Ref HAL: hal-00349154_v1
Ref Arxiv: 0812.4219
DOI: 10.1088/1126-6708/2009/03/044
WoS: 000265600800044
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55 Citations
Résumé:

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds still poses an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instanton contributions are captured by contact transformations between different locally flat patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions. We conclude with some comments on the relation to microscopic degeneracies of four-dimensional BPS black holes and to the wall-crossing formula of Kontsevich and Soibelman, and on the form of the yet unknown NS5-brane instanton contributions.

Ref HAL: hal-00328291_v1
Ref Arxiv: 0810.1675
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We extend the twistor methods developed in our earlier work on linear deformations of hyperkahler manifolds [arXiv:0806.4620] to the case of quaternionic-Kahler manifolds. Via Swann's construction, deformations of a 4d-dimensional quaternionic-Kahler manifold $M$ are in one-to-one correspondence with deformations of its $4d+4$-dimensional hyperkahler cone $S$. The latter can be encoded in variations of the complex symplectomorphisms which relate different locally flat patches of the twistor space $Z_S$, with a suitable homogeneity condition that ensures that the hyperkahler cone property is preserved. Equivalently, we show that the deformations of $M$ can be encoded in variations of the complex contact transformations which relate different locally flat patches of the twistor space $Z_M$ of $M$, by-passing the Swann bundle and its twistor space. We specialize these general results to the case of quaternionic-Kahler metrics with $d+1$ commuting isometries, obtainable by the Legendre transform method, and linear deformations thereof. We illustrate our methods for the hypermultiplet moduli space in string theory compactifications at tree- and one-loop level.

Commentaires: 55 pages, 1 figure, uses JHEP3.cls

Ref HAL: hal-00326626_v1
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After a brief sketch of covariant loop quantization I'll demonstrate that the consistent implementation of second class constraints in the discretized path integral for 4d general relativity leads to a spin foam model with boundary states identical to the kinematical states of the loop approach. The identification works perfectly well for any signature and any value of the Immirzi parameter. An expression for the vertex amplitude is given in terms of integrated (over a still unknown measure) projected spin networks.

Ref HAL: hal-00326622_v1
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After a brief review of a covariant approach to loop quantum gravity and of important notion of projected spin networks, I revise the spin foam quantization procedure of 4-dimensional general relativity. In particular, I discuss how the simplicity and the closure constraints should be implemented and demonstrate the precise agreement between the canonical and the path integral quantizations at the kinematical level.

Ref HAL: hal-00325481_v1
Ref Arxiv: 0809.4763
DOI: 10.1088/0264-9381/26/5/055005
WoS: 000263493200006
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33 Citations
Résumé:

We consider non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Phi with ``internal'' indices. The Hamiltonian analysis of this version of the theory turns out to be simpler than in the previously considered in the literature version with Phi carrying spacetime indices. We then extend the Hamiltonian analysis to a more general class of theories whose action contains scalars invariants constructed from Phi. Such theories have recently been considered in the context of unification of gravity with other forces. We show that these more general theories have six additional propagating degrees of freedom as compared to general relativity, something that has not been appreciated in the literature treating them as being not much different from GR.

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Ref Arxiv: 0806.4620
DOI: 10.1007/s11005-009-0305-8
WoS: 000263918200003
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26 Citations
Résumé:

We study general linear perturbations of a class of 4d real-dimensional hyperkahler manifolds obtainable by the (generalized) Legendre transform method. Using twistor methods, we show that deformations can be encoded in a set of holomorphic functions of 2d+1 variables, as opposed to the functions of d+1 variables controlling the unperturbed metric. Such deformations generically break all tri-holomorphic isometries of the unperturbed metric. Geometrically, these functions generate the symplectomorphisms which relate local complex Darboux coordinate systems in different patches of the twistor space. The deformed Kahler potential follows from these data by a Penrose-type transform. As an illustration of our general framework, we determine the leading exponential deviation of the Atiyah-Hitchin manifold away from its negative mass Taub-NUT limit. In a companion paper, we extend these techniques to quaternionic-Kahler spaces with isometries.

Commentaires: 44 pages, 2 figures, uses JHEP3.cls

Ref HAL: hal-00264038_v1
Ref Arxiv: 0802.3389
DOI: 10.1103/PhysRevD.78.044033
WoS: 000259368500081
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35 Citations
Résumé:

We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the discretized path integral. At the same time, the closure constraint must be relaxed so that the new constraint expresses covariance of intertwiners assigned to tetrahedra by spin foam quantization. As a result, the spin foam boundary states are shown to be realized in terms of projected spin networks of the covariant loop approach to quantum gravity.