qft in curved spacetime
In the past four years, works about classical and quantum fields in curved spacetimes was continued. It was obtained from what is sometimes called ”conformal space”, that is the SO(d,2) dimensional space of reals endowed with the metric invariant under the conformal group SO(d, 2), denoted R^(d+2). The main idea is that the field equations are somehow simpler in R^(d+2). A formalism in which the spacetime is realized as the intersection of the null cone of R^(d+2) and a hyper-surface was developed.
The restriction from the conformal to the Robertson-Walker spacetime of the Laplace-Beltrami operator for scalar field was obtained in work with J. P. Arias Zappata, A. Belokogne (respectively intern and post-doc in 2017) and J. Qu´eva (Universit´e de Corse) Zapata:2017gqg.
We also showed, with J. Qu´eva, how field equations for scalar fields (massive or not) on (Anti)-de Sitter space can obtained from ”massless” conformal scalar in R^(d+2) and the constraints defining the space Huguet:2016szt.
In parallel, our team has developed specific Wilsonian renormalisation group tools to address the question of nonperturbative infrared fluctuations of quantum fields in de Sitter space, of direct relevance to inflationary cosmologyGuilleux:2016oqv.
In Moreau:2018lmz and Moreau:2018ena, we have applied these tools to compute the backreaction of scalar fields on the geometry through self-consistent semiclassical Einstein equations. We have shown that the apparent instability of de Sitter space predicted by perturbation theory, proposed as a possible ex- planation of the cosmological constant problem in earlier literature, is in fact screened by nonperturbative effects in the case of scalar fields. The de Sitter space is stable against quantum fluctuations of such fields.
A. Belokogne(PostDoc 2016-2017), M. Guilleux (PhD 2013-2016), E. Huguet(MCF U-Paris), J. Maelger(PhD 2016-2019), G. Moreau(PhD 2017-2020), J. Renaud(Pr.~Emeritus, U-Gustave Eiffel), J. Serreau (MCF U-Paris)
Dynamics of strong interactions and confinement
Since 2010, our group develops, together with collaborators at Sorbonne Uni- versit´es (M. Tissier), Ecole Polytechnique (U. Reinosa) and University of Mon- tevideo (M. Pelaez and N. Wschebor), a novel approach to describe the infrared regime of non-Abelian Yang-Mills theories and of qcd, based on a modified perturbation theory in the Landau gauge, the perturbative Curci-Ferrari model.
The approach allows to successfully reproduce various results from numerical lattice simulations, both in vacuumReinosa:2017qtf and at nonzero temperature and chemical potentialReinosa:2016iml. For instance, a simple one-loop calculation in our approach gives an accurate description of the confinement- deconfinement transition in Yang-Mills theories and of the temperature dependence of the order parameter of the transition (the Polyakov loop)vanEgmond:2021jyx.
In the period 2017-2021, we have applied our approach to treat the quark sector of qcd. We have computed the phase diagram of qcd-like theories with heavy quarks at one Maelger:2018vow and two-loop Maelger:2017amh orders, in very good agreement with lattice results.
In Ref. Pelaez:2017bhh and Pelaez:2020ups, we have further developed the approach to deal with (realistic) light quark dynamics, which requires a proper description of the dynamical breaking of chiral symmetry. Combining our per- turbative approach in the pure gauge sector and the t’hooft expansion in the inverse number of colors, we have proposed a novel systematic, controlled approximation scheme to describe the infrared regime of qcd.
Our results for the quark propagator at leading order in this expansion compares very well with lattice simulations, down to the deep infrared, where the spontaneous breaking of chiral symmetry results in the dynamical generation of the constituent quark mass. The perturbative Curci-Ferrari approach to qcd has been and its many results have been described in detail in a recent reviewPelaez:2021tpq.
Finally, we have investigated the possible origin of the dynamically generated gluon mass observed in lattice simulations in the Landau gauge in relation with the issue of Gribov ambiguities when fixing the gauge in nonAbelian theories.
We have proposed a gauge fixing that properly accounts for the Gribov copies (unlike the standard Faddeev-Popov approach) and where a gluon mass is dynamically generated through a mecanism of symmetry restauration similar to what happens in the nonlinear sigma modelReinosa:2020skx.
M. Guilleux, E. Huguet, J. Maelger, G. Moreau, J. Serreau