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Théorie des Champs & Physique Mathématique
(5) Production(s) de l'année 2020
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Mock modularity and refinement: from BPS black holes to Vafa-Witten theory
Auteur(s): Alexandrov S.
Conférence invité: Workshop on Black Holes: BPS, BMS and Integrability. (Lisbonne, PT, 2020-09-07)
Ref HAL: hal-02986300_v1
Exporter : BibTex | endNote
Résumé: The generating functions of degeneracies of D4-D2-D0 black holes in Type IIstring compactifications on Calabi-Yau threefolds are examples of (higher depth) mock modular forms. I'll explain how S-duality can be used to derive an explicit form for their modular completions, which becomes particularly simple in the presence of a refinement. This result turns out to have many applications going beyond the original context. In particular, I'll show that it can be usedi) to reproduce and generalize in an easy way the known results on modular properties of the generating functions of BPS dyons in N=4 string compactifications;ii) to find Vafa-Witten invariants of arbitrary(!) rank on CP^2, Hirzebruch and del Pezzo surfaces; iii) to obtain holomorphic anomaly equations for BPS partition functions;iv) to reveal a non-commutative structure induced by the refinement on the moduli space of compactified theory.
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On the concept of a generalized law of refraction: A phenomenological model
Auteur(s): Rousseau E., Felbacq D.
(Article) Publié:
Acs Photonics, vol. p. (2020)
Texte intégral en Openaccess :
Ref HAL: hal-02863987_v1
Ref Arxiv: 2006.06203
DOI: 10.1021/acsphotonics.0c00639
WoS: 000551497000010
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
8 Citations
Résumé: This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to the generalized Snell-Descartes laws. Our main finding is that the generalized laws of refrac-tion and reflection as previously stated have to be modified in order to describe the propagation of light through metasurfaces made of diffractive elements. We provide the appropriate laws that take a different form depending on the properties of the metasurface. Our models apply to both periodic and non-periodic metasurfaces. We show that the generalized law of refraction strictly exists only for linear-phase profiles and sawtooth-wave phase profiles under constraints that we specify. It can be approximatively defined for non-linear phase profiles. This document includes the article as the part I and the supporting informations as the part II.
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Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
Auteur(s): Kneur J.-L., Neveu A.
(Article) Publié:
Physical Review D, vol. p.074009 (2020)
Texte intégral en Openaccess :
Ref HAL: hal-02464734_v1
Ref Arxiv: 2001.11670
DOI: 10.1103/PhysRevD.101.074009
WoS: 000525109000003
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé: We reconsider our former determination of the chiral quark condensate $\langle \bar q q \rangle$ from the related QCD spectral density of the Euclidean Dirac operator, using our Renormalization Group Optimized Perturbation (RGOPT) approach. Thanks to the recently available {\em complete} five-loop QCD RG coefficients, and some other related four-loop results, we can extend our calculations exactly to $N^4LO$ (five-loops) RGOPT, and partially to $N^5LO$ (six-loops), the latter within a well-defined approximation accounting for all six-loop contents exactly predictable from five-loops RG properties. The RGOPT results overall show a very good stability and convergence, giving primarily the RG invariant condensate, $\langle \bar q q\rangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) \bar\Lambda_0 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019}) \bar\Lambda_2 $, $\langle\bar q q\rangle^{1/3}_{RGI}(n_f=3) = -(0.751_{-.010}^{+0.019}) \bar\Lambda_3 $, where $\bar\Lambda_{n_f}$ is the basic QCD scale in the \overline{MS} scheme for $n_f$ quark flavors, and the range spanned is our rather conservative estimated theoretical error. This leads {\it e.g.} to $ \langle\bar q q\rangle^{1/3}_{n_f=3}(2\, {\rm GeV}) = -(273^{+7}_{-4}\pm 13)$ MeV, using the latest $\bar\Lambda_3$ values giving the second uncertainties. We compare our results with some other recent determinations. As a by-product of our analysis we also provide complete five-loop and partial six-loop expressions of the perturbative QCD spectral density, that may be useful for other purposes.
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Global properties of the growth index: mathematical aspects and physical relevance
Auteur(s): Calderon R., Felbacq D., Gannouji R., Polarski D., Starobinsky A.A.
(Article) Publié:
-Phys.rev.d, vol. 101 p.103501 (2020)
Texte intégral en Openaccess :
Ref HAL: hal-02423733_v1
Ref Arxiv: 1912.06958
Ref INSPIRE: 1770954
DOI: 10.1103/PhysRevD.101.103501
WoS: 000529824500006
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé: We analyze the global behavior of the growth index of cosmic inhomogeneities in an isotropic homogeneous universe filled by cold nonrelativistic matter and dark energy (DE) with an arbitrary equation of state. Using a dynamical system approach, we find the critical points of the system. That unique trajectory for which the growth index γ is finite from the asymptotic past to the asymptotic future is identified as the so-called heteroclinic orbit connecting the critical points (Ωm=0,γ∞) in the future and (Ωm=1,γ-∞) in the past. The first is an attractor while the second is a saddle point, confirming our earlier results. Further, in the case when a fraction of matter (or DE tracking matter) ϵΩmtot remains unclustered, we find that the limit of the growth index in the past γ-∞ϵ does not depend on the equation of state of DE, in sharp contrast with the case ϵ=0 (for which γ-∞ is obtained). We show indeed that there is a mathematical discontinuity: one cannot obtain γ-∞ by taking limϵ→0γ-∞ϵ (i.e., the limits ϵ→0 and Ωmtot→1 do not commute). We recover in our analysis that the value γ-∞ϵ corresponds to tracking DE in the asymptotic past with constant γ=γ-∞ϵ found earlier.
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S-duality and refined BPS indices
Auteur(s): Alexandrov S., Manschot Jan, Pioline Boris
(Article) Publié:
Communications In Mathematical Physics, vol. 380 p.755–810 (2020)
Texte intégral en Openaccess :
Ref HAL: hal-02313772_v1
Ref Arxiv: 1910.03098
DOI: 10.1007/s00220-020-03854-6
WoS: 000574083100002
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Résumé: Whenever available, refined BPS indices provide considerably more information on the spectrum of BPS states than their unrefined version. Extending earlier work on the modularity of generalized Donaldson-Thomas invariants counting D4-D2-D0 brane bound states in type IIA strings on a Calabi-Yau threefold $\mathfrak{Y}$, we construct the modular completion of generating functions of refined BPS indices supported on a divisor class. Although for compact $\mathfrak{Y}$ the refined indices are not protected, switching on the refinement considerably simplifies the construction of the modular completion. Furthermore, it leads to a non-commutative analogue of the TBA equations, which suggests a quantization of the moduli space consistent with S-duality. In contrast, for a local CY threefold given by the canonical bundle over a complex surface $S$, refined DT invariants are well-defined, and equal to Vafa-Witten invariants of $S$. Our construction provides a modular completion of the generating function of these refined invariants for arbitrary rank. In cases where all reducible components of the divisor class are collinear (which occurs e.g. when $b_2(\mathfrak{Y})=1$, or in the local case), we show that the holomorphic anomaly equation satisfied by the completed generating function truncates at quadratic order. In the local case, it agrees with an earlier proposal by Minahan et al for unrefined invariants, and extends it to the refined level using the afore-mentioned non-commutative structure. Finally, we show that these general predictions reproduce known results for $U(2)$ and $U(3)$ Vafa-Witten theory on $\mathrm{P}^2$, and make them explicit for $U(4)$.
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