One Monopole with k Singularities

We present all charge one monopole solutions of the Bogomolny equation with k prescribed Dirac singularities for the gauge groups U(2), SO(3), or SU(2). We analyze these solutions comparing them to the previously known expressions for the cases of one or two singularities.Comment: 12 pages, LaTe

Hyperkahler Metrics from Periodic Monopoles

Relative moduli spaces of periodic monopoles provide novel examples of Asymptotically Locally Flat hyperkahler manifolds. By considering the interactions between well-separated periodic monopoles, we infer the asymptotic behavior of their metrics. When the monopole moduli space is four-dimensional, this construction yields interesting examples of metrics with self-dual curvature (gravitational instantons). We discuss their topology and complex geometry. An alternative construction of these gravitational instantons using moduli spaces of Hitchin equations is also described.Comment: 23 pages, latex. v2: an erroneous formula is corrected, and its derivation is given. v3 (published version): references adde

Moduli Spaces of Instantons on the Taub-NUT Space

We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. We motivate our construction by identifying a corresponding string theory brane configuration. By following string theory dualities we are led to supersymmetric gauge theories with impurities.Comment: 26 pages, 7 figure

Heterotic Action in SUGRA-SYM Background

We consider the generalization of the heterotic action considered by Cherkis and Schwarz where the chiral bosons are introduced in a manifestly covariant way using an auxiliary field. In particular, we construct the kappa-symmetric heterotic action in ten-dimensional supergravity background coupled to super Yang-Mills theory and prove its kappa-symmetry. The usual Bianchi identity of Type I supergravity with super Yang-Mills dH_3= -\tr F\wedge F is crucially used. For technical reason, the Yang-Mills field is restricted to be abelian.Comment: 12 pages, no figures, added comments in the acknowledgmen

Multiple M2-branes and Generalized 3-Lie algebras

We propose a generalization of the Bagger-Lambert-Gustavsson action as a candidate for the description of an arbitrary number of M2-branes. The action is formulated in terms of N=2 superfields in three dimensions and corresponds to an extension of the usual superfield formulation of Chern-Simons matter theories. Demanding gauge invariance of the resulting theory does not imply the total antisymmetry of the underlying 3-Lie algebra structure constants. We relax this condition and propose a class of examples for these generalized 3-Lie algebras. We also discuss how to associate various ordinary Lie algebras.Comment: 1+19 pages, version published in Phys. Rev.

Thermodynamics of the localized D2-D6 system

An exact fully-localized extremal supergravity solution for N_2 D2 branes and N_6 D6 branes, which is dual to 3-dimensional supersymmetric SU(N_2) gauge theory with N_6 fundamentals, was found by Cherkis and Hashimoto. In order to consider the thermal properties of the gauge theory we present the non-extremal extension of this solution to first order in an expansion near the core of the D6 branes. We compute the Hawking temperature and the black brane horizon area/entropy. The leading order entropy, which is proportional to N_2^{3/2} N_6^{1/2} T_H^2, is not corrected to first order in the expansion. This result is consistent with the analogous weak-coupling result at the correspondence point N_2 ~ N_6.Comment: 14 page

The Viscosity Bound Conjecture and Hydrodynamics of M2-Brane Theory at Finite Chemical Potential

Kovtun, Son and Starinets have conjectured that the viscosity to entropy density ratio $\eta/s$ is always bounded from below by a universal multiple of $\hbar$ i.e., $\hbar/(4\pi k_{B})$ for all forms of matter. Mysteriously, the proposed viscosity bound appears to be saturated in all computations done whenever a supergravity dual is available. We consider the near horizon limit of a stack of M2-branes in the grand canonical ensemble at finite R-charge densities, corresponding to non-zero angular momentum in the bulk. The corresponding four-dimensional R-charged black hole in Anti-de Sitter space provides a holographic dual in which various transport coefficients can be calculated. We find that the shear viscosity increases as soon as a background R-charge density is turned on. We numerically compute the few first corrections to the shear viscosity to entropy density ratio $\eta/s$ and surprisingly discover that up to fourth order all corrections originating from a non-zero chemical potential vanish, leaving the bound saturated. This is a sharp signal in favor of the saturation of the viscosity bound for event horizons even in the presence of some finite background field strength. We discuss implications of this observation for the conjectured bound.Comment: LaTeX, 26+1 Pages, 4 Figures, Version 2: references adde

Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model

We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to a zero-dimensional 3-Lie algebra model and construct various stable solutions corresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgs mechanism reduces this model to the IKKT matrix model. We find that in the strong coupling limit, our solutions correspond to ordinary noncommutative spaces arising as stable solutions in the IKKT model with D-brane backgrounds. In particular, this happens for S^3, R^3 and five-dimensional Neveu-Schwarz Hpp-waves. We expand our model around these backgrounds and find effective noncommutative field theories with complicated interactions involving higher-derivative terms. We also describe the relation of our reduced model to a cubic supermatrix model based on an osp(1|32) supersymmetry algebra.Comment: 22 page

Regge Trajectories for Mesons in the Holographic Dual of Large-N_c QCD

We discuss Regge trajectories of dynamical mesons in large-N_c QCD, using the supergravity background describing N_c D4-branes compactified on a thermal circle. The flavor degrees of freedom arise from the addition of N_f<<N_c D6 probe branes. Our work provides a string theoretical derivation, via the gauge/string correspondence, of a phenomenological model describing the meson as rotating point-like massive particles connected by a flux string. The massive endpoints induce nonlinearities for the Regge trajectory. For light quarks the Regge trajectories of mesons are essentially linear. For massive quarks our trajectories qualitatively capture the nonlinearity detected in lattice calculations.Comment: 21 pages, 4 figures. v2: typos corrected, references and acknowledgments adde

Supersymmetry and generalized calibrations

A static minimal energy configuration of a super p-brane in a supersymmetric (n+1)-dimensional spacetime is shown to be a `generalized calibrated' submanifold. Calibrations in \bE^{(1,n)} and $AdS_{n+1}$ are special cases. We present several M-brane examples.Comment: Revtex. 11 pp. Minor corrections made and references added. To appear in Phys. Rev.