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.
122293144
WIGHTMAN FORMULATION FOR THE QUANTIZATION OF THE GRAVITATIONAL FIELD.
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.
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 
$$\mathfrak{G}$$
.
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.
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.
119108532
Helical Luttinger Liquids and three dimensional black holes
We use the AdS/CFT correspondence to discuss an equivalence between a helical, strongly coupled Luttinger liquid and a fermion propagating in the background of a topologically charged black hole in three dimensions. The Fermi level is set by the topological charges, thus surmounting difficulties in low dimensions of the standard approach using Coulomb charged black holes. The construction is fully embeddable in string theory, and the microscopic Lagrangian is explicitly known. The retarded Green function at low temperature and energy arises from the geometry very near the black hole horizon, a structure that is universal for all cold, charged liquids with a dual $\mathbb{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}^{s}$ invariant description in gravity. This explains a subtle relationship between Luttinger physics and the infrared behavior of higher dimensional non-Fermi liquids in the AdS/CFT correspondence.
15296521
Null orbifolds in AdS, Time Dependence and Holography
We study M/D-branes in a null-brane background. By taking a near horizon limit, one is left with cosmological models in the corresponding Poincarpatches. To deal with their usual horizons, we either extend these models to global AdS or remain in the Poincarpatch and apply a T-duality transformation whenever the efiective radius of the compact dimension associated with the null-brane probes distances smaller than the string scale. The flrst scenario gives rise to null orbifolds in AdS spaces, which are described in detail. Their conformal boundaries are singular. The second has a dual gauge theory description in terms of Super Yang-Mills in the null-brane background. The latter is a good candidate for a non-perturbative deflnition of string theory in a time- dependent background.
14309262
A Fermi surface model for large supersymmetric AdS5 black holes
We identify a large family of 1/16 BPS operators in = 4 SYM that qualitatively reproduce the relations between charge, angular momentum and entropy in regular supersymmetric AdS5 black holes when the main contribution to their masses is given by their angular momentum.