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.
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.
16140829
Typicality versus thermality: an analytic distinction
In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.
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.
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.
56350886
EXTREMAL BLACK HOLES, HOLOGRAPHY AND COARSE GRAINING
I review some of the concepts at the crossroads of gravitational thermodynamics, holography and quantum mechanics. First, the origin of gravitational thermodynamics due to coarse graining of quantum information is exemplified using the half-BPS sector of SYM and its LLM description in type IIB supergravity. The notion of black holes as effective geometries, its relation to the fuzzball programme and some of the puzzles raising for large black holes are discussed. Second, I review recent progress for extremal black holes, both microscopically, discussing a constituent model for stationary extremal non-BPS black holes, and semiclassically, discussing the extremal black hole/CFT conjecture. The latter is examined from the AdS3/CFT2 perspective. Third, I review the importance of the holographic principle to encode nonlocal gravity features allowing us to relate the gravitational physics of local observers with thermodynamics and the role causality plays in these arguments by identifying horizons (screens) as diathermic walls. I speculate with the emergence of an approximate CFT in the deep IR close to any horizon and its relation with an effective dynamical description of the degrees of freedom living on these holographic screens.
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.
120008134
A wave operator for a non-linear Klein-Gordon equation
We prove the existence of a set of initial data to which correspond solutions of the nonlinear Klein-Gordon equation with a polynomial nonlinear term, which converge asymptotically, when t→+∞, to solutions of the linear Klein-Gordon equation.
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.
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.
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.