<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>Supergravity with loop quantum gravity methods and quantization of the SUSY constraint

Eder, Konstantin; Sahlmann, Hanno

doi:10.1103/physrevd.103.046010

Cited by 9 publications

(11 citation statements)

References 31 publications

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“…Hence, in this way, one reobtains the ordinary field equations of real N = 1 supergravity. The canonical analysis of chiral N = 1 supergravity has been investigated in [8,9,14] and, for arbitrary (real) Barbero-Immirzi parameters in [28,30,31] and even higher spacetime dimensions in [16,17]. Here, we will follow [28], where the results for the 3+1decomposition of the Holst action are summarized in the appendix B.…”

Section: Jhep03(2021)064mentioning

confidence: 99%

“…This is an important feature in canonical quantum supergravity and the Poisson relation (3.76) poses strong reglementations on the quantization of the constraints and therefore may fix also some of the quantization ambiguities. In [28], the SUSY constraint has been investigated in the full theory of LQG with real variables. However, the precise relation to the Hamiltonian constraint via studying the quantum algebra has not been considered yet, due to the complexity of the resulting quantum operators.…”

Section: The Susy Constraints and The Quantum Algebramentioning

confidence: 99%

“…We would like to highlight the following points. Some of the apparent difficulties with quantizing the full theory while maintaining manifest supersymmetry are the necessity of a non-compact structure group, the complicated reality conditions, the fact that Haar measures on quantum groups are typically not positive definite, and the complicated constraints [27,28]. However, one can take some encouragement from the fact that in the model we considered, these problems turned out to be solvable.…”

Section: Jhep03(2021)064mentioning

confidence: 99%

“…with γ * := iγ 0 γ 1 γ γ 3 the highest rank Clifford algebra element also commonly denoted by γ In [28], the canonical analysis of the Holst action of non-extended D = 4 anti-de Sitter supergravity for arbitrary Barbero-Immirzi parameters was considered. As we will need the results for the special case β = ±i in the main text, especially in section 2, let us briefly state the form of the constraints in the canonical theory.…”

Section: Jhep03(2021)064mentioning

confidence: 99%

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Supersymmetric minisuperspace models in self-dual loop quantum cosmology

Eder

Sahlmann

2021

J. High Energ. Phys.

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In this paper, we study a class of symmetry reduced models of $$ \mathcal{N} $$ N = 1 super- gravity using self-dual variables. It is based on a particular Ansatz for the gravitino field as proposed by D’Eath et al. We show that the essential part of the constraint algebra in the classical theory closes. In particular, the (graded) Poisson bracket between the left and right supersymmetry constraint reproduces the Hamiltonian constraint.For the quantum theory, we apply techniques from the manifestly supersymmetric approach to loop quantum supergravity, which yields a graded analog of the holonomy-flux algebra and a natural state space.We implement the remaining constraints in the quantum theory. For a certain subclass of these models, we show explicitly that the (graded) commutator of the supersymmetry constraints exactly reproduces the classical Poisson relations. In particular, the trace of the commutator of left and right supersymmetry constraints reproduces the Hamilton constraint operator. Finally, we consider the dynamics of the theory and compare it to a quantization using standard variables and standard minisuperspace techniques.

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Section: Jhep03(2021)064mentioning

confidence: 99%

Section: The Susy Constraints and The Quantum Algebramentioning

confidence: 99%

Section: Jhep03(2021)064mentioning

confidence: 99%

Section: Jhep03(2021)064mentioning

confidence: 99%

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Supersymmetric minisuperspace models in self-dual loop quantum cosmology

Eder

Sahlmann

2021

J. High Energ. Phys.

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“…in [54,57], and terms of a constrained super BF-theory in [55]. Finally, these considerations have also been extended to include real variables in [37,53,56] as well as Bodendorfer et al [62][63][64] in context of higher dimensional SUGRA theories. Finally boundaries in supergravity in the framework of LQG have been discussed using self-dual variables already a long time ago in [49,50].…”

Section: Introductionmentioning

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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