Ref HAL: hal-01341951_v1
Ref Arxiv: 1606.01018
DOI: 10.1088/1751-8113/49/37/375201
WoS: WOS:000383514700006
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17 Citations
Résumé:

The first result of the present paper is to provide classes of explicitsolutions for integrable boundary matrices for the multi-species ASEP with anarbitrary number of species. All the solutions we have obtained can be seen as representations of a newalgebra that contains the boundary Hecke algebra. The boundary Hecke algebra isnot sufficient to build these solutions. This is the second result of ourpaper.

Ref HAL: hal-01348152_v1
Ref Arxiv: 1607.05293
DOI: 10.1007/JHEP11(2016)066
WoS: 000387691500005
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1 Citation
Résumé:

Motivated by a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we derive a non-perturbative potential of all scalar fields from the exact D-instanton corrected metric on the hypermultiplet moduli space. Applying this potential to moduli stabilization, we find a discrete set of exact vacua for axions. At these critical points, the stability problem is decoupled into two subspaces spanned by the axions and the other fields (dilaton and Kähler moduli), respectively. Whereas the stability of the axions is easily achieved, numerical analysis shows instabilities in the second subspace.

Ref HAL: hal-01338274_v1
Ref Arxiv: 1512.02877
DOI: 10.1007/s10955-016-1507-y
WoS: WOS:000375579300009
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3 Citations
Résumé:

We prove the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y) $, for $0<\alpha<2$ and all real $m$, in the lattice ${\mathbf Z}^{d}$ as well as in the continuum ${\mathbf R}^{d}$ for dimension $d\ge 2$. This resolvent occurs as the covariance of the Gaussian measure underlying weakly self- avoiding walks with long range jumps (stable L\'evy walks) as well as continuous spin ferromagnets with long range interactions in the long wavelength or field theoretic approximation. The finite range decomposition should be useful for the rigorous analysis of both critical and off-critical renormalisation group trajectories. The decomposition for the special case $m=0$ was known and used earlier in the renormalisation group analysis of critical trajectories for the above models below the critical dimension $d_c =2\alpha$.

Commentaires: 16 pages, 1 figure, typos corrected, corrected, reference added, one sentence added

Ref HAL: hal-01292660_v1
Ref Arxiv: 1603.06648v1
DOI: 10.1088/1475-7516/2016/05/048
WoS: 000378041500049
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10 Citations
Résumé:

We consider the possibility to produce a bouncing universe in the framework of scalar-tensor gravity when the scalar field has a nonconformal coupling to the Ricci scalar. We prove that bouncing universes regular in the future with essentially the same dynamics as for the conformal coupling case do exist when the coupling deviates slightly from it. This is found numerically for more substantial deviations as well. In some cases however new features are found like the ability of the system to leave the effective phantom regime.

Ref HAL: hal-01264155_v1
Ref Arxiv: 1512.03406
DOI: 10.1016/j.nuclphysbps.2016.02.021
WoS: WOS:000375626800021
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Résumé:

Our renormalization group consistent variant of optimized perturbation, RGOPT, is used to calculate the nonperturbative QCD spectral density of the Dirac operator and the related chiral quark condensate $\langle \bar q q \rangle$, for $n_f=2$ and $n_f=3$ massless quarks. Sequences of approximations at two-, three-, and four-loop orders are very stable and give $\langle \bar q q \rangle^{1/3}_{n_f=2}(2\, {\rm GeV}) = -(0.833-0.845) \bar\Lambda_2 $, and $ \langle \bar q q \rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(0.814-0.838) \bar\Lambda_3 $ where the range is our estimated theoretical error and $\bar\Lambda_{n_f}$ the basic QCD scale in the $\rm \bar{MS}$-scheme. We compare those results with other recent determinations (from lattice calculations and spectral sum rules).

Commentaires: 5 pages, talk given at 18th International Conference in Quantum Chromodynamics (QCD 15) Montpellier, published in the proceedings

Ref HAL: hal-01229341_v1
Ref Arxiv: 1511.02892
DOI: 10.1007/s11005-016-0857-3
WoS: 000379609000002
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2 Citations
Résumé:

Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau string vacua, such theta series encode instanton corrections from $k$ Neveu-Schwarz five-branes. The theta series are determined by vector-valued wave-functions, and in this work we obtain the transformation of these wave-functions induced by Kontsevich-Soibelman symplectomorphisms. This effectively provides a quantum version of these transformations, where the quantization parameter is inversely proportional to the five-brane charge $k$. Consistency with wall-crossing implies a new five-term relation for Faddeev's quantum dilogarithm $\Phi_b$ at $b=1$, which we prove. By allowing the torus to be non-commutative, we obtain a more general five-term relation valid for arbitrary $b$ and $k$, which may be relevant for the physics of five-branes at finite chemical potential for angular momentum.

Commentaires: 26 pages

Ref HAL: hal-01177137_v1
PMID 26849585
Ref Arxiv: 1507.03508
DOI: 10.1103/PhysRevLett.116.031601
WoS: 000368523200003
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11 Citations
Résumé:

We use the scalar model with quartic interaction to illustrate how a nonperturbative variational technique combined with renormalization group (RG) properties efficiently resums perturbative expansions in thermal field theories. The resulting convergence and scale dependence of optimized thermodynamical quantities, here illustrated up to two-loop order, are drastically improved as compared to standard perturbative expansions, as well as to other related methods such as the screened perturbation or (resummed) hard-thermal-loop perturbation, that miss RG invariance (as we explain). Being very general and easy to implement, our method is a potential analytical alternative to dealing with the phase transitions of field theories such as thermal QCD.

Commentaires: 5 pages, 1 figure