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.
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.
122293144
WIGHTMAN FORMULATION FOR THE QUANTIZATION OF THE GRAVITATIONAL FIELD.
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 
$$\mathfrak{G}$$
.
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.
117745756
Using cosmology to constrain the topology of hidden dimensions
A four-dimensional universe, arising from a flux compactification of Type IIB string theory, contains scalar fields with a potential determined by topological and geometric parameters of the internal -hidden- dimensions. We show that inflation can be realized via rolling towards the large internal volume minima that are generic in these scenarios, and we give explicit formulae relating the microscopic parameters (e.g., the Euler number of the internal space) to the cosmological observables (e.g., the spectral index). We find that the tensor-to-scalar ratio, the running of the spectral index, and the potential energy density at the minimum are related by consistency relations and are exponentially small in the number of e-foldings. Further, requiring that these models arise as low-energy limits of string theory eliminates most of them, even if they are phenomenologically valid. In this context, this approach provides a strategy for systematically falsifying stringy inflation models.
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.
123342407
General relativity in a (2+1)-dimensional space-time: An electrically charged solution
AbstractWe have found a static electrically charged solution to the Einstein-Maxwell equations in a (2+1)-dimensional space-time. Studies of general relativity in lower dimensional space-times provide many new insights and a simplified arena for doing quantum mechanics. In (2+1)-dimensional space-time, solutions to the vacuum field equations are locally flat (point masses are conical sigularities), but when electromagnetic fields are presentTab≠O and the solutions are curved. For a static chargeQ we find
$$\mathop E\limits^ \to = Q\hat r/r$$
 andds2= −(kQ2/2π)In(rc/r)dt2 + (2π/kQ2[ln(rc/r)]−1dr2 +r2dφ2 whererc is a constant. There is a horizon atr =rc like the inner horizon of the Reisner-Nordström solution. We have produced a Kruskal extension of this metric which shows two static regions (I and III) withr rc. A spacelike slice across regions I and III shows a football-shaped universe with chargeQ at one end and −Q at the other. Slices in the dynamical regions (II and IV) show a cylindrical universe that is expanding in region II and contracting in region IV. Electromagnetic solutions to the Einstein-Maxwell field equations in lower dimensional space-times can be used to provide new insights into Kaluza-Klein theories. In terms of the Kaluza-Klein theory, for example, electromagnetic radiation in a (2+1)-dimensional space-time is really gravitational radiation in the associated (3+1)-dimensional Kaluza-Klein space-time. According to Kaluza Klein theory the absence of gravitational radiation in (2+1)-dimensional space-time implies (correctly) the absence of electromagnetic radiation in (1+1)-dimensional space-time.
119287778
Strings vs. spins on the null orbifold
A bstractWe study the null orbifold singularity in 2+1 d flat space higher spin theory as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein gravity, we first observe that despite the singular nature of this geometry, the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a resolution of the singularity in higher spin theory: a Kundt spacetime with vanishing scalar curvature invariants. We also point out that the UV divergences previously observed in the 2-to-2 tachyon tree level string amplitude on the null orbifold do not arise in the α′ → ∞ limit. We find all the divergences of the amplitude and demonstrate that the ones remaining in the tensionless limit are physical IR-type divergences. We conclude with a discussion on the meaning and limitations of higher spin (cosmological) singularity resolution and its potential connection to string theory.