Towards an Ashtekar formalism in eight dimensions

2007

Gen Relativ Gravit

We discuss the Ashtekar formalism from the point of view of 12 dimensions. We first focus on the 2 + 10 spacetime signature and then we consider the transition 2 + 10 → (2 + 2) + (0 + 8). We argue that both sectors 2 + 2 and 0 + 8, which are exceptional signatures, can be analyzed from the point of view of a self-dual action associated with the Ashtekar formalism.Keywords Ashtekar theory · 12 dimensions · Two time physics Over the years it has become clear that considering gravitational and gauge theories with more than one time coordinate is a very interesting and useful idea for understanding different aspects of traditional gravitational and gauge field theories with only one time (see [1] and references therein). In particular, the 2 + 10-dimensional spacetime signature has emerged as an interesting possibility for the understanding of both supergravity and super Yang-Mills theory in D = 11 (see [2]). Thus, by seriously taking a 2 + 10-dimensional gravity one may be interested in various possibilities offered by this theory. For instance, one may be interested in a realistic theory in four-dimensions via the symmetry braking 2 + 10 → (1 + 3) + (1 + 7). However, this may not be the only attractive possibility. In fact, one may think on the alternative transition 2 + 10 → (2 + 2) + (0 + 8).(1) Dedicated to Octavio Obregón on the occasion of his 60th birthday.

“…It is worth mentioning that the action (39) is the analogue of the action proposed by Nieto [17] in eight dimensions with signature 1 + 7. Let us start observing that since…”

mentioning

confidence: 91%

“…Let us now consider a MacDowell-Mansouri type action [13][14][15][16] in a 2 + 10-dimensional spacetime [17] …”

mentioning

confidence: 99%

Towards an Ashtekar formalism in 12 dimensions

2007

Gen Relativ Gravit

“…[6][7][8][9][10]). The main physical reason for this is that it allows a possible connection with string theory [11]; an alternative approach for quantum gravity.…”

Section: -Introductionmentioning

confidence: 99%

“…The main physical reason for this is that it allows a possible connection with string theory [11]; an alternative approach for quantum gravity. However, except for the 8-dimensional Ashtekar formalism [6] the concept so important in 4-dimensions of the self duality curvature concept is lost. Such an 8-dimensional Ashtekar formalism is an interesting approach based on the octonionic structure.…”

Section: -Introductionmentioning

confidence: 99%

Alternative self-dual gravity in eight dimensions

2016

Mod. Phys. Lett. A

We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell-Mansouri physical framework and a self-dual curvature symmetry we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein-Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions.

“…There are attempts to make sense of loop quantum gravity in higher dimensions [7]- [8], but the central concept in four dimensions of duality seems to be lost. (However, it is interesting that, by means of the octonion structure, the duality concept may still be recasted in eight dimensions [9]- [10].) One may view such a difficulties as an opportunity to look for other unexpected alternatives for quantum gravity.…”

mentioning

confidence: 99%

Towards an alternative gravitational theory

Beltrán

2015

Mod. Phys. Lett. A

In 1680 Cassini proposed oval curves as alternative trajectories for the visible planets around the sun. The Cassini ovals were of course overshadow by the Kepler's first law (1609), namely the planets move around the sun describing conic orbits. Here we describe the possibility that the Cassini's idea works at larger or smaller scales. Indeed, we consider the Spiric curves (which are a generalization of the Cassini oval) and present the first steps towards a Spiric gravitational theory. We show that from our formalism an ellipse associated with a planet can be obtained as a particular case.