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Induced Spin from the $ISO(2,1)$ Gauge Theory with the Gravitational Chern-Simons Term  [PDF]
Jin-Ho Cho,Hyuk-jae Lee
Physics , 1995, DOI: 10.1016/0370-2693(95)00360-W
Abstract: In the context of $ISO(2,1)$ gauge theory, we consider $(2+1)$-dimensional gravity with the gravitational Chern-Simons term (CST). This formulation allows the `exact' solution for the system coupled to a massive point particle (which is not the case in the conventional Chern-Simons gravity). The solution exhibits locally trivial structure even with the CST, although still shows globally nontrivialness such as the conical space and the helical time structure. Since the solution is exact, we can say the CST induces spin even for noncritical case of $\s+\al m\ne 0$.
Chern-Simons formulation of three-dimensional gravity with torsion and nonmetricity  [PDF]
Sergio L. Cacciatori,Marco M. Caldarelli,Alex Giacomini,Dietmar Klemm,Diego S. Mansi
Physics , 2005, DOI: 10.1016/j.geomphys.2006.01.006
Abstract: We consider various models of three-dimensional gravity with torsion or nonmetricity (metric affine gravity), and show that they can be written as Chern-Simons theories with suitable gauge groups. Using the groups ISO(2,1), SL(2,C) or SL(2,R) x SL(2,R), and the fact that they admit two independent coupling constants, we obtain the Mielke-Baekler model for zero, positive or negative effective cosmological constant respectively. Choosing SO(3,2) as gauge group, one gets a generalization of conformal gravity that has zero torsion and only the trace part of the nonmetricity. This characterizes a Weyl structure. Finally, we present a new topological model of metric affine gravity in three dimensions arising from an SL(4,R) Chern-Simons theory.
Killing spinors, the adS black hole and I(ISO(2,1)) gravity  [PDF]
R. B. Mann,G. Papadopoulos
Physics , 1996, DOI: 10.1103/PhysRevD.55.2119
Abstract: We construct a supersymmetric extension of the $I\big(ISO(2,1)\big)$ Chern-Simons gravity and show that certain particle-like solutions and the adS black-hole solution of this theory are supersymmetric.
ISO_q(3) and ISO_q(2,1)  [PDF]
S. Sachse,R. Weixler
Mathematics , 1995, DOI: 10.1063/1.531405
Abstract: We prove the embedding of $ ISO_q(3) \hook ISU^{ex}_{\sqrt{q}}(2) $ and $ ISO_q(2,1) \hook ISL^{ex}_q(2,R)$ as $^*$-algebras and give a Hilbert space representation of $ISU^{ex}_{\sqrt{q}}(2)$
Hamiltonian formulation of tetrad gravity: three dimensional case  [PDF]
A. M. Frolov,N. Kiriushcheva,S. V. Kuzmin
Physics , 2009, DOI: 10.1134/S0202289310030011
Abstract: The Hamiltonian formulation of the tetrad gravity in any dimension higher than two, using its first order form when tetrads and spin connections are treated as independent variables, is discussed and the complete solution of the three dimensional case is given. For the first time, applying the methods of constrained dynamics, the Hamiltonian and constraints are explicitly derived and the algebra of the Poisson brackets among all constraints is calculated. The algebra of the Poisson brackets among first class secondary constraints locally coincides with Lie algebra of the ISO(2,1) Poincare group. All the first class constraints of this formulation, according to the Dirac conjecture and using the Castellani procedure, allow us to unambiguously derive the generator of gauge transformations and find the gauge transformations of the tetrads and spin connections which turn out to be the same found by Witten without recourse to the Hamiltonian methods [\textit{Nucl. Phys. B 311 (1988) 46}]. The gauge symmetry of the tetrad gravity generated by Lie algebra of constraints is compared with another invariance, diffeomorphism. Some conclusions about the Hamiltonian formulation in higher dimensions are briefly discussed; in particular, that diffeomorphism invariance is \textit{not derivable} as a \textit{gauge symmetry} from the Hamiltonian formulation of tetrad gravity in any dimension when tetrads and spin connections are used as independent variables.
Three dimensional gravity from ISO(2,1) coset models  [PDF]
R. Casadio,B. Harms
Physics , 2000, DOI: 10.1103/PhysRevD.62.105003
Abstract: Starting from a WZWN action in the ISO(2,1) Poincare' group which describes a bosonized spinning string in 2+1 Minkowski space-time, we show that a sequence of non-trivial compactifications leads to the description of a spinless string which moves in a (linear dilaton) vacuum, AdS_3 or BTZ black hole background. Other solutions are also obtained and their T-duals analyzed.
Topology change in ISO(2,1) Chern-Simons gravity  [PDF]
K. Amano,S. Higuchi
Physics , 1992, DOI: 10.1016/0550-3213(92)90022-4
Abstract: In 2+1 dimensional gravity, a dreibein and the compatible spin connection can represent a space-time containing a closed spacelike surface $\Sigma$ only if the associated SO(2,1) bundle restricted to $\Sigma$ has the same non-triviality (Euler class) as that of the tangent bundle of $\Sigma.$ We impose this bundle condition on each external state of Witten's topology-changing amplitude. The amplitude is non-vanishing only if the combination of the space topologies satisfies a certain selection rule. We construct a family of transition paths which reproduce all the allowed combinations of genus $g \ge 2$ spaces.
Gauge fixing and classical dynamical r-matrices in ISO(2,1)-Chern-Simons theory  [PDF]
Catherine Meusburger,Torsten Sch?nfeld
Physics , 2012, DOI: 10.1007/s00220-014-1938-8
Abstract: We apply Dirac's gauge fixing procedure to Chern-Simons theory with gauge group ISO(2,1) on manifolds RxS, where S is a punctured oriented surface of general genus. For all gauge fixing conditions that satisfy certain structural requirements, this yields an explicit description of the Poisson structure on the moduli space of flat ISO(2,1)-connections on S via the resulting Dirac bracket. The Dirac bracket is determined by classical dynamical r-matrices for ISO(2,1). We show that the Poisson structures and classical dynamical r-matrices arising from different gauge fixing conditions are related by dynamical ISO(2,1)-valued transformations that generalise the usual gauge transformations of classical dynamical r-matrices. By means of these transformations, it is possible to classify all Poisson structures and classical dynamical r-matrices obtained from such gauge fixings. Generically these Poisson structures combine classical dynamical r-matrices for non-conjugate Cartan subalgebras of iso(2,1).
Contractions Which Obtained by Equivalent Metric of Cone Metric  [PDF]
Mehdi Asadi
Mathematics , 2014,
Abstract: In this paper we try to collect certain contractions which can be obtained by equivalent metric of cone metric.
Space-time singularities and the axion in the Poincare coset models ISO(2,1)/H  [PDF]
Roberto Casadio,Benjamin Harms
Physics , 1996, DOI: 10.1016/S0370-2693(96)01253-1
Abstract: By promoting an invariant subgroup $H$ of $ISO(2,1)$ to a gauge symmetry of a WZWN action, we obtain the description of a bosonic string moving either in a curved 4-dimensional space--time with an axion field and curvature singularities or in 3-dimensional Minkowski space--time.
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