted earlier.Comment: 8 pages 5 figure

Tunneling conductance of graphene ferromagnet-insulator-superconductor junctions

We study the transport properties of a graphene ferromagnet-insulator superconductor (FIS) junction within the Blonder-Tinkham-Klapwijk formalism by solving spin-polarized Dirac-Bogoliubov-de-Gennes equation. We find that the retro and specular Andreev reflections in the graphene FIS junction are drastically modified in the presence of exchange interaction and that the spin-polarization ($P_T$) of tunneling current can be tuned from the positive to negative value by bias voltage ($V$). In the thin-barrier limit, the conductance $G$ of a graphene FIS junction oscillates as a function of barrier strength $\chi$. Both the amplitude and phase of the conductance oscillation varies with the exchange energy $E_{ex}$. For $E_{ex}<E_F$ (Fermi energy), the amplitude of oscillation decreases with $E_{ex}$. For $E_{ex}^{c}>E_{ex}>E_F$, the amplitude of oscillation increases with $E_{ex}$, where $E_{ex}^{c}=2E_{F}+U_{0}$ ($U_{0}$ is the applied electrostatic potential on the superconducting segment of the junction). For $E_{ex} > E_{ex}^{c}$, the amplitude of oscillation decreases with $E_{ex}$ again. Interestingly, a universal phase difference of $\pi/2$ in $\chi$ exists between the $G-\chi$ curves for $E_{ex}>E_F$ and $E_{ex}<E_F$. Finally, we find that the transitions between retro and specular Andreev reflections occur at $eV=|E_{F}-E_{ex}|$ and $eV=E_{ex}+E_{F}$, and hence the singular behavior of the conductance near these bias voltages results from the difference in transport properties between specular and retro Andreev reflections.Comment: Accepted for publication in Physical Review

A Note on Einstein Sasaki Metrics in D \ge 7

In this paper, we obtain new non-singular Einstein-Sasaki spaces in dimensions D\ge 7. The local construction involves taking a circle bundle over a (D-1)-dimensional Einstein-Kahler metric that is itself constructed as a complex line bundle over a product of Einstein-Kahler spaces. In general the resulting Einstein-Sasaki spaces are singular, but if parameters in the local solutions satisfy appropriate rationality conditions, the metrics extend smoothly onto complete and non-singular compact manifolds.Comment: Latex, 13 page

The central charge of supersymmetric AdS_5 solutions of type IIB supergravity

We show that generic supersymmetric AdS_5 solutions of type IIB supergravity admit a canonical contact structure. This structure determines the central charge of the dual field theory and the conformal dimension of operators dual to supersymmetric wrapped D3-branes. Hence both quantities can be calculated using incomplete information about the solutions, allowing us to prove that they are rational numbers for solutions with a U(1) R-symmetry, in agreement with field theory expectations. We also discuss related Duistermaat-Heckman integrals and localization formulae.Comment: 4 page

On the Ricci tensor in type II B string theory

Let $\nabla$ be a metric connection with totally skew-symmetric torsion \T on a Riemannian manifold. Given a spinor field $\Psi$ and a dilaton function $\Phi$, the basic equations in type II B string theory are \bdm \nabla \Psi = 0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi = b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations between the length ||\T||^2 of the torsion form, the scalar curvature of $\nabla$, the dilaton function $\Phi$ and the parameters $a,b,\mu$. The main results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the connection. In particular, if the supersymmetry $\Psi$ is non-trivial and if the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d \T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is divergence-free. We show that the latter condition is satisfied in many examples constructed out of special geometries. A special case is $a = b$. Then the divergence of the energy-momentum tensor vanishes if and only if one condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T = 0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq 0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2

Supersymmetric AdS_5 solutions of M-theory

We analyse the most general supersymmetric solutions of D=11 supergravity consisting of a warped product of five-dimensional anti-de-Sitter space with a six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that M_6 is partly specified by a one-parameter family of four-dimensional Kahler metrics. We find a large family of new explicit regular solutions where M_6 is a compact, complex manifold which is topologically a two-sphere bundle over a four-dimensional base, where the latter is either (i) Kahler-Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki-Einstein spaces which includes T^{1,1}/Z_2. Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.Comment: 40 pages. v2: minor changes, eqs. (2.22) and (D.12) correcte

M-Theory solutions with AdS factors

Solutions of D=7 maximal gauged supergravity are constructed with metrics that are a product of a n-dimensional anti-de Sitter (AdS) space, with n=2,3,4,5, and certain Einstein manifolds. The gauge fields have the same form as in the recently constructed solutions describing the near-horizon limits of M5-branes wrapping supersymmetric cycles. The new solutions do not preserve any supersymmetry and can be uplifted to obtain new solutions of D=11 supergravity, which are warped and twisted products of the D=7 metric with a squashed four-sphere. Some aspects of the stability of the solutions are discussed.Comment: 30 pages. References adde