Classical and quantum gravity in dimensions: I. A unifying approach

Klösch, Thomas; Strobl, Thomas

doi:10.1088/0264-9381/13/5/015

Cited by 114 publications

(161 citation statements)

References 73 publications

Supporting

Mentioning

160

Contrasting

Order By: Relevance

“…Two spacetime dimensions already provides an example where these concepts have been realized successfully in terms of Poisson Sigma Models (PSMs) [5,6], which, on the physical side, permit to unify gravitational and YM gauge theories [7]. Using the PSM, as well as Chern-Simons (CS) theory defined in d = 3, as a guideline, we will leave behind low dimensions in this Letter and, besides suggesting possibly also interesting topological models, permit theories with propagating degrees of freedom.…”

mentioning

confidence: 99%

Algebroid Yang-Mills Theories

Strobl¹

2004

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently many E-Killing vectors leads to an astonishingly mild deformation of ordinary Yang-Mills theories: Additional fields turn out to carry no propagating modes. Instead they serve as moduli parameters gluing together in part different Yang-Mills theories. This leads to a symmetry enhancement at critical points of these fields, as is also typical for String effective field theories.Yang-Mills (YM) theories and Lie group symmetries are part and parcel of present day fundamental physics. Both of these concepts are "nondeformable" under very mild assumptions [1]. The advent of supersymmetry, possible after changing the perspective on symmetries, is an example of the fruitfulness of enlarging that framework. In the present Letter we suggest a possibly similar broadening, which in its essence replaces Lie groups by Lie groupoids in the context of Yang-Mills theories; for trivial bundles this reduces to replacing the structural Lie algebra of a YM-theory by a Lie algebroid. In part this generalization is related to rather old attempts [2] for constructing so-called "non-linear gauge theories"; the recent mathematical understanding of Lie algebroids and groupoids [3,4], however, provides new tools and a new focus for approaching such a generalization.In the theories under discussion generically one encounters structure functions in the symmetry algebra, typical for gravitational theories; but there will exist a finite dimensional object underlying the infinite dimensional space of symmetries: infinitesimally the symmetries are generated by sections in a Lie algebroid. Two spacetime dimensions already provides an example where these concepts have been realized successfully in terms of Poisson Sigma Models (PSMs) [5,6], which, on the physical side, permit to unify gravitational and YM gauge theories [7]. Using the PSM, as well as Chern-Simons (CS) theory defined in d = 3, as a guideline, we will leave behind low dimensions in this Letter and, besides suggesting possibly also interesting topological models, permit theories with propagating degrees of freedom.We briefly recall some mathematical background For later use we remark that the image of ρ is integrable so that M is foliated into orbits. Moreover, due to the Leibniz rule, the bracket reduces to a fiberwise Lie algebra structure for elements in the kernel of ρ, which is isomorphic for any two points in the same orbit.In local coordinates (and frame (b I ) rankE I=1the Lie algebroid data are encoded in structural functionsGuided by the other obvious example of a Lie algebroid, E = T M with ρ = id, one may introduce differential geometrical notions on Lie algebroids. With b I denoting the dual basis in E * , the Leibniz extension ofentails all the differenti...

show abstract

mentioning

confidence: 99%

Algebroid Yang-Mills Theories

Strobl¹

2004

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Implicitly plotting the function (64) allows us to find the causal structure of the spacetimes. We construct the Penrose diagrams using the method outlined in [11], where we represent a horizon with a dashed line, a non-singular boundary with a thin black line is, and a singularity with a solid black line.…”

Section: Bosonic Condensatementioning

confidence: 99%

Super Liouville black holes

Kamnitzer¹,

Mann²

2001

Nuclear Physics B

View full text Add to dashboard Cite

We describe in superspace a classical theory of of two dimensional (1, 1) dilaton supergravity coupled to a super-Liouville field, and find exact super black hole solutions to the field equations that have non-constant curvature. We consider the possibility that a gravitini condensate forms and look at the implications for the resultant spacetime structure. We find that all such condensate solutions have a condensate and/or naked curvature singularity.

show abstract

“…Its counterpart, lineal gravity (the same system with the S 1 topology replaced by R 1 ), has been the subject of much investigation over the past twenty years, motivated by the desire to understand black holes [2], space-time structure [3,4], canonical quantum gravity [5], string physics [6], information loss in black hole evaporation [7] and the N −body problem [8,9].…”

Section: Introductionmentioning

confidence: 99%

Dynamical charged N -body equilibrium in circular dilaton gravity

Kerner¹,

Mann²

2004

Class. Quantum Grav.

View full text Add to dashboard Cite

We extend the problem of (1 + 1) circular dilaton gravity to include charged particles. We examine the two (charged) particle case in detail and find an exact equilibrium solution. We then extend this to N −particles and obtain a solution for this case as well. This class of solutions corresponds to N -particles of the same mass, spaced evenly around the circle with charges chosen so that the electric field satisfies E 2 =constant. We discuss the relation of these solutions to the previous uncharged equilibrium solutions and examine the behavior when the number of particles is large. We comment on the challenges in further generalizing the solutions we obtain.

show abstract

Classical and quantum gravity in dimensions: I. A unifying approach

Cited by 114 publications

References 73 publications

Algebroid Yang-Mills Theories

Algebroid Yang-Mills Theories

Super Liouville black holes

Dynamical charged N -body equilibrium in circular dilaton gravity

Contact Info

Product

Resources

About