Immirzi parameter and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>θ</mml:mi></mml:math>ambiguity in de Sitter MacDowell-Mansouri supergravity

Obregón, O.; Ortega-Cruz, M.; Sabido, M.

doi:10.1103/physrevd.85.124061

Cited by 11 publications

(14 citation statements)

References 29 publications

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“…This explicit identification of the Immirzi parameter in terms of the ambiguity for the classical description of three dimensional gravity is a novel result of this work. As already suggested in [12,21,23] the "Immirzi parameter" is analogous to the "θ-term" in Yang-Mills theories. Furthermore in [13] the transformation of the Chern-Simons gravity partition function was studied and it was concluded that eq.…”

Section: Reduction To (2+1)-dimmentioning

confidence: 67%

“…global coefficients that can be reabsorbed in the bare values of λ and G N . An action similar to (18) was obtained in [21] (see also [23]) from different arguments that led to a modification of the MM action by the introduction of a θ-term -in analogy to a Yang-Mills theory -whose coefficient is related to our + τ + − τ .…”

Section: (Anti-)self-dual Gauge Theory Of Gravitymentioning

confidence: 86%

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Topological M-theory, self-dual gravity and the Immirzi parameter

Chagoya

Sabido

2018

Class. Quantum Grav.

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Working in the first order formalism of gravity, we propose an action that combines the self and anti-self-dual parts of the curvature and comprises all the diffeomorphism invariant Lagrangians that one can consider in this formalism. The action that we propose is motivated by (A)dS gauge theories of gravity. We use this action to derive the (2+1)-dimensional version of the Immirzi parameter. Our derivation relates explicitly the Immirzi parameter to the existence of two classically equivalent actions for the description of gravity in (2+1) dimensions, namely the standard and exotic actions introduced by Witten in the description of (2+1) gravity as a gauge theory. This relation had been conjectured previously in the literature, but not derived.

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Section: Reduction To (2+1)-dimmentioning

confidence: 67%

Section: (Anti-)self-dual Gauge Theory Of Gravitymentioning

confidence: 86%

Topological M-theory, self-dual gravity and the Immirzi parameter

Chagoya

Sabido

2018

Class. Quantum Grav.

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“…Thus, we see, up to a topological term, (11) indeed reduces to the Holst action of N = 1, D = 4 AdS supergravity [61] and which in the limit of a vanishing cosmological constant yields the respective action of Poincaré supergravtiy [37,56,58]. To see that ( 20) is in fact purely topological, note that, by the Bianchi-identity, we have…”

Section: Holst-macdowell-mansouri Action Of N = 1 Sugramentioning

confidence: 79%

“…A derivation of the Holst action of D = 4, N = 1 supergravity via a MacDowell-Mansouri action, by adding a suitable topological term and treating β as kind of a θ-ambiguity similar to Yang-Mills theory, has been given in [61] and for the special case of the chiral theory in [60]. Here, we want to follow the ideas of [70,71] in the context of classical first order Einstein gravity and its reformulation in terms of constrained BF-theory [72].…”

Section: Holst-macdowell-mansouri Action Of N = 1 Sugramentioning

confidence: 99%

Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

Eder,

Sahlmann

2021

Preprint

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In this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the Holst variant of the MacDowell-Mansouri action for N = 1 and N = 2 pure AdS supergravity in D = 4 for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the N = 2 case, it follows that this amounts to the introduction of a θ-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the θ-ambiguity of gauge theory. We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry. Moreover, we will show that demanding supersymmetry invariance at the boundary yields a boundary term corresponding to a super Chern-Simons theory with OSp(N |2) gauge group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D'Auria-Fré approach in context of the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravity.

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“…In the 70's MacDowell and Mansouri (MM) [10][11][12] were successful in finding a gauge theory for gravity following this strategy. In MM formulation, SO(4, 1) symmetry must be spontaneously broken down to SO(3, 1) in order to reproduce the usual four-dimensional geometry of gravity.…”

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confidence: 99%

Comments on the symmetry breaking condition in MacDowell-Mansouri action

Díaz-Saldaña,

Sabido,

López-Domínguez

et al. 2020

Preprint

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In this work we study the symmetry breaking conditions, given by a (anti)de Sittervalued vector field, of a full (anti)de Sitter-invariant MacDowell-Mansouri inspired action. We show that under these conditions the action breaks down to General Relativity with a cosmological constant, the four dimensional topological invariants, as well as the Holst term. We obtain the equations of motion of this action, and analyze the symmetry breaking conditions.

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Immirzi parameter andθambiguity in de Sitter MacDowell-Mansouri supergravity

Cited by 11 publications

References 29 publications

Topological M-theory, self-dual gravity and the Immirzi parameter

Topological M-theory, self-dual gravity and the Immirzi parameter

Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

Comments on the symmetry breaking condition in MacDowell-Mansouri action

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