Supersymmetric minisuperspace models in self-dual loop quantum cosmology

Eder, Konstantin; Sahlmann, Hanno

doi:10.1007/jhep03(2021)064

Cited by 9 publications

(22 citation statements)

References 40 publications

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“…This scalar product is then invariant under local SL(2, C)-gauge transformations. As it is shown in [45], in the framework of symmetry reduced models, this in fact solves the reality conditions (176). This is also precisely the standard scalar product as used for instance in [21] in context of Dirac fermions or in [23] in context of the Rarita-Schwinger field in a complementary approach to LQSG with real variables.…”

mentioning

confidence: 57%

“…The construction of the full state space of manifest LQSG, however, still remains incomplete, due to the non-compactness of the underlying gauge group as well as the implementation of the reality conditions. However, in [45] we made some progress in this direction studying certain symmetry reduced models where the reality conditions can be implemented exactly. We therefore have provided the required mathematical tools in the last section of this present article.…”

Section: Discussionmentioning

confidence: 99%

“…The canonical analysis of chiral N = 1 supergravity has been investigated in [13] and [14] and, for arbitrary (real) Barbero-Immirzi parameters in [18,19,46] and even higher spacetime dimensions in [23,24]. Here, we will follow [45,46], where, for β = −i, the action takes the form…”

Section: The Canonical Theory and The Constraint Algebramentioning

confidence: 99%

“…models in the context supersymmetric field theories. We will use these results in [45] to study minisuperspace models in the framework of loop quantum cosmology with local supersymmetry. Let M be a H ∞ supermanifold and S be a super Lie group which in the most situations of interest will be the super Lie group of isometries of M (in fact, in most cases M will be an ordinary smooth manifold).…”

Section: A Super Linear Algebramentioning

confidence: 99%

“…Finally, the generalzation of the concept of invariant connections to the super category will be considered. This provides a mathematical solid basis to apply these results to symmetry reduced models in the framework of supersymmetric LQC which will be studied in more detail in [45].…”

Section: Introductionmentioning

confidence: 99%

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Super Cartan geometry and the super Ashtekar connection

Eder¹

2020

Preprint

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This work is devoted to the geometric approach to supergravity. More precisely, we interpret N = 1 supergravity as a super Cartan geometry which provides a link between supergravity and super Yang-Mills theory. To this end, we first review important aspects of the theory of supermanifolds and we establish a link between various different approaches. We will then use this gauge-theoretic interpretation and the methods of loop quantum gravity to canonically quantize this theory which preserves some of the underyling supersymmetry in a manifest way. More precisely, studying the chiral structure of the underlying supersymmetry algebra, we derive a graded analog of Ashtekar's self-dual variables and interpret them in terms of generalized super Cartan connections. This gives canonical supergravity the structure of a super Yang-Mills theory similar to the self-dual variables in ordinary first-order Einstein gravity which was first observed by Fülöp [14]. We then construct the parallel transport map corresponding to the super connection in mathematical rigorous way using the concept of enriched categories. This then provides the possibility of quantizing gravity and matter degrees of freedom in loop quantum gravity in a unified way. Finally, we study spatially symmetry reduced models and discuss possible applications of this approach in supersymmetric loop quantum cosmology.

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mentioning

confidence: 57%

Section: Discussionmentioning

confidence: 99%

Section: The Canonical Theory and The Constraint Algebramentioning

confidence: 99%

Section: A Super Linear Algebramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Super Cartan geometry and the super Ashtekar connection

Eder¹

2020

Preprint

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Super Cartan Geometry and the Super Ashtekar Connection

Eder

2023

Ann. Henri Poincaré

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This work is devoted to the geometric approach to supergravity. More precisely, we interpret $$\mathcal {N}=1$$ N = 1 , $$D=4$$ D = 4 supergravity as a super Cartan geometry which provides a link between supergravity and Yang–Mills theory. To this end, we first review important aspects of the theory of supermanifolds and we establish a link between various different approaches. We then introduce super Cartan geometries using the concept of so-called enriched categories. This, among other things, will enable us to implement anticommutative fermionic fields. We will then also show that non-extended $$D=4$$ D = 4 supergravity naturally arises in this framework. Finally, using this gauge-theoretic interpretation as well as the chiral structure of the underlying supersymmetry algebra, we will derive graded analoga of Ashtekar’s self-dual variables and interpret them in terms of generalized super Cartan connections. This gives canonical chiral supergravity the structure of a Yang–Mills theory with gauge supergroup similar to the self-dual variables in ordinary first-order Einstein gravity. We then construct the parallel transport map corresponding to the super connection in mathematical rigorous way using again enriched categories. This provides the possibility of quantizing gravity and matter degrees of freedom in loop quantum gravity in a unified way. Kindly check and confirm inserted city and country name are correctly identified.City and country name are correct.

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Simplicial graviton from selfdual Ashtekar variables

Wieland

2023

Class. Quantum Grav.

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In perturbative gravity, it is straight-forward to characterize the two local degrees of freedom of the gravitational field in terms of a mode expansion of the linearized perturbation. In the non-perturbative regime, we are in a more difficult position. It is not at all obvious how to construct Dirac observables that can separate the gauge orbits. Standard procedures rely on asymptotic boundary conditions or formal Taylor expansions of relational observables. In this paper, we lay out a new non-perturbative lattice approach to tackle the problem in terms of Ashtekar's self-dual formulation. Starting from a simplicial decomposition of space, we introduce a local kinematical phase space at the lattice sites. At each lattice site, we introduce a set of constraints that replace the generators of the hypersurface deformation algebra in the continuum. We show that the discretized constraints close under the Poisson bracket. The resulting reduced phase space describes two complex physical degrees of freedom representing the two radiative modes at the discretized level. The paper concludes with a discussion of the key open problems ahead and the implications for quantum gravity.

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Supersymmetric minisuperspace models in self-dual loop quantum cosmology

Cited by 9 publications

References 40 publications

Super Cartan geometry and the super Ashtekar connection

Super Cartan geometry and the super Ashtekar connection

Super Cartan Geometry and the Super Ashtekar Connection

Simplicial graviton from selfdual Ashtekar variables

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