The project  Horizons  (ANR-16-CE40-0012-01) is funded by the Young Researcher (Jeunes Chercheuses et Jeunes Chercheurs)  programme of the ANR.

It runs from December 2016 to September 2020. The main host institution is the Institut Fourier (Université Grenoble Alpes)

Abstract of the project

The main topic is the application of techniques of asymptotic and global analysis to Quantum Field Theory on curved spacetimes and General Relativity, with the goal of studying quantum phenomena near and beyond spacetime horizons.

Striking physical phenomena are indeed believed to occur in setups where global and asymptotic aspects enter, geometrically often indicated by the presence of a horizon. Presently, conjectures regarding Hawking radiation, existence of the Hartle-Hawking and Unruh states on black hole spacetimes, or AdS-CFT duality remain unsolved due to significant gaps in our understanding of how the asymptotic analysis of hyperbolic differential equations relates to eg. propagation of singularities. The core idea is to implement a mixture of recently developed techniques from eg. asymptotic and microlocal analysis, as well as scattering and index theory to investigate and extend QFT to new curved backgrounds. Ultimately, the project seeks to explore extensions of quantum fields across spacetime horizons.

Members

Activities and events

Seminars

Workgroup seminar General Relativity and QFT, Institut Fourier (Grenoble)

Meetings and conferences

Quantum fields, scattering and spacetime horizons: mathematical challenges,                Les Houches, 22-25 May 2018 

Relativistic Mathematical Physics in Grenoble, Institut Fourier (Grenoble), 22-25 May 2019 

Positive commutators and propagation phenomena, Cergy-Pontoise, 28-29 May 2020 (cancelled due to COVID-19 outbreak)

Scattering, microlocal analysis and renormalisation, Institut Mittag-Leffler, 01-05 June 2020

Mini lectures series

Christian Gérard (Paris-Saclay), Quantum Field Theory on Curved Spacetimes ,  Institut Fourier, Grenoble, 2018    [ Lecture notes ]

Michał Wrochna (CY Cergy Paris Université), An Invitation to QFT on Curved Spacetimes,  MSRI, Berkeley, 2020    [ Slides ]

Publications

Publications and preprints of the project

[1] O. Gannot, M. Wrochna: „Propagation of singularities on AdS spacetimes for general boundary conditions and the holographic Hadamard condition", to appear in Journal of the Institute of Mathematics of Jussieu, arXiv:1812.06564 (2018)
[2] D. Häfner, P. Hintz, A. Vasy: „Linear stability of slowly rotating Kerr black holes", arXiv:1906.00860 (2019)
[3] N. V. Dang, C. Guillarmou, G. Rivière et S. Shen: „Fried conjecture in small dimensions", Inventiones Mathematicae 220, 525–579 (2020)
[4] C. Huneau, J. Luk: „High-frequency backreaction for the Einstein equations under polarized U(1) symmetry", Duke Math. J., 67(18):3315-3402, arXiv:1706.09501 (2018)
[5] C. Gérard, M. Wrochna: „Analytic Hadamard states, Calderón projectors and Wick rotation near analytic Cauchy surfaces", Communications in Mathematical Physics 366 (1), arXiv:1609.00192, (2019)
[6] W. Dybalski, M. Wrochna: „A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes", Classical and Quantum Gravity 36 (8), arXiv:1809.05123, (2019)
[7] M. Wrochna: „The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes", Letters in Mathematical Physics, 107 (12), 2291-2331, arXiv:1612.01203 (2017)
[8] C. Gérard, M. Wrochna: „The massive Feynman propagator on asymptotically Minkowski spacetimes", American Journal of Mathematics 141 (6), arXiv:1609.00192, (2019)
[9] C. Gérard, M. Wrochna: „The massive Feynman propagator on asymptotically Minkowski spacetimes II", accepted in International Mathematics Research Notices, arXiv:1806.05076, (2018)
[10] N. V. Dang, G. Rivière: „Spectral analysis of Morse-Smale gradient flows", Annales de l'ENS 52 (6), 1403-1458 (2019)
[11] N. V. Dang, G. Rivière: „Spectral analysis of Morse-Smale flows II: resonances and resonant states", American Journal of Mathematics 142, (2), (2020)
[12] D. Häfner, C. Huneau: „Instability of infinitely many stationary solutions of the SU(2) Yang-Mills fields on the exterior of the Schwarzschild black hole", Adv. Diff. Equ. 24, 435-464, arXiv:1612.064596 (2019)
[13] N. V. Dang, G. Rivière: „Spectral analysis of Morse-Smale flows I: construction of the anisotropic spaces", Journal of the Institute of Mathematics of Jussieu, doi:10.1017/S1474748018000439 (2018)
[14] T. Daudé, N. Kamran, F. Nicoleau: „On the hidden mechanism behind non-uniqueness for the anisotropic Calderón problem with data on disjoint sets", Annales Henri Poincaré 20, 859–887, arXiv:1510.06559 (2019)
[15] N. V. Dang, E. Herscovich: „Renormalization of quantum field theory on Riemannian manifolds", Reviews in Mathematical Physics 31 (06), 1950017 (2019)
[16] M. Wrochna: „Wick rotation of the time variables for two-point functions on analytic backgrounds", Letters in Mathematical Physics, 110, 585–609, arXiv:1808.03859 (2020)
[17] N. V. Dang, G. Rivière: „Equidistribution of the conormal cycle of random nodal sets", Journal of Eur. Math. Soc. 20 (12), 3017–3071 (2018)
[18] J.-P. Nicolas, P. T. Xuan: "Peeling of Dirac field on Kerr spacetime", Journal of Mathematical Physics 61, 032501 (2020)
[19] L. Di Menza, J.-P. Nicolas, M. Pellen: "A new type of charged black hole bomb", to appear in Gener. Relat. Gravit. (2020)
[20] N. V. Dang: „Renormalization of determinant lines in Quantum Field Theory", arXiv:1901.10542 (2019)
[21] T. Daudé, N. Kamran, F. Nicoleau: „Separability and Symmetry Operators for Painlevé Metrics and their Conformal Deformations",  arXiv:1903.10573 (2019)
[22] A. Strohmaier, S. Zelditch: "A Gutzwiller trace formula for stationary space-times", arXiv:1808.08425 (2018)
[23] T. Daudé, N. Kamran, F. Nicoleau: „The anisotropic Calderón problem on 3-dimensional conformally Stäckel manifolds", arXiv:1909.01669 (2016)
[24] N. V. Dang: „Wick squares of the Gaussian Free Field and Riemannian rigidity", arXiv:1902.07315 (2019)
[25] T. Daudé, N. Kamran, F. Nicoleau: „Stability in the inverse Steklov problem on warped product Riemannian manifolds", arXiv:1812.07235 (2018)
[26] M. Wrochna: „Conformal extension of the Bunch-Davies state across the de Sitter boundary", Journal of Mathematical Physics 60 (2), 022301, arXiv:1711.04011, (2019)
[27] T. Daudé, N. Kamran, F. Nicoleau: „The anisotropic Calderón problem for singular metrics of warped product type: the borderline between uniqueness and invisibility", arXiv:1805.05627 (2018)
[28] C. Gérard, O. Oulghazi, M. Wrochna „Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry”, Communications in Mathematical Physics, 352 (2), 519-583, arXiv:1602.00930 (2017)
[29] S. Ghanem, D. Häfner: „The decay of the SU(2) Yang-Mills fields on the Schwarzschild black hole for spherically symmetric small energy initial data", J. Geom. Phys. 123, 310-342, arXiv:1604.04477 (2018)
[30] C. Brouder, N. V. Dang, C. Laurent-Gengoux, K. Rejzner: „Properties of field functionals and characterization of local functionals", arXiv:1705.01937 (2017)
[31] C. Huneau, J. Luk: „Trilinear compensated compactness and Burnett's conjecture in general relativity", arXiv:1907.10743.pdf (2019)
[32] T. Daudé, F. Nicoleau: „Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes", Mem. Amer. Math. Soc. 247, no. 1170, iv+113 pp., arXiv:1307.2842 (2017)
[33] N. Besset, D. Häfner: „Existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric", arXiv:2004.02483 (2020)
[34] C. Huneau, J. Luk: „Einstein equations under polarized U(1) symmetry in an elliptic gauge", Comm. Math. Phys., 361(3):873-949, arXiv:1706.09499 (2018)
[35] N.V. Dang, B. Zhang: „Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-ups", to appear in Journal of Eur. Math. Soc., arXiv:1712.03490 (2017)