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 
$$\mathfrak{G}$$
.
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.
122293708
On a linearization program of non-linear field equations
Abstract The relevance of a recently developed theory of non-linear representations of Lie groups to the problem of linearization of non-linear field equations covariant under the action of a Lie group is discussed. Some basic definitions and results of this theory are then summarized. The article ends with a discussion of the physical meaning, consequences, and further possible developments of the non-linear representation theory.
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.
28853641
BPS states and automorphisms
The purpose of the present paper is twofold. In the first part, we provide an algebraic characterization of several families of $\nu= \frac{1}{2^n}$ $n\leq 5$ BPS states in M theory, at threshold and non-threshold, by an analysis of the BPS bound derived from the ${\cal N}=1$ D=11 SuperPoincar\'e algebra. We determine their BPS masses and their supersymmetry projection conditions, explicitly. In the second part, we develop an algebraic formulation to study the way BPS states transform under $GL(32,\bR)$ transformations, the group of automorphisms of the corresponding SuperPoincar\'e algebra. We prove that all $\nu={1/2}$ non-threshold bound states are SO(32) related with $\nu={1/2}$ BPS states at threshold having the same mass. We provide further examples of this phenomena for less supersymmetric $\nu={1/4},{1/8}$ non-threshold bound states.
119491620
Supersymmetric Kerr-Anti-de Sitter solutions
We prove the existence of one quarter supersymmetric type IIB configurations that arise as nontrivial scaling solutions of the standard five-dimensional Kerr-anti-de Sitter black holes by the explicit construction of its Killing spinors. This neutral, spinning solution is asymptotic to the static anti-de Sitter space-time with cosmological constant -(1/l{sup 2}), it has two finite equal angular momenta J{sub 1}={+-}J{sub 2}, mass M=(1/l)(|J{sub 1}|+|J{sub 2}|) and a naked singularity. We also address the scaling limit associated with one-half supersymmetric solution with only one angular momentum.
140116815
What is a chiral 2 d CFT ? And what does it have to do with extremal black holes ?
The near horizon limit of the extremal BTZ black hole is a “self-dual orbifold” of AdS3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.
118845292
The Relaxed Three-Algebras: Their Matrix Representation and Implications for Multi M2-brane Theory
We argue that one can relax the requirements of the non-associative threealgebras recently used in constructing D = 3 N = 8 superconformal field theories, and introduce the notion of “relaxed three-algebras”. We present a specific realization of the relaxed three-algebras in terms of classical Lie algebras with a matrix representation, endowed with a non-associative four-bracket structure which is prescribed to replace the three-brackets of the three-algebras. We show that both the so(4)-based solutions as well as the cases with non-positive definite metric find a uniform description in our setting. We discuss the implications of our four-bracket representation for the D = 3, N = 8 and multi M2-brane theory and show that our setup can shed light on the problem of negative kinetic energy degrees of freedom of the Lorentzian case.
882035
Black holes in supergravity: the non-BPS branch
We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire moduli space and that there is always a non-zero gap above the BPS bound.