A quantization of topological <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">M</mml:mi></mml:math> theory

Inspired by the low wave-length limit of topological M-theory, which reconstructs the theory of 3 + 1D gravity in the self-dual variables' formulation, and by the realization that in Loop Quantum Gravity the holonomy of a flat connection can be non-trivial if and only if a non-trivial (space-like) line defect is localized inside the loop, we argue that non-trivial gravitational holonomies can be put in correspondence with space-like M-branes. This suggests the existence of a new duality, which we call H duality, interconnecting topological M-theory with Loop Quantum Gravity. We spell some arguments to show that fundamental S-strings are serious candidates to be considered in order to instantiate this correspondence to classes of LQG states. In particular, we consider the case of the holonomy flowers in LQG, and show that for this type of states the action of the Hamiltonian constraint, from the M-theory side, corresponds to a linear combination of appearance and disappearance of a SNS1-strings. Consequently, these processes can be reinterpreted, respectively, as enucleations or decays into open or closed strings.

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“…In Ref. [17] Smolin suggested a quantization scheme, defining the holonomy of the 1-form β and its conjugate variables, respectively, as…”

Section: Reducing Topological M-theory To Gravitymentioning

confidence: 99%

Self-dual formulation of gravity in topological M-theory

Addazi

Marcianò

2020

Int. J. Geom. Methods Mod. Phys.

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“…We expect that the relations found here will allow us to apply the results and tools of topological M-theory, and more generically of exceptional manifolds, to the study of the quantization ambiguities in gravity from a different point of view. For example, a quantization of the Hitchin functional has been proposed in [33].…”

Section: +1 Gravity Actions From Topological M-theorymentioning

confidence: 99%

Topological M-theory, self-dual gravity and the Immirzi parameter

Chagoya

Sabido

2018

Class. Quantum Grav.

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Working in the first order formalism of gravity, we propose an action that combines the self and anti-self-dual parts of the curvature and comprises all the diffeomorphism invariant Lagrangians that one can consider in this formalism. The action that we propose is motivated by (A)dS gauge theories of gravity. We use this action to derive the (2+1)-dimensional version of the Immirzi parameter. Our derivation relates explicitly the Immirzi parameter to the existence of two classically equivalent actions for the description of gravity in (2+1) dimensions, namely the standard and exotic actions introduced by Witten in the description of (2+1) gravity as a gauge theory. This relation had been conjectured previously in the literature, but not derived.

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“…Also, the Ashtekar variables are restricted to four spacetime dimensions and thus not applicable to higher dimensional supergravities. Aiming at a unification of String theory and LQG, Smolin explored non-perturbative formulations of certain parts of eleven-dimensional supergravity [48,49]. The generalization of the loop quantum gravity methods to antisymmetric tensors was considered by Arias, di Bartolo, Fustero, Gambini and Trias [50].…”

Section: Status Of Canonical Supergravitymentioning

confidence: 99%

Towards loop quantum supergravity (LQSG): I. Rarita–Schwinger sector

Bodendorfer

Thiemann

Thurn

2013

Class. Quantum Grav.

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In our companion papers, we managed to derive a connection formulation of Lorentzian General Relativity in D+1 dimensions with compact gauge group SO(D+1) such that the connection is Poisson commuting, which implies that Loop Quantum Gravity quantisation methods apply. We also provided the coupling to standard matter.In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature Supergravity theories, in particular 11d SUGRA and 4d, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in presence of the Rarita-Schwinger field. This is non trivial because SUSY typically requires the Rarita-Schwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signature.We resolve the arising tension and provide a background independent representation of the non trivial Dirac antibracket

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A quantization of topological M theory

Cited by 8 publications

References 27 publications

Self-dual formulation of gravity in topological M-theory

Self-dual formulation of gravity in topological M-theory

Topological M-theory, self-dual gravity and the Immirzi parameter

Towards loop quantum supergravity (LQSG): I. Rarita–Schwinger sector

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