Dirac field and gravity in NC SO(2,3)⋆SO(2,3)_\star 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 $SO(2,3)$ gauge transformations can be exactly reduced to the Dirac action in curved space-time after breaking the original symmetry down to the local Lorentz $SO(1,3)$ symmetry. The commutative, $SO(2,3)$ invariant action can be straightforwardly deformed via Moyal-Weyl $\star$-product to its NC $SO(2,3)_\star$ 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 SO(2,3)⋆SO(2,3)_\star Model of Noncommutative Gravity

In our previous work we have constructed a model of noncommutative (NC) gravity based on $SO(2,3)_\star$ gauge symmetry. In this paper we extend the model by adding matter fields: fermions and a $U(1)$ 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 $SO(1,3)_\star$ 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 SO(2,3)⋆SO(2,3)_{\star} Gauge Theory of Gravity

Topological gravity (in the sense that it is metric-independent) in a $2n$-dimensional spacetime can be formulated as a gauge field theory for the AdS gauge group $SO(2,2n-1)$ 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 $\theta$ using the Seiberg-Witten map. The leading-order term of the expansion is the classical action, while the higher-order $\theta$-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

L∞L_{\infty}-Algebras of Einstein-Cartan-Palatini Gravity

We give a detailed account of the cyclic $L_\infty$-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 $L_\infty$-algebras in the case of parallelizable spacetimes. By duality, we show that our $L_\infty$-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 $L_\infty$-algebras. We use this to extend the on-shell equivalence between gravity and Chern-Simons theory in three dimensions to an explicit $L_\infty$-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 $L_\infty$-algebra underlying gravity and the differential graded Lie algebra governing $BF$ 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