Law Department

The undersigned, under the sanction of the Board of Trustees, will open in Athens, on 1st of October next, a Law School, in connection with the University of Georgia. Believing that such a school is demanded by the wants of the profession and of the State, and looking alone to its own income for the reward of our labor, we shall devote our energies to the effort, which we will not lightly abandon. We expect success only by deserving it. If we deserve it, we shall not fear obtaining it

BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.Comment: 41 pages, no figures, corrected typos, updated introduction, sections 5, 7.1, 7.2 with examples, conclusion with all basic results unchanged, corrected formulae (3.27), (7.138), (7.140), added dimensional reduction part with formulae (5.34)-(5.48), (7.8)-(7.10), (7.131)-(7.136), (7.143)-(7.164), added Refs. 52, 53, 54, examples for massive fields developed by 2 way

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2

Braneworld Cosmology in (Anti)--de Sitter Einstein--Gauss--Bonnet--Maxwell Gravity

Braneworld cosmology for a domain wall embedded in the charged (Anti)-de Sitter-Schwarzschildblack hole of the five--dimensional Einstein-Gauss-Bonnet-Maxwell theory is considered. The effective Friedmann equation for the brane is derived by introducing the necessary surface counterterms required for a well-defined variational principlein the Gauss--Bonnet theory and for the finiteness of the bulk space. The asymptotic dynamics of the brane cosmology is determined and it is found that solutions with vanishingly small spatial volume are unphysical. The finiteness of the bulk action is related to the vanishing of the effective cosmological constant on the brane. An analogy between the Friedmann equation and a generalized Cardy--Verlinde formula is drawn.Comment: LaTex file 28 pages, typos corrected, one reference is adde

(Twisted) Toroidal Compactification of pp-Waves

The maximally supersymmetric type IIB pp-wave is compactified on spatial circles, with and without an auxiliary rotational twist. All spatial circles of constant radius are identified. Without the twist, an S$^1$ compactification can preserve 24, 20 or 16 supercharges. $T^2$ compactifications can preserve 20, 18 or 16 supercharges; $T^3$ compactifications can preserve 18 or 16 supercharges and higher compactifications preserve 16 supercharges. The worldsheet theory of this background is discussed. The T-dual and decompactified type IIA and M-theoretic solutions which preserve 24 supercharges are given. Some comments are made regarding the AdS parent and the CFT description.Comment: 22 pages REVTeX 4 and AMSLaTeX. v3: References and a paragraph on nine dimensional Killing spinors were added. v4: A few typos corrected and a footnote was modifie

Dynamics of Higher Spin Fields and Tensorial Space

The structure and the dynamics of massless higher spin fields in various dimensions are reviewed with an emphasis on conformally invariant higher spin fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal higher spin fields constitute the quantum spectrum of a twistor-like particle propagating in tensorial spaces of corresponding dimensions. We give a detailed analysis of the field equations of the model and establish their relation with known formulations of free higher spin field theory.Comment: JHEP3 style, 40 pages; v2 typos corrected, comments and references added; v3 published versio

The dS/CFT Correspondence and the Big Smash

Recent observations suggest that the cosmological equation-of-state parameter w is close to -1. To say this is to imply that w could be slightly less than -1, which leads to R.Caldwell's "Phantom cosmologies". These often have the property that they end in a "Big Smash", a final singularity in which the Universe is destroyed in a finite proper time by excessive *expansion*. We show that, classically, this fate is not inevitable: there exist Smash-free Phantom cosmologies, obtained by a suitable perturbation of the deSitter equation of state, in which the spacetime is in fact asymptotically deSitter. [Contrary to popular belief, such cosmologies, which violate the Dominant Energy Condition, do not necessarily violate causality.] We also argue, however, that the physical interpretation of these classically acceptable spacetimes is radically altered by ``holography'', as manifested in the dS/CFT correspondence. It is shown that, if the boundary CFTs have conventional properties, then recent ideas on "time as an inverse renormalization group flow" can be used to rule out these cosmologies. Very recently, however, it has been argued that the CFTs in dS/CFT are of a radically unconventional form, and this opens up the possibility that Smash-free Phantom spacetimes offer a simple model of a "bouncing" cosmology in which the quantum-mechanical entanglement of the field theories in the infinite past and future plays an essential role.Comment: 22 pages, clarification of triple analytic continuation, additional Comments added in the light of hep-th/020724

Uniqueness of M-theory PP-Wave Background with Extra Supersymmetries

We examine Killing spinor equations of the general eleven-dimensional pp-wave backgrounds, which contain a scalar H(x^m,x^-) in the metric and a three-form \xi(x^m,x^-) in the flux. Considering non-harmonic extra Killing spinors, we show that if the backgrounds admit at least one extra Killing spinor in addition to the standard 16 Killing spinors, they can be reduced to the form with H=A_{mn}(x^-)x^mx^n and \xi(x^-) modulo coordinate transformations. We further examine the cases in which the extra Killing spinor is characterized by a set of Cartan matrices. The super-isometry algebras of the resulting backgrounds are also derived.Comment: 25 pages, LaTeX2e, comments added, version to appear in PR

Localized Intersections of Non-Extremal p-branes and S-branes

A class of solutions to Supergravity in 10 or 11 dimensions is presented which extends the non-standard or semi-local intersections of Dp-branes to the case of non-extremal p-branes. The type of non-extremal solutions involved in the intersection is free and we provide two examples involving black-branes and/or D-\bar{D} systems. After a rotation among the time coordinate and a relatively transverse radial direction the solutions admit the interpretation of an intersection among D-branes and S-branes. We speculate on the relevance of these configurations both to study time dependent phenomena in the AdS/CFT correspondence as well as to construct cosmological brane-world scenarios within String Theory admitting accelerating expansion of the Universe.Comment: 31 pages, latex file; v2: typos corrected and references adde