Effective action for $ϕ^4$-Yukawa theory via 2PI formalism in the inflationary de Sitter spacetime

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Main Authors: Bhattacharya, Sourav, Roy, Kinsuk
Format: Preprint
Published: 2025
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author Bhattacharya, Sourav
Roy, Kinsuk
author_facet Bhattacharya, Sourav
Roy, Kinsuk
contents We consider a scalar field theory with quartic self interaction, Yukawa coupled to fermions in the inflationary de Sitter spacetime background. The scalar has a classical background plus quantum fluctuations, whereas the fermions are taken to be quantum. We derive for this system the effective action and the effective potential via the two particle irreducible (2PI) formalism. This formalism provides an opportunity to find out resummed or non-perturbative expressions for some series of diagrams. We have considered the two loop vacuum graphs and have computed the local part of the effective action. The various resummed counterterms corresponding to self energies, vertex functions and the tadpole have been explicitly found out. The variation of the renormalised effective potential for massless fields has been investigated numerically. We show that for the potential to be bounded from below, we must have $λ\gtrsim 16 g^2$, where $λ$ and $g$ are respectively the quartic and Yukawa couplings. We emphasise the qualitative differences of this non-perturbative calculation with that of the standard 1PI perturbative ones in de Sitter. The qualitative differences of our result with that of the flat spacetime has also been pointed out.
format Preprint
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institution arXiv
publishDate 2025
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spellingShingle Effective action for $ϕ^4$-Yukawa theory via 2PI formalism in the inflationary de Sitter spacetime
Bhattacharya, Sourav
Roy, Kinsuk
High Energy Physics - Theory
General Relativity and Quantum Cosmology
We consider a scalar field theory with quartic self interaction, Yukawa coupled to fermions in the inflationary de Sitter spacetime background. The scalar has a classical background plus quantum fluctuations, whereas the fermions are taken to be quantum. We derive for this system the effective action and the effective potential via the two particle irreducible (2PI) formalism. This formalism provides an opportunity to find out resummed or non-perturbative expressions for some series of diagrams. We have considered the two loop vacuum graphs and have computed the local part of the effective action. The various resummed counterterms corresponding to self energies, vertex functions and the tadpole have been explicitly found out. The variation of the renormalised effective potential for massless fields has been investigated numerically. We show that for the potential to be bounded from below, we must have $λ\gtrsim 16 g^2$, where $λ$ and $g$ are respectively the quartic and Yukawa couplings. We emphasise the qualitative differences of this non-perturbative calculation with that of the standard 1PI perturbative ones in de Sitter. The qualitative differences of our result with that of the flat spacetime has also been pointed out.
title Effective action for $ϕ^4$-Yukawa theory via 2PI formalism in the inflationary de Sitter spacetime
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2503.21578