Narrow Results

We deform the anti-de Sitter algebra by adding additional generators , forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained BF theory. It turns out that the resulting theory is described by the Einstein–Cartan action with Holst term, and the gauge fields associated with the Maxwell generators appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics.

In this paper we derive the anti-de Sitter counterpart of the super-Maxwell algebra presented recently by Bonanos et al. Then we gauge this algebra and derive the corresponding supergravity theory, which turns out to be described by the standard N = 1 supergravity Lagrangian, up to topological terms.

In this paper, we consider topological gauge theories in three dimensions which are defined by metric independent lagrangians. It has been claimed that the functional integration necessarily depends nontrivially on the gauge-fixing metric. We demonstrate that the partition function and the mean values of the gauge invariant observables do not really depend on the gauge-fixing metric.

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

The purpose of this Comment is to point out that the results presented in the appendix of M. Mondragon and M. Montesinos, J. Math. Phys.47, 022301 (2006) provides a generic method so as to deal with cases as those of Sec. 6 of R. Cartas-Fuentevilla, A. Escalante-Hernández, and J. Berra-Montiel, Int. J. Mod. Phys. A26, 3013 (2011). The results already reported are: the canonical analysis, the transformations generated by the constraints, and the analysis of the reducibility of the constraints for SO(3, 1) and SO(4) four-dimensional BF theory coupled or not to a cosmological constant. But such results are generic and hold actually for any Lie algebra having a nondegenerate inner product invariant under the action of the gauge group.

We will review the non-Lorentzian (nonrelativistic and ultrarelativistic) Jackiw–Teitelboim supergravity theories, which are the limits of relativistic Jackiw–Teitelboim supergravity. The construction is based on BF theory formalism and also the extended Newton–Hooke and extended AdS Carroll superalgebras in two space–time dimensions. It is also shown that nonrelativistic and ultrarelativistic supergravity actions are related to each other by a map which is shown explicitly in this review. This is supersymmetric version of Galilei/Carroll duality in two dimensions.

In this paper, the isolated horizons (IHs) with rotation are considered. It is shown that the symplectic form is the same as that in the nonrotating case. As a result, the boundary degrees of freedom can be also described by an SO$(1,1)$ BF theory. The entropy of the rotating IH satisfies the Bekenstein–Hawking area law with the same Barbero–Immirzi parameter.

We present a Lagrangian formulation for the Husain-Kuchar model as a constrained BF theory. Due to the absence of the Hamiltonian constraint, a spin foam model based in this action principle might be useful to better understand the Hamiltonian constraint of general relativity.

This article presents an extended model of gravity obtained by gauging the AdS-Mawell algebra. It involves additional fields that shift the spin connection, leading effectively to theory of two independent connections. Extension of algebraic structure by another tetrad gives rise to the model described by a pair of Einstein equations.