18036483
Deconstructing the D0-D6 system
We find the complete classical moduli space of two-centered supersymmetric solutions carrying D0 and D6 brane charge in the STU model delimited by walls of marginal stability of co-dimension one. U-duality guarantees our conclusions hold for any BPS state with negative quartic invariant. The analysis explicitly shows that the conditions of marginal stability, i.e. the integrability conditions, are generically insufficient to provide a regular supergravity solution in this model.
18424501
Typicality, Black Hole Microstates and Superconformal Field Theories
We analyze the structure of heavy multitrace BPS operators in N = 1 superconformal quiver gauge theories that arise on the worldvolume of D3-branes on an affine toric cone. We exhibit a geometric procedure for counting heavy mesonic operators with given U(1) charges. We show that for any fixed linear combination of the U(1) charges, the entropy is maximized when the charges are in certain ratios. This selects preferred directions in the charge space that can be determined with the help of a piece of string. We show that almost all heavy mesonic operators of fixed U(1) charges share a universal structure. This universality reflects the properties of the dual extremal black holes whose microstates they create. We also interpret our results in terms of typical configurations of dual giant gravitons in AdS space.
3214344
A multi-boundary AdS orbifold and DLCQ holography: a universal holographic description of extremal black hole horizons
We examine a stationary but non-static asymptotically AdS3 spacetime with two causally connected conformal boundaries, each of which is a ``null cylinder'', namely a cylinder with a null direction identified. This spacetime arises from three different perspectives: (i) as a non-singular, causally regular orbifold of global AdS3 by boosts, (ii) as a Penrose-like limit focusing on the horizon of extremal BTZ black holes, and (iii) as an S1 fibration over AdS2. Each of these perspectives sheds an interesting light on holography. Examination of the conformal boundary of the spacetime shows that the dual to the space should involve DLCQ limits of the D1-D5 conformal field theory. The Penrose-like limit approach leads to a similar conclusion, by isolating a sector of the complete D1-D5 CFT that describes the physics in the vicinity of the horizon of an extremal black hole. As such this is a holographic description of the universal horizon dynamics of the extremal black holes in AdS3 and also of the four and five dimensional stringy black holes whose states were counted in string theory. The AdS2 perspective draws a connection to a 0+1d quantum mechanical theory. Various dualities lead to a Matrix model description of the spacetime. Many interesting issues that are related to both de Sitter physics and attempts to ``see behind a horizon'' using AdS/CFT arise from (a) the presence of two disconnected components to the boundary, and (b) the analytic structure of bulk physics in the complex coordinate plane.
15394078
Brane Effective Actions, Kappa-Symmetry and Applications
This is a review on brane effective actions, their symmetries and some of their applications. Its first part covers the Green-Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects: the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry to achieve manifest spacetime covariance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds.Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as Bogomol’nyi-Prasad-Sommerfield (BPS) states carrying (topological) charges in the supersymmetry algebra and the connection between supersymmetry and Hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approximations to infer about the non-trivial dynamics of strongly-coupled gauge theories using the anti de Sitter/conformal field theory (AdS/CFT) correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description.Its final part briefly discusses effective actions for N D-branes and M2-branes. This includes both Super-Yang-Mills theories, their higher-order corrections and partial results in covariantising these couplings to curved backgrounds, and the more recent supersymmetric Chern-Simons matter theories describing M2-branes using field theory, brane constructions and 3-algebra considerations.
15838992
Killing spectroscopy of closed timelike curves
We analyse the existence of closed timelike curves in spacetimes which possess an isometry. In particular we check which discrete quotients of such spaces lead to closed timelike curves. As a by-product of our analysis, we prove that the notion of existence or non-existence of closed timelike curves is a T-duality invariant notion, whenever the direction along which we apply such transformations is everywhere spacelike. Our formalism is straightforwardly applied to supersymmetric theories. We provide some new examples in the context of D-branes and generalized pp-waves.
16320487
Gödel-type universes and the Landau problem
We point out a close relation between a family of Godel-type solutions of 3+1 general relativity and the Landau problem in and ; in particular, the classical geodesics correspond to Larmor orbits in the Landau problem. We discuss the extent of this relation, by analysing the solutions of the Klein–Gordon equation in these backgrounds. For the case, this relation was independently noticed in hep-th/0306148. Guided by the analogy with the Landau problem, we speculate on the possible holographic description of a single chronologically safe region.
120096829
Lie algebras associated with topological nilpotent groups
Abstract A Lie algebra structure is defined on the set of all continuous one-parameter groups of nilpotent topological groups. Extensions are given to some inductive and projective limits.
119881917
Linearization of relativistic nonlinear wave equations
Some linearization theorems for relativistic nonlinear wave equations are formulated and proved. Examples are discussed and the physical meaning of such a linearization is sketched. Finally, some remarks concerning gauge theories are presented.
119567009
Yang-Mills equations are formally linearizable
It is proved, in the framework of a recent theory of non-linear group representations elaborated by the authors, that the non-linear Yang-Mills equations are formally linearizable: there exists a formal non-linear operator which intertwins the non-linear Yang-Mills equations with their free (linear) part.
15382595
Hamiltonian thermodynamics of a Lovelock black hole
We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensional Lovelock theories. We adopt boundary conditions that make every classical solution part of a black hole exterior, with the spacelike hypersurfaces extending from the horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic metric. The constraints are simplified by a Kuchar ˇ-type canonical transformation, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the trace of the analytically continued Lorentzian time evolution operator is interpreted as the partition function of a thermodynamical canonical ensemble. Whenever the partition function is dominated by a Euclidean black hole solution, the entropy is given by the Lovelock analogue of the Bekenstein-Hawking entropy; in particular, in the low temperature limit the system exhibits a dominant classical solution that has no counterpart in Einstein’s theory. The asymptotically flat space limit of the partition function does not exist. The results indicate qualitative robustness of the thermodynamics of five-dimensional Einstein theory upon the addition of a nontrivial Lovelock term. @S0556-2821~97!03806-X#
116894284
The cauchy problem for non-linear Klein-Gordon equations
We consider in ℝn+1,n≧2, the non-linear Klein-Gordon equation. We prove for such an equation that there is a neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincaré covariant then the non-linear representation of the Poincaré Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincaré group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincaré group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra.