Phase Structure of Non-Commutative Field Theories and Spinning Brane Bound States

General spinning brane bound states are constructed, along with their near-horizon limits which are relevant as dual descriptions of non-commutative field theories. For the spinning D-brane world volume theories with a B-field a general analysis of the gauge coupling phase structure is given, exhibiting various novel features, already at the level of zero angular momenta. We show that the thermodynamics is equivalent to the commutative case at large N and we discuss the possibility and consequences of finite N. As an application of the general analysis, the range of validity of the thermodynamics for the NCSYM is discussed. In view of the recently conjectured existence of a 7-dimensional NCSYM, the thermodynamics of the spinning D6-brane theory, for which a stable region can be found, is presented in detail. Corresponding results for the spinning M5-M2 brane bound state, including the near-horizon limit and thermodynamics, are given as well.Comment: 34 pages, JHEP class. minor corrections, final JHEP versio

New nonuniform black string solutions

We present nonuniform vacuum black strings in five and six spacetime dimensions. The conserved charges and the action of these solutions are computed by employing a quasilocal formalism. We find qualitative agreement of the physical properties of nonuniform black strings in five and six dimensions. Our results offer further evidence that the black hole and the black string branches merge at a topology changing transition. We generate black string solutions of the Einstein-Maxwell-dilaton theory by using a Harrison transformation. We argue that the basic features of these solutions can be derived from those of the vacuum black string configurations.Comment: 30 pages, 12 figures; v2: more details on numerical method, references added; v3: references added, minor revisions, version accepted by journa

Three-Charge Black Holes on a Circle

We study phases of five-dimensional three-charge black holes with a circle in their transverse space. In particular, when the black hole is localized on the circle we compute the corrections to the metric and corresponding thermodynamics in the limit of small mass. When taking the near-extremal limit, this gives the corrections to the constant entropy of the extremal three-charge black hole as a function of the energy above extremality. For the partial extremal limit with two charges sent to infinity and one finite we show that the first correction to the entropy is in agreement with the microscopic entropy by taking into account that the number of branes shift as a consequence of the interactions across the transverse circle. Beyond these analytical results, we also numerically obtain the entire phase of non- and near-extremal three- and two-charge black holes localized on a circle. More generally, we find in this paper a rich phase structure, including a new phase of three-charge black holes that are non-uniformly distributed on the circle. All these three-charge black hole phases are found via a map that relates them to the phases of five-dimensional neutral Kaluza-Klein black holes.Comment: 58 pages, 10 figures; v2: Corrected typos, version appearing in JHE

The First Law for Boosted Kaluza-Klein Black Holes

We study the thermodynamics of Kaluza-Klein black holes with momentum along the compact dimension, but vanishing angular momentum. These black holes are stationary, but non-rotating. We derive the first law for these spacetimes and find that the parameter conjugate to variations in the length of the compact direction is an effective tension, which generally differs from the ADM tension. For the boosted black string, this effective tension is always positive, while the ADM tension is negative for large boost parameter. We also derive two Smarr formulas, one that follows from time translation invariance, and a second one that holds only in the case of exact translation symmetry in the compact dimension. Finally, we show that the `tension first law' derived by Traschen and Fox in the static case has the form of a thermodynamic Gibbs-Duhem relation and give its extension in the stationary, non-rotating case.Comment: 20 pages, 0 figures; v2 - reference adde

Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

We construct and analyze a large class of exact five- and six-dimensional regular and static solutions of the vacuum Einstein equations. These solutions describe sequences of Kaluza-Klein bubbles and black holes, placed alternately so that the black holes are held apart by the bubbles. Asymptotically the solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In particular, they occupy a hitherto unexplored region of the phase diagram, since their relative tension exceeds that of the uniform black string. The solutions contain bubbles and black holes of various topologies, including six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against gravitational collapse. We find two maps between solutions, one that relates five- and six-dimensional solutions, and another that relates solutions in the same dimension by interchanging bubbles and black holes. To illustrate the richness of the phase structure and the non-uniqueness in the (\mu,n) phase diagram, we consider in detail particular examples of the general class of solutions.Comment: 71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.

Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order

The "dialogue of multipoles" matched asymptotic expansion for small black holes in the presence of compact dimensions is extended to the Post-Newtonian order for arbitrary dimensions. Divergences are identified and are regularized through the matching constants, a method valid to all orders and known as Hadamard's partie finie. It is closely related to "subtraction of self-interaction" and shows similarities with the regularization of quantum field theories. The black hole's mass and tension (and the "black hole Archimedes effect") are obtained explicitly at this order, and a Newtonian derivation for the leading term in the tension is demonstrated. Implications for the phase diagram are analyzed, finding agreement with numerical results and extrapolation shows hints for Sorkin's critical dimension - a dimension where the transition turns second order.Comment: 28 pages, 5 figures. v2:published versio