| 1. |
- Bonelli, Giulio, et al.
(författare)
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On topological M-theory
- 2006
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. ; 10:2, s. 239-260
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Tidskriftsartikel (refereegranskat)abstract
- We construct a gauge-fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that the path integral in this gauge localizes on associative submanifolds. Moreover on M × S1, the theory naturally reduces to the standard A-model on Calabi-Yau manifold and to a membrane theory localized on special Lagrangian submanifolds. We discuss some properties of topological membrane theory on G2-manifolds. We also generalize our construction to topological p-branes on special manifolds by exploring a relation between vector cross product structures and TFTs.
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| 2. |
- Ekstrand, Joel, et al.
(författare)
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Non-linear sigma models via the chiral de Rham complex
- 2009
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. ; 13:4, s. 1221-1254
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Tidskriftsartikel (refereegranskat)abstract
- We propose a physical interpretation of the chiral de Rham complex as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model. We show that the chiral de Rham complex on a Calabi-Yau manifold carries all information about the classical dynamics of the sigma model. Physically, this provides an opera- tor realization of the non-linear sigma model. Mathematically, the idea suggests the use of Hamiltonian flow equations within the vertex algebra formalism with the pos- sibility to incorporate both left and right moving sectors within one mathematical framework.
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| 3. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Uniqueness of open/closed rational CFT with given algebra of open states
- 2008
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Ingår i: Adv. in Theor. and Math. Phys. 12 (2008). - : International Press. ; 12:6, s. 1283-1375
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Tidskriftsartikel (refereegranskat)abstract
- We study the sewing constraints for rational two-dimensional conformal fieldtheory on oriented surfaces with possibly non-empty boundary. The boundarycondition is taken to be the same on all segments of the boundary.The following uniqueness result is established: For a solution to the sewingconstraints with nondegenerate closed state vacuum and nondegenerate two-pointcorrelators of boundary fields on the disk and of bulk fields on the sphere, upto equivalence all correlators are uniquely determined by the one-, two,- andthree-point correlators on the disk. Thus for any such theory every consistentcollection of correlators can be obtained by the TFT approach of [hep-th/0204148] and [hep-th/0503194].As morphisms of the category of world sheets we includenot only homeomorphisms, but also sewings; interpreting the correlatorsas a natural transformation then encodes covariance both under homeomorphismsand under sewings of world sheets.
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| 4. |
- Uggla, Claes, et al.
(författare)
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The cosmological billiard attractor
- 2009
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Ingår i: Advances in Theoretical and Mathematical Physics. - 1095-0761 .- 1095-0753. ; 13:2, s. 293-407
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Tidskriftsartikel (refereegranskat)abstract
- This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike singularities we derive in a step-by-step manner the cosmological billiard conjecture: we show that the generic asymptotic dynamics of solutions is represented by (randomized) sequences of heteroclinic orbits on the `billiard attractor'. Our analysis rests on two pillars: (i) a dynamical systems formulation based on the conformal Hubble-normalized orthonormal frame approach expressed in an Iwasawa frame; (ii) stochastic methods and the interplay between genericity and stochasticity. Our work generalizes and improves the level of rigor of previous work by Belinskii, Khalatnikov, and Lifshitz; furthermore, we establish that our approach and the Hamiltonian approach to `cosmological billiards', as elaborated by Damour, Hennaux, and Nicolai, can be viewed as yielding `dual' representations of the asymptotic dynamics
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