175 research outputs found
Twistors, CFT and Holography
According to one of many equivalent definitions of twistors a (null) twistor
is a null geodesic in Minkowski spacetime. Null geodesics can intersect at
points (events). The idea of Penrose was to think of a spacetime point as a
derived concept: points are obtained by considering the incidence of twistors.
One needs two twistors to obtain a point. Twistor is thus a ``square root'' of
a point. In the present paper we entertain the idea of quantizing the space of
twistors. Twistors, and thus also spacetime points become operators acting in a
certain Hilbert space. The algebra of functions on spacetime becomes an
operator algebra. We are therefore led to the realm of non-commutative
geometry. This non-commutative geometry turns out to be related to conformal
field theory and holography. Our construction sheds an interesting new light on
bulk/boundary dualities.Comment: 21 pages, figure
Gravitons and a complex of differential operators
Gravity is now understood to become simple on-shell. We sketch how it becomes
simple also off-shell, when reformulated appropriately. Thus, we describe a
simple Lagrangian for gravitons that makes use of a certain complex of
differential operators. The Lagrangian is constructed analogously to that of
Maxwell's theory, just using a different complex. The complex, and therefore
also our description of gravitons, makes sense on any half-conformally flat
four-dimensional manifold.Comment: 8 pages, 2 diagram
GR uniqueness and deformations
In the metric formulation gravitons are described with the parity symmetric
representation of Lorentz group. General Relativity is
then the unique theory of interacting gravitons with second order field
equations. We show that if a chiral representation is used
instead, the uniqueness is lost, and there is an infinite-parametric family of
theories of interacting gravitons with second order field equations. We use the
language of graviton scattering amplitudes, and show how the uniqueness of GR
is avoided using simple dimensional analysis. The resulting distinct from GR
gravity theories are all parity asymmetric, but share the GR MHV amplitudes.
They have new all same helicity graviton scattering amplitudes at every
graviton order. The amplitudes with at least one graviton of opposite helicity
continue to be determinable by the BCFW recursion.Comment: v2: published version, 19 pages, description of the complexified
setting expande
One-loop beta-function for an infinite-parameter family of gauge theories
We continue to study an infinite-parametric family of gauge theories with an
arbitrary function of the self-dual part of the field strength as the
Lagrangian. The arising one-loop divergences are computed using the background
field method. We show that they can all be absorbed by a local redefinition of
the gauge field, as well as multiplicative renormalisations of the couplings.
Thus, this family of theories is one-loop renormalisable. The infinite set of
beta-functions for the couplings is compactly stored in a renormalisation group
flow for a single function of the curvature. The flow is obtained explicitly.Comment: 17 pages, no figure
Gravity as BF theory plus potential
Spin foam models of quantum gravity are based on Plebanski's formulation of
general relativity as a constrained BF theory. We give an alternative
formulation of gravity as BF theory plus a certain potential term for the
B-field. When the potential is taken to be infinitely steep one recovers
general relativity. For a generic potential the theory still describes gravity
in that it propagates just two graviton polarizations. The arising class of
theories is of the type amenable to spin foam quantization methods, and, we
argue, may allow one to come to terms with renormalization in the spin foam
context.Comment: 7 pages, published in Proceedings of the Second Workshop on Quantum
Gravity and Noncommutative Geometry (Lisbon, Portugal
Metric Lagrangians with two propagating degrees of freedom
There exists a large class of generally covariant metric Lagrangians that
contain only local terms and describe two propagating degrees of freedom.
Trivial examples can be be obtained by applying a local field redefinition to
the Lagrangian of general relativity, but we show that the class of two
propagating degrees of freedom Lagrangians is much larger. Thus, we exhibit a
large family of non-local field redefinitions that map the Einstein-Hilbert
Lagrangian into ones containing only local terms. These redefinitions have
origin in the topological shift symmetry of BF theory, to which GR is related
in Plebanski formulation, and can be computed order by order as expansions in
powers of the Riemann curvature. At its lowest non-trivial order such a field
redefinition produces the (Riemann)^3 invariant that arises as the two-loop
quantum gravity counterterm. Possible implications for quantum gravity are
discussed.Comment: 4 page
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