43 research outputs found
Dirac field and gravity in NC model
Action for the Dirac spinor field coupled to gravity on noncommutative (NC)
Moyal-Weyl space-time is obtained without prior knowledge of the metric tensor.
We emphasise gauge origins of gravity (i.e. metric structure) and its
interaction with fermions by demonstrating that a classical action invariant
under gauge transformations can be exactly reduced to the Dirac
action in curved space-time after breaking the original symmetry down to the
local Lorentz symmetry. The commutative, invariant action
can be straightforwardly deformed via Moyal-Weyl -product to its NC
invariant version which can be expanded perturbatively in the
powers of the deformation parameter using the Seiberg-Witten map. The
gravity-matter couplings in the expansion arise as an effect of the gauge
symmetry breaking. We calculate in detail the first order NC correction to the
classical Dirac action in curved space-time and show that it does not vanish.
This significant feature of the presented model enables us to potentially
observe the NC effects already at the lowest perturbative order. Moreover, NC
effects are apparent even in the flat space-time limit. We analyse NC
modification of the Dirac equation, Feynman propagator and dispersion relation
for electrons in Minkowski space-time.Comment: 37 pages, no figures, expanded version, misprints correcte
SO(2; 3) NONCOMMUTATIVE GRAVITY MODEL
In this paper the noncommutative gravity is treated as a gauge theory ofthe noncommutative SO(2; 3)* group, while the noncommutativity is canonical. The Seiberg-Witten (SW) map is used to express noncommutative elds in terms of the corresponding commutative elds. The commutative limit of the model is the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are zeroth, rst, . . . and fourth power of the curvature tensor. Finally, we discuss physical conse-quences of those correction terms in the limit of big cosmological constant
Page Curve for Eternal Schwarzschild Black Hole in Dimensionally-Reduced Model of Dilaton Gravity
As a contribution to the subject of the information loss paradox in
(1+1)-dimensional gravitational systems, we study a model of (1+1)-dimensional
dilaton gravity derived from the four-dimensional Einstein-Hilbert action by
dimensional reduction. The reduced action involves the cosmological constant
and admits black hole solutions. After including the back-reaction of quantum
fields to 1-loop order, we solve the semi-classical field equations
perturbatively and compute the quantum correction to the Hawking temperature.
We consider the quantum extremal surface approach and invoke the ``island
rule'' to compute the fine-grained entropy of the Hawking radiation for an
eternal Schwarzschild black hole and demonstrate that it follows the unitary
Page curve.Comment: 11 pages, 4 figure
Noncommutative Electrodynamics from Model of Noncommutative Gravity
In our previous work we have constructed a model of noncommutative (NC)
gravity based on gauge symmetry. In this paper we extend the
model by adding matter fields: fermions and a gauge field. Using the
enveloping algebra approach and the Seiberg-Witten map we construct actions for
these matter fields and expand the actions up to first order in the
noncommutativity (deformation) parameter. Unlike in the case of pure NC
gravity, first non-vanishing NC corrections are linear in the noncommutativity
parameter. In the flat space-time limit we obtain a non-standard NC
Electrodynamics. Finally, we discuss effects of noncommutativity on
relativistic Landau levels of an electron in a constant background magnetic
field and in addition we calculate the induced NC magnetic dipole moment of the
electron.Comment: 21 pages, no figure
AdS-inspired noncommutative gravity on the Moyal plane
We consider noncommutative gravity on a space with canonical noncommutativity
that is based on the commutative MacDowell-Mansouri action. Gravity is treated
as gauge theory of the noncommutative group and the
Seiberg-Witten (SW) map is used to express noncommutative fields in terms of
the corresponding commutative fields. In the commutative limit the
noncommutative action reduces to the Einstein-Hilbert action plus the
cosmological term and the topological Gauss-Bonnet term. After the SW expansion
in the noncommutative parameter the first order correction to the action, as
expected, vanishes. We calculate the second order correction and write it in a
manifestly gauge covariant way.Comment: 22 pages, no figures, final versio
Noncommutative Gauge Theory of Gravity
Topological gravity (in the sense that it is metric-independent) in a
-dimensional spacetime can be formulated as a gauge field theory for the
AdS gauge group by adding a multiplet of scalar fields. These
scalars can break the gauge invariance of the topological gravity action, thus
making a connection with Einstein's gravity. This review is about a
noncommutative (NC) star-product deformation of the four-dimensional AdS gauge
theory of gravity, including Dirac spinors and the Yang-Mills field. In
general, NC actions can be expanded in powers of the canonical noncommutativity
parameter using the Seiberg-Witten map. The leading-order term of the
expansion is the classical action, while the higher-order -dependent
terms are interpreted as new types of coupling between classical fields due to
spacetime noncommutativity. We study how these perturbative NC corrections
affect the field equations of motion and derive some phenomenological
consequences, such as NC-deformed Landau levels of an electron. Finally, we
discuss how topological gravity in four dimensions (both classical and
noncommutative) appears as a low-energy sector of five-dimensional Chern-Simons
gauge theory in the sense of Kaluza-Klein reduction.Comment: 18 pages; Contribution to the special issue of the European Physical
Journal on "Noncommutativity and Physics
Two-loop Back-reaction in 2D Dilaton Gravity
We calculate the two-loop quantum corrections, including the back-reaction of
the Hawking radiation, to the one-loop effective metric in a unitary gauge
quantization of the CGHS model of 2d dilaton gravity. The corresponding
evaporating black hole solutions are analysed, and consistent semi-classical
geometries appear in the weak-coupling region of the spacetime when the width
of the matter pulse is larger then the short-distance cutoff. A consistent
semi-classical geometry also appears in the limit of a shock-wave matter. The
Hawking radiation flux receives non-thermal corrections such that it vanishes
for late times and the total radiated mass is finite. There are no static
remnants for matter pulses of finite width, although a BPP type static remnant
appears in the shock-wave limit. Semi-classical geometries without curvature
singularities can be obtained as well. Our results indicate that higher-order
loop corrections can remove the singularities encountered in the one-loop
solutions.Comment: 28 pages, 6 Postscript figures, LaTe
-Algebras of Einstein-Cartan-Palatini Gravity
We give a detailed account of the cyclic -algebra formulation of
general relativity with cosmological constant in the Einstein-Cartan-Palatini
formalism on spacetimes of arbitrary dimension and signature, which encompasses
all symmetries, field equations and Noether identities of gravity without
matter fields. We present a local formulation as well as a global covariant
framework, and an explicit isomorphism between the two -algebras in
the case of parallelizable spacetimes. By duality, we show that our
-algebras describe the complete BV-BRST formulation of
Einstein-Cartan-Palatini gravity. We give a general description of how to
extend on-shell redundant symmetries in topological gauge theories to off-shell
correspondences between symmetries in terms of quasi-isomorphisms of
-algebras. We use this to extend the on-shell equivalence between
gravity and Chern-Simons theory in three dimensions to an explicit
-quasi-isomorphism between differential graded Lie algebras which
applies off-shell and for degenerate dynamical metrics. In contrast, we show
that there is no morphism between the -algebra underlying gravity and
the differential graded Lie algebra governing theory in four dimensions.Comment: 84 pages; v2: minor corrections and changes; v3: exposition improved
and references added; Final version to be published in Journal of
Mathematical Physic