Ref HAL: hal-01157692_v1
Ref Arxiv: 1406.2360
DOI: 10.1103/PhysRevLett.114.121601
WoS: 000351579000002
Ref. & Cit.: NASA ADS
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16 Citations
Résumé:

In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a supersymmetric index $I$ which receives contributions from 1/2-BPS states, generalizing the familiar Witten index $Tr (-1)^F e^{-\beta H}$. We expect $I$ to be smooth away from loci where massless particles appear, thanks to contributions from the continuum of multi-particle states. Taking inspiration from a similar phenomenon in the hypermultiplet moduli space of $N=2$ string vacua, we conjecture a formula expressing $I$ in terms of the BPS indices $\Omega(\gamma,u)$, which is continuous across the walls and exhibits the expected contributions from single particle states at large $\beta$. This gives a universal prediction for the contributions of multi-particle states to the index $I$. This index is naturally a function on the moduli space after reduction on a circle, closely related to the canonical hyperk\"ahler metric and hyperholomorphic connection on this space.

Commentaires: 7 pages; v2: introduction expanded, minor corrections, differs from published version in PRL in that supplemental material is included as an Appendix. Réf Journal: Phys. Rev. Lett. 114, 121601 (2015)

Ref HAL: hal-01157624_v1
Ref Arxiv: 1412.6057
DOI: 10.1103/PhysRevD.91.064043
WoS: 000351428400006
Ref. & Cit.: NASA ADS
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16 Citations
Résumé:

We study the canonical structure of the real first order formulation of general relativity on a null foliation. We use a tetrad decomposition which allows to elegantly encode the nature of the foliation in the norm of a vector in the fibre bundle. The resulting constraint structure shows some peculiarities. In particular, the dynamical Einstein equations propagating the physical degrees of freedom appear in this formalism as second class tertiary constraints, which puts them on the same footing as the Hamiltonian constraint of the Ashtekar's connection formulation. We also provide a framework to address the issue of zero modes in gravity, in particular, to study the non-perturbative fate of the zero modes of the linearized theory. Our results give a new angle on the dynamics of general relativity and can be used to quantize null hypersurfaces in the formalism of loop quantum gravity or spin foams.

Commentaires: 35 pages, 1 figure; minor corrections, added references. Réf Journal: Phys. Rev. D 91, 064043 (2015)

Résumé:

I'll review the progress achieved in constructing the non-perturbative hypermultiplet moduli space using twistorial methods. The metric on this space determines the low-energy effective action of Type II string theory compactified on a Calabi-Yau threefold. It receives instanton corrections due to D-branes and NS5-branes and I'll show how all of them can be nicely incorporated at the level of the twistor space. I'll argue that the inclusion of NS5-brane instantons might be closely related to quantization of a certain integrable structure. If the time permits, I'll present also a conjecture for the Witten index of 4d N=2 gauge theories inspired by the twistorial description of the hypermultiplet moduli space.

Résumé:

I'll review the progress achieved in constructing the non-perturbative hypermultiplet moduli space using twistorial methods. The metric on this space determines the low-energy effective action of Type II string theory compactified on a Calabi-Yau threefold. It receives instanton corrections due to D-branes and NS5-branes and I'll show how all of them can be nicely incorporated at the level of the twistor space. I'll argue that the inclusion of NS5-brane instantons might be closely related to quantization of a certain integrable structure. If the time permits, I'll present also a conjecture for the Witten index of 4d N=2 gauge theories inspired by the twistorial description of the hypermultiplet moduli space.

Résumé:

After a brief review of unusual features of the light front canonical formulations of field theories, I'll present the analysis of the canonical structure of the first order formulation of general relativity on a lightlike foliation. It appears to be quite different from the usual spacelike case leading, for instance, to the presence of tertiary constraints. Besides, I'll discuss the issue of the zero modes and argue that there might be some hidden correspondence with two-dimensional theories.

Ref HAL: hal-01101042_v1
Exporter : BibTex | endNote
Résumé:

I'll review the current understanding of the low energy effective theory resulting from compactifications of Type II superstrings on Calabi-Yau manifolds. The effective action can be encoded into the metric on a moduli space which is known to receive quantum stringy corrections, both perturbative and non-perturbative. The description of instanton effects crucially relies on twistorial methods and points toward a deep relation to integrable structures.

Ref HAL: hal-01160240_v1
Ref Arxiv: 1410.2897
DOI: 10.1088/1475-7516/2015/03/043
WoS: 000355633800043
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
17 Citations
Résumé:

We analyze the first-order formulation of the ghost-free bigravity model in three-dimensions known as zwei-dreibein gravity. For a special choice of parameters, it was argued to have an additional gauge symmetry and give rise to a partially massless theory. We provide a thorough canonical analysis and identify that whether the theory becomes partially massless depends on the form of the stability condition of the secondary constraint responsible for the absence of the ghost. Generically, it is found to be an equation for a Lagrange multiplier implying that partially massless zwei-dreibein gravity does not exist. However, for special backgrounds this condition is identically satisfied leading to the presence of additional symmetries, which however disappear at quadratic order in perturbations.

Commentaires: 21 pages