Dual description of supergravity MacDowell-Mansouri theory (original) (raw)

Gravitational duality in MacDowell-Mansouri gauge theory

Physical Review D, 1998

Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show that an analogous procedure allows to find the dual action to the gauge theory of gravity constructed by the MacDowell-Mansouri model plus the superposition of a Theta\ThetaTheta term.

Pursuing gravitational S-duality

Chaos, Solitons & Fractals, 1999

Recently a strong-weak coupling duality in non-abelian non-supersymmetric theories in four dimensions has been found. An analogous procedure is reviewed, which allows to find the 'dual action' to the gauge theory of dynamical gravity constructed by the MacDowell-Mansouri model plus the superposition of a Θ term.

The coupling of non-linear supersymmetry to supergravity

The European Physical Journal C, 2015

We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R − λ) 2 = 0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f (R) supergravity theories.

Nonlinear self-duality and supergravity

Journal of High Energy Physics, 2003

The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N = 1 supergravity, for both the old minimal and the new minimal versions of N = 1 supergravity. We derive the self-duality equation, which has to be satisfied by the action functional of any U(1) duality invariant model of a massless vector multiplet, and construct a family of self-dual nonlinear models. This family includes a curved superspace extension of the N = 1 super Born-Infeld action. The supercurrent and supertrace in such models are proved to be duality invariant. The most interesting and unexpected result is that the requirement of nonlinear self-duality yields nontrivial couplings of the vector multiplet to Kähler sigma models. We explicitly derive the couplings to general Kähler sigma models in the case when the matter chiral multiplets are inert under the duality rotations, and more specifically to the dilaton-axion chiral multiplet when the group of duality rotations is enhanced to SL(2, R).

Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity

Nuclear Physics B, 1995

We consider duality transformations in N = 2 , d = 4 Y ang{Mills theory coupled to N = 2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy`classical and quantum duality symmetries' (monodromies), incorporating T and S dualities. In particular, we shall be able to study theories (like N = 2 heterotic strings) which are formulated in symplectic basis where a`holomorphic prepotential' F does not exist, and yet give general expressions for all relevant p h ysical quantities. Duality transformations and symmetries for the N = 1 matter coupled Yang{Mills supergravity system are also exhibited. The implications of duality symmetry on all N > 2 extended supergravities are briey mentioned. We nally give the general form of the central charge and the N = 2 semiclassical spectrum of the dyonic BPS saturated states (as it comes by truncation of the N = 4 spectrum).

mathcalN\mathcal{N}mathcalN = 2 extended MacDowell-Mansouri supergravity

Journal of High Energy Physics

We construct a gauge theory based in the supergroup G = SU(2, 2|2) that generalizes MacDowell-Mansouri supergravity. This is done introducing an extended notion of Hodge operator in the form of an outer automorphism of su(2, 2|2)-valued 2-form tensors. The model closely resembles a Yang-Mills theory — including the action principle, equations of motion and gauge transformations — which avoids the use of the otherwise complicated component formalism. The theory enjoys H = SO(3, 1) × ℝ × U(1) × SU(2) off-shell symmetry whilst the broken symmetries G/H, translation-type symmetries and supersymmetry, can be recovered on surface of integrability conditions of the equations of motion, for which it suffices the Rarita-Schwinger equation and torsion-like constraints to hold. Using the matter ansatz —projecting the 1 ⊗ 1/2 reducible representation into the spin-1/2 irreducible sector — we obtain (chiral) fermion models with gauge and gravity interactions.

Gauge theory of gravity and supergravity

Physical Review D, 2006

We present a formulation of gravity in terms of a theory based on complex SU (2) gauge fields with a general coordinate invariant action functional quadratic in the field strength. Self-duality or anti-selfduality of the field strength emerges as a constraint from the equations of motion of this theory. This in turn leads to Einstein gravity equations for a dilaton and an axion conformally coupled to gravity for the self-dual constraint. The analysis has also been extended to N = 1 and 2 super Yang-Mills theory of complex SU (2) gauge fields. This leads, besides other equations of motion, to self-duality/anti-self-duality of generalized supercovariant field-strengths. The self-dual case is then shown to yield as its solutions N = 1, 2 supergravity equations respectively.

Self-Dual Supergravity and Supersymmetric Yang-Mills Theory Coupled to Green-Schwarz Superstring

International Journal of Modern Physics A, 1994

We present the canonical set of superspace constraints for self-dual supergravity, a “self-dual” tensor multiplet and a self-dual Yang-Mills multiplet with N=1 supersymmetry in the space-time with signature (+,+, −, −). For this set of constraints, the consistency of the self-duality conditions on these multiplets with supersymmetry is manifest. The energy-momentum tensors of all the self-dual “matter” multiplets vanish, to be consistent with the self-duality of the Riemann tensor. In particular, the special significance of the “self-dual” tensor multiplet is noted. This result fills the gap left over in our previous series of papers, with respect to the consistent couplings among the self-dual matter multiplets. We also couple these nontrivial backgrounds to a Green-Schwarz superstring σ model, under the requirement of invariance under fermionic (kappa) symmetry. The finiteness of the self-dual supergravity is discussed, based on its “off-shell” structure. A set of exact solutions ...