Dual description of supergravity MacDowell-Mansouri theory

García‐Compeán, Hugo; Nieto, J. A.; Obregón, O.; Ramı́rez, C.

doi:10.1103/physrevd.59.124003

Cited by 20 publications

(26 citation statements)

References 29 publications

(47 reference statements)

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“…This is done simply by promoting the gauge group SO(3,2) to the supergroup OSp(1|4). This theory was also studied in the context of gravitational duality and a parent action was constructed and its dual action was given in [30]. For 3D Chern-Simons theories this approach simplifies considerably.…”

Section: Gravitational Duality In Form Theories Of Gravitymentioning

confidence: 99%

New Reflections on Gravitational Duality

2018

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In general terms duality consists of two descriptions of one physical system by using degrees of freedom of different nature. There are different kinds of dualities and they have been extremely useful to uncover the underlying strong coupling dynamics of gauge theories in various dimensions and those of the diverse string theories. Perhaps the oldest example exhibiting this property is Maxwell theory, which interchanges electric and magnetic fields. An extension of this duality involving the sources is also possible if the magnetic monopole is incorporated. At the present time a lot has been understood about duality in non-Abelian gauge theories as in the case of N = 4 supersymmetric gauge theories in four dimensions or in the Seiberg-Witten duality for N = 2 theories. Moreover, a duality that relates a gravitational theory (or a string theory) and a conformal gauge theory, as in the case of gauge/gravity correspondence, have been also studied with considerable detail. The case of duality between two gravitational theories is the so called gravitational duality. At the present time, this duality has not been exhaustively studied, however some advances have been reported in the literature. In the present paper we give a general overview of this subject. In particular we will focus on non-Abelian dualities, applied to various theories of gravity as developed by the authors, based in the Rocek-Verlinde duality procedure. Finally, as a new development in this direction, we study the gravitational duality in Hitchin's gravity in seven and six dimensions and their relation is also discussed.

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Section: Gravitational Duality In Form Theories Of Gravitymentioning

confidence: 99%

New Reflections on Gravitational Duality

2018

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“…11 Sometimes also called exterior covariant differential. 12 Which is not the case of the connection 1-forms ω α β , despite the name. More precisely, the ω α β are not true indexed forms, i.e., there does not exist a tensor field ω such that ω(e i , e β , ϑ α ) = ω α β (e i ).…”

Section: A1 Properties Of Dmentioning

confidence: 99%

Rigorous formulation of duality in gravitational theories

Rocha¹,

Rodrigues²

2010

J. Phys. A: Math. Theor.

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“…In this expression, we recognize the Lagrangian proposed by Nieto, Socorro and Obregón [10], which generalizes the corresponding Lagrangian (27) to the self-dual case. A generalization of (39) can be achieved by means of the action [19]…”

Section: -Superfield Formalism Of Self-dual Macdowell-mansourimentioning

confidence: 99%

Superfield description of a self-dual supergravity in the context of MacDowell–Mansouri theory

Nieto¹

2006

Class. Quantum Grav.

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Using MacDowell-Mansouri theory, in this work, we investigate a superfield description of the self-dual supergravity a la Ashtekar. We find that in order to reproduce previous results on supersymmetric Ashtekar formalism, it is necessary to properly combine the supersymmetric field-strength in the Lagrangian. We extend our procedure to the case of supersymmetric Ashtekar formalism in eight dimensions.

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Dual description of supergravity MacDowell-Mansouri theory

Cited by 20 publications

References 29 publications

New Reflections on Gravitational Duality

New Reflections on Gravitational Duality

Rigorous formulation of duality in gravitational theories

Superfield description of a self-dual supergravity in the context of MacDowell–Mansouri theory

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