121596909
RESTRICTIONS FROM GEOMETRY ON QUANTIZATION IN CURVED SPACE--TIME.
122293144
WIGHTMAN FORMULATION FOR THE QUANTIZATION OF THE GRAVITATIONAL FIELD.
119610987
Asymptotic Completeness, Global Existence and the Infrared Problem for the Maxwell-Dirac Equations
Introduction The nonlinear representation $T$ and spaces of differentiable vectors The asymptotic nonlinear representation Construction of the approximate solution Energy estimates and $L^2-L^\infty$ estimates for the Dirac field Construction of the modified wave operator and its inverse Appendix.
122340661
Wave operators and analytic solutions for systems of non-linear Klein-Gordon equations and of non-linear Schrödinger equations
We consider, in a 1+3 space time, arbitrary (finite) systems of nonlinear Klein-Gordon equations (respectively Schrödinger equations) with an arbitrary local and analytic non-linearity in the unknown and its first and second order space-time (respectively first order space) derivatives, having no constant or linear terms. No restriction is given on the frequency sign of the initial data. In the case of non-linear Klein-Gordon equations all masses are supposed to be different from zero.We prove, for such systems, that the wave operator (fromt=∞ tot=0) exists on a domain of small entire test functions of exponential type and that the analytic Cauchy problem, in ℝ+×ℝ3, has a unique solution for each initial condition (att=0) being in the image of the wave operator. The decay properties of such solutions are discussed in detail.
122524343
A Garding domain for representations of some Hilbert Lie groups
AbstractGiven a Banach representation of a Hilbert Lie group, the Lie algebra 
$$\mathfrak{G}$$
 of which is the closure of the union of an increasing sequence of finite dimensional subalgebras, we construct a Gårding domain on which we differentiate the group representation to a representation of a dense subalgebra of 
$$\mathfrak{G}$$
.
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.
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.
15656106
T-duality covariance of SuperD-branes
T-duality realized on SuperD-brane effective actions probing in constant Gmn and bmn backgrounds is studied from a pure world volume point of view. It is proved that requiring T-duality covariance of such actions “fixes” the T-duality transformations of the world volume dynamical fields, and consequently, of the NS–NS and R–R coupling superfields. The analysis is extended to uncover the mapping of the symmetry structure associated with these SuperD-brane actions. In particular, we determine the T-duality transformation properties of kappa symmetry and supersymmetry, which allow us to prove that bosonic supersymmetric world volume solitons of the original theory generate, through T-duality, the expected ones in the T-dual theory. The latter proof is generalized to arbitrary bosonic backgrounds. We conclude with some comments on extensions of our approach to arbitrary kappa symmetric backgrounds, non-BPS D-branes and non-abelian SuperD-branes.
55394540
Near Horizon Limits of Massless BTZ and Their CFT Duals
We consider the massless BTZ black hole and show that it is possible to take its "near horizon" limit in two distinct ways. The first one leads to a null self-dual orbifold of AdS3 and the second to a spacelike singular AdS3/Z_K orbifold in the large K limit, the "pinching orbifold". We show that from the dual 2d CFT viewpoint, the null orbifold corresponds to the p^+=0 sector of the Discrete Light-Cone Quantisation (DLCQ) of the 2d CFT where a chiral sector of the CFT is decoupled, while the pinching orbifold corresponds to taking an infinite mass gap limit in both the right and left sectors of the 2d CFT, essentially leaving us with the states L_0=\bar L_0=c/24 only. In the latter case, one can combine the near horizon limit with sending the 3d Planck length l_P to zero, or equivalently the dual CFT central charge c to infinity. We provide preliminary evidence that in that case some nontrivial dynamics may survive the limit.
55066831
The electrostatic view on M-theory LLM geometries
We describe the geometry of the $ \mathbb{R} \times {\text{SO}}(3) \times {\text{SO}}(6) \times {\text{U}}(1) $ invariant half-BPS M-theory configurations considered in LLM in terms of their electrostatic variables. We discuss both regular configurations, such as AdS4 × S7 and AdS7 × S4 vacua or simple excited solutions, and singular ones such as the superstar geometries. This allows us to identify the appropriate boundary conditions describing the most general smooth and superstar-like singular configurations. We also compute their masses, matching the expected result from their microscopic interpretation, but now at finite radius of curvature.
14354084
The geometry of null rotation identifications
The geometry of flat spacetime modded out by a null rotation (boost + rotation) is analysed. When embedding this quotient spacetime in String/M-theory, it still preserves one half of the original supersymmetries. Its connection with the BTZ black hole, supersymmetric dilatonic waves and one possible resolution of its singularity in terms of nullbranes are also discussed.