Plebański formulation of self-dual gravity

E811628

differential-form formulation of gravity formulation of general relativity self-dual gauge theory theory of gravity

The Plebański formulation of self-dual gravity is a reformulation of general relativity that expresses gravity as a self-dual gauge theory using differential forms, providing a powerful framework for studying classical and quantum aspects of spacetime.

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All labels observed (3)

Label	Occurrences
Plebański formulation of self-dual gravity canonical	1
chiral (self-dual) Plebański action	1
self-dual Ashtekar connection	1

How this entity was disambiguated

This entity first appeared as the object of triple T9637314 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Plebański formulation of self-dual gravity
Context triple: [Jerzy Plebański, hasConcept, Plebański formulation of self-dual gravity]

A. Einstein–Yang–Mills equations
The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
B. Bondi–Metzner–Sachs symmetry
Bondi–Metzner–Sachs symmetry is an infinite-dimensional group of asymptotic spacetime symmetries in general relativity that characterizes the gravitational field at null infinity, especially in the context of gravitational radiation.
C. Born–Infeld electrodynamics
Born–Infeld electrodynamics is a nonlinear modification of classical Maxwell theory proposed to remove the infinite self-energy of point charges by introducing an upper bound on the electromagnetic field strength.
D. Polyakov action in string theory
The Polyakov action in string theory is a reformulation of the string’s dynamics that treats the worldsheet metric as an independent field, providing a convenient starting point for quantizing strings and analyzing their conformal symmetry.
E. Klebanov–Tseytlin background in type IIB supergravity
The Klebanov–Tseytlin background in type IIB supergravity is a celebrated solution describing fractional D3-branes on a conifold, providing a key holographic dual for a four-dimensional cascading gauge theory.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Plebański formulation of self-dual gravity
Target entity description: The Plebański formulation of self-dual gravity is a reformulation of general relativity that expresses gravity as a self-dual gauge theory using differential forms, providing a powerful framework for studying classical and quantum aspects of spacetime.

A. Einstein–Yang–Mills equations
The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
B. Bondi–Metzner–Sachs symmetry
Bondi–Metzner–Sachs symmetry is an infinite-dimensional group of asymptotic spacetime symmetries in general relativity that characterizes the gravitational field at null infinity, especially in the context of gravitational radiation.
C. Born–Infeld electrodynamics
Born–Infeld electrodynamics is a nonlinear modification of classical Maxwell theory proposed to remove the infinite self-energy of point charges by introducing an upper bound on the electromagnetic field strength.
D. Polyakov action in string theory
The Polyakov action in string theory is a reformulation of the string’s dynamics that treats the worldsheet metric as an independent field, providing a convenient starting point for quantizing strings and analyzing their conformal symmetry.
E. Klebanov–Tseytlin background in type IIB supergravity
The Klebanov–Tseytlin background in type IIB supergravity is a celebrated solution describing fractional D3-branes on a conifold, providing a key holographic dual for a four-dimensional cascading gauge theory.
F. None of above. chosen

Statements (45)

Predicate	Object
instanceOf	differential-form formulation of gravity ⓘ formulation of general relativity ⓘ self-dual gauge theory ⓘ theory of gravity ⓘ
aimsTo	provide a convenient starting point for quantization of gravity ⓘ reformulate general relativity as a gauge theory ⓘ
allows	inclusion of a cosmological constant ⓘ
applicableTo	Euclidean signature ⓘ Lorentzian signature ⓘ
category	geometric formulations of gravity ⓘ self-dual gravity theories ⓘ
coreConcept	BF-type action with constraints ⓘ self-dual curvature ⓘ self-dual part of the spin connection ⓘ simplicity constraints ⓘ
describes	Einstein’s equations ⓘ linked to: Einstein field equations gravity as a gauge theory ⓘ vacuum general relativity ⓘ
dimension	four-dimensional spacetime ⓘ
feature	equations of motion reproduce Einstein’s equations with or without cosmological constant ⓘ uses complex self-dual variables ⓘ
field	general relativity ⓘ quantum gravity ⓘ theoretical physics ⓘ
historicalDevelopment	precedes the introduction of Ashtekar variables ⓘ
inspired	Ashtekar’s self-dual formulation of general relativity ⓘ
involves	SU(2) or SL(2,C) gauge symmetry ⓘ chiral decomposition of the Lorentz group ⓘ
mathematicalStructure	action principle written in terms of a two-form field and a connection ⓘ constraints that enforce metricity ⓘ
namedAfter	Jerzy Plebański ⓘ
relatedTo	Ashtekar variables ⓘ BF theory ⓘ Palatini formulation of general relativity ⓘ chiral formulations of gravity ⓘ loop quantum gravity ⓘ spin foam models ⓘ tetrad formulation of gravity ⓘ
usedIn	classical analysis of gravitational instantons ⓘ construction of spin foam amplitudes ⓘ studies of self-dual solutions in general relativity ⓘ
uses	Lagrange multipliers ⓘ connection one-forms ⓘ differential forms ⓘ self-dual two-forms ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Jerzy Plebański → hasConcept → Plebański formulation of self-dual gravity ⓘ

Plebański action for gravity → relatedTo → self-dual Ashtekar connection ⓘ

linked to: Plebański formulation of self-dual gravity

Plebański action for gravity → hasVariant → chiral (self-dual) Plebański action ⓘ