693 research outputs found
Generating Functional in CFT on Riemann Surfaces II: Homological Aspects
We revisit and generalize our previous algebraic construction of the chiral
effective action for Conformal Field Theory on higher genus Riemann surfaces.
We show that the action functional can be obtained by evaluating a certain
Deligne cohomology class over the fundamental class of the underlying
topological surface. This Deligne class is constructed by applying a descent
procedure with respect to a \v{C}ech resolution of any covering map of a
Riemann surface. Detailed calculations are presented in the two cases of an
ordinary \v{C}ech cover, and of the universal covering map, which was used in
our previous approach. We also establish a dictionary that allows to use the
same formalism for different covering morphisms. The Deligne cohomology class
we obtain depends on a point in the Earle-Eells fibration over the
Teichm\"uller space, and on a smooth coboundary for the Schwarzian cocycle
associated to the base-point Riemann surface. From it, we obtain a variational
characterization of Hubbard's universal family of projective structures,
showing that the locus of critical points for the chiral action under fiberwise
variation along the Earle-Eells fibration is naturally identified with the
universal projective structure.Comment: Latex, xypic, and AMS packages. 53 pages, 1 figur
Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces
We formulate and solve the analog of the universal Conformal Ward Identity
for the stress-energy tensor on a compact Riemann surface of genus , and
present a rigorous invariant formulation of the chiral sector in the induced
two-dimensional gravity on higher genus Riemann surfaces. Our construction of
the action functional uses various double complexes naturally associated with a
Riemann surface, with computations that are quite similar to descent
calculations in BRST cohomology theory. We also provide an interpretation for
the action functional in terms of the geometry of different fiber spaces over
the Teichm\"{u}ller space of compact Riemann surfaces of genus .Comment: 38 pages. Latex2e + AmsLatex2.1. One embedded figure. One section on
the relation with the geometry of fiber spaces on the Teichmueller space and
several important references adde
Spacetime algebraic skeleton
The cosmological constant Lambda, which has seemingly dominated the primaeval
Universe evolution and to which recent data attribute a significant
present-time value, is shown to have an algebraic content: it is essentially an
eigenvalue of a Casimir invariant of the Lorentz group which acts on every
tangent space. This is found in the context of de Sitter spacetimes but, as
every spacetime is a 4-manifold with Minkowski tangent spaces, the result
suggests the existence of a "skeleton" algebraic structure underlying the
geometry of general physical spacetimes. Different spacetimes come from the
"fleshening" of that structure by different tetrad fields. Tetrad fields, which
provide the interface between spacetime proper and its tangent spaces, exhibit
to the most the fundamental role of the Lorentz group in Riemannian spacetimes,
a role which is obscured in the more usual metric formalism.Comment: 13 page
de Sitter geodesics: reappraising the notion of motion
The de Sitter spacetime is transitive under a combination of translations and
proper conformal transformations. Its usual family of geodesics, however, does
not take into account this property. As a consequence, there are points in de
Sitter spacetime which cannot be joined to each other by any one of these
geodesics. By taking into account the appropriate transitivity properties in
the variational principle, a new family of maximizing trajectories is obtained,
whose members are able to connect any two points of the de Sitter spacetime.
These geodesics introduce a new notion of motion, given by a combination of
translations and proper conformal transformations, which may possibly become
important at very-high energies, where conformal symmetry plays a significant
role.Comment: 9 pages. V2: Presentation changes aiming at clarifying the text;
version accepted for publication in Gen. Rel. Gra
A coordinate-dependent superspace deformation from string theory
Starting from a type II superstring model defined on in
a linear graviphoton background, we derive a coordinate dependent -deformed
, superspace. The chiral fermionic coordinates
satisfy a Clifford algebra, while the other coordinate algebra remains
unchanged. We find a linear relation between the graviphoton field strength and
the deformation parameter. The null coordinate dependence of the graviphoton
background allows to extend the results to all orders in .Comment: 14 pages, reference added, accepted for publication in JHE
Closed Expressions for Lie Algebra Invariants and Finite Transformations
A simple procedure to obtain complete, closed expressions for Lie algebra
invariants is presented. The invariants are ultimately polynomials in the group
parameters. The construction of finite group elements require the use of
projectors, whose coefficients are invariant polynomials. The detailed general
forms of these projectors are given. Closed expressions for finite Lorentz
transformations, both homogeneous and inhomogeneous, as well as for Galilei
transformations, are found as examples.Comment: 34 pages, ps file, no figure
de Sitter relativity: a natural scenario for an evolving Lambda
The dispersion relation of de Sitter special relativity is obtained in a
simple and compact form, which is formally similar to the dispersion relation
of ordinary special relativity. It is manifestly invariant under change of
scale of mass, energy and momentum, and can thus be applied at any energy
scale. When applied to the universe as a whole, the de Sitter special
relativity is found to provide a natural scenario for the existence of an
evolving cosmological term, and agrees in particular with the present-day
observed value. It is furthermore consistent with a conformal cyclic view of
the universe, in which the transition between two consecutive eras occurs
through a conformal invariant spacetime.Comment: V1: 11 pages. V2: Presentation changes, new discussion added, 13
page
Kinematics of a Spacetime with an Infinite Cosmological Constant
A solution of the sourceless Einstein's equation with an infinite value for
the cosmological constant \Lambda is discussed by using Inonu-Wigner
contractions of the de Sitter groups and spaces. When \Lambda --> infinity,
spacetime becomes a four-dimensional cone, dual to Minkowski space by a
spacetime inversion. This inversion relates the four-cone vertex to the
infinity of Minkowski space, and the four-cone infinity to the Minkowski
light-cone. The non-relativistic limit c --> infinity is further considered,
the kinematical group in this case being a modified Galilei group in which the
space and time translations are replaced by the non-relativistic limits of the
corresponding proper conformal transformations. This group presents the same
abstract Lie algebra as the Galilei group and can be named the conformal
Galilei group. The results may be of interest to the early Universe Cosmology.Comment: RevTex, 7 pages, no figures. Presentation changes, including a new
Title. Version to appear in Found. Phys. Let
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