New gauge supergravity in seven and eleven dimensions (original) (raw)

Gauge supergravities for all odd dimensions

International journal of theoretical physics, 1999

Recently proposed supergravity theories in odd dimensions whose fields are connection one-forms for the minimal supersymmetric extensions of anti-de Sitter gravity are discussed. Two essential ingredients are required for this construction:

Standard supergravity in eleven dimensions as a sector of Chern-Simons theory

Arxiv preprint arXiv:1103.2182, 2011

We probe the relationship between two supergravity theories in eleven-dimensional spacetime: the "standard" 1978 theory of Cremmer, Julia and Scherk (CJS) and osp (32|1)-based Chern-Simons (CS) supergravity, as first put forward by Troncoso and Zanelli in 1997. The comparison is carried out at the Lagrangian level for both theories, which is nontrivial because, when written in a way suitable for our purposes, the CS Lagrangian has roughly a thousand terms. We find that the CS Lagrangian can be cast as a polynomial in 1/l, where l is a length, and that the CJS Lagrangian may appear only as one distinct term. For the particular case when the CJS three-form A 3 and the CS five-index one-form b abcde vanish, the match between both Lagrangians turns out to be almost complete. This matching sheds new light on the long-standing issue of the gauge-theory structure of CJS supergravity, since the CS supergravity Lagrangian defines a true gauge system in the fiber-bundle sense. We also provide a general ansatz for A 3 in terms of the CS fields. Solving the full comparison, with nonvanishing A 3 and b abcde , is important in deciding which rôle could CS supergravity theories play in the context of M Theory.

Extended supergravity: Chern–Simons theories in 2+1 dimensions

Journal of Mathematical Physics, 1991

In this paper de Sitter supergravity theories in 2+1 dimensions with positive cosmological constant as Chern–Simons gauge theories of the algebra OSp(M‖2;C) are constructed. Starting from anti-de Sitter supergravity theories based on OSp(M‖2;R)×OSp(M‖2;R) algebras, a particular Inonu–Wigner contraction is used to construct a large class of super Poincaré supergravity theories with nontrivial internal symmetries. Other models based on algebras SL(M‖N) and the exceptional super Lie algebras are also discussed. The classical consistency of our de Sitter supergravity theories is discussed.

Higher dimensional Chern-Simons supergravity

Physical Review D, 1996

A Chern-Simons action for supergravity in odddimensional spacetimes is proposed. For all odd dimensions, the local symmetry group is a non trivial supersymmetric extension of the Poincaré group. In 2 + 1 dimensions the gauge group reduces to super-Poincaré, while for D = 5 it is super-Poincaré with a central charge. In general, the extension is obtained by the addition of a 1-form field which transforms as an antisymmetric fifth-rank tensor under Lorentz rotations. Since the Lagrangian is a Chern-Simons density for the supergroup, the supersymmetry algebra closes off shell without the need of auxiliary fields.

On eleven-dimensional supergravity and Chern–Simons theory

Nuclear Physics B, 2012

We probe in some depth into the structure of eleven-dimensional, osp (32|1)-based Chern-Simons supergravity, as put forward by Troncoso and Zanelli (TZ) in 1997. We find that the TZ Lagrangian may be cast as a polynomial in 1/l, where l is a length, and compute explicitly the first three dominant terms. The term proportional to 1/l 9 turns out to be essentially the Lagrangian of the standard 1978 supergravity theory of Cremmer, Julia and Scherk, thus establishing a previously unknown relation between the two theories. The computation is nontrivial because, when written in a sufficiently explicit way, the TZ Lagrangian has roughly one thousand non-explicitly Lorentz-covariant terms. Specially designed algebraic techniques are used to accomplish the results.

(Super-)Gravities of a different sort

Journal of Physics: Conference Series, 2006

We review the often forgotten fact that gravitation theories invariant under local de Sitter, anti-de Sitter or Poincaré transformations can be constructed in all odd dimensions. These theories belong to the Chern-Simons family and are particular cases of the so-called Lovelock gravities, constructed as the dimensional continuations of the lower dimensional Euler classes. The supersymmetric extensions of these theories exist for the AdS and Poincaré groups, and the fields are components of a single connection for the corresponding Lie algebras. In 11 dimensions these supersymmetric theories are gauge theories for the osp(1|32) and the M algebra, respectively. The relation between these new supergravities and the standard theories, as well as some of their dynamical features are also discussed.

ℵ0-extended supergravity and Chern-Simons theories

Nuclear Physics B, 1996

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in threedimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ 0 (Aleph-Null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ 0 supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three-dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ 0 globally and locally supersymmetric theories in three-dimensions. As an interesting application, we present ℵ 0 supergravity Liouville theory in two-dimensions after appropriate dimensional reduction from threedimensions.

CHERN-SIMONS SUPERGRAVITIES WITH OFF-SHELL LOCAL SUPERALGEBRAS

Black Holes and the Structure of the Universe, 2000

A new family of supergravity theories in odd dimensions is presented. The Lagrangian densities are Chern-Simons forms for the connection of a supersymmetric extension of the antide Sitter algebra. The superalgebras are the supersymmetric extensions of the AdS algebra for each dimension, thus completing the analysis of van Holten and Van Proeyen, which was valid for N = 1 and for D = 2, 3, 4, mod 8. The Chern-Simons form of the Lagrangian ensures invariance under the gauge supergroup by construction and, in particular, under local supersymmetry. Thus, unlike standard supergravity, the local supersymmetry algebra closes off-shell and without requiring auxiliary fields. The Lagrangian is explicitly given for D = 5, 7 and 11. In all cases the dynamical field content includes the vielbein (e a µ ), the spin connection (ω ab µ ), N gravitini (ψ i µ ), and some extra bosonic "matter" fields which vary from one dimension to another. The superalgebras fall into three families: osp(m|N ) for D = 2, 3, 4, mod 8, osp(N |m) for D = 6, 7, 8, mod 8, and su(m − 2, 2|N ) for D = 5 mod 4, with m = 2 [D/2] . The possible connection between the D = 11 case and M-Theory is also discussed.

Alephnull Anti-de Sitter supergravity with Lorentz Chern–Simons term in 3D

Physics Letters B, 2010

We formulate supergravity in three dimensional anti-de Sitter (AdS) space-time with an arbitrary number of supersymmetries with a Lorentz Chern-Simons term. Our field content is (e µ m , ψ µ A , A µ AB , ω µ mn , λ mn A), where the gravitino ψ µ A and the gaugino λ mn A are in the vectorial representation of SO(N) for ∀ N , whose gauge field is A µ AB. The ω µ mn is a spin connection regarded as an independent field. Both ω µ mn and A µ AB have their Chern-Simons (CS) terms. Local ∀ N (ℵ 0) supersymmetry requires the coefficients of these CS terms be proportional to the gravitino mass. Differently from most conventional works, our supersymmetry transformation for ω µ mn is proportional to the gaugino λ mnA. The solution for the scalar curvature is a negative constant, and our space-time is AdS. Despite the Lorentz CS term, ω µ mn can be algebraically solved. The Lorentz and SO(N) CS terms serve as the gravitational and SO(N) gauge anomalies for the two-dimensional boundary superconformal field theory. We also compute the charges for ℵ 0 supersymmetry, SO(N) and Lorentz symmetries, and also show that Witten-Nester charges are positive definite.