arXiv subjects

Kinsuk Roy

Publications and source records attributed to Kinsuk Roy.

3 recordsLinked to original sources

arXiv2025

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

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.

hep-th↗

arXiv2025

Spontaneous symmetry breaking induced by curvature : Analysis via non-perturbative 2PI Hartree approximation

In this work we investigate the spontaneous symmetry breaking (SSB) induced by a classical background spacetime's curvature, via the 2 particle irreducible (2PI) non-perturbative effective action formalism. We use the standard Schwinger-DeWitt local expansion of the Feynman propagator, appropriate to probe the effect of spacetime curvature on the local or short scale physics. Recently it was shown using perturbative computations that such SSB is possible with a scalar with a quartic self interaction, positive rest mass squared and positive non-minimal coupling. Here we confirm in the two loop Hartree approximation that curvature can indeed induce SSB for such a theory. SSB for such a model is not possible in a flat spacetime. The 2PI technique does not only resum the self energy resulting in mass generation, but also resums, as we have discussed, curvature terms through such mass generation. We have explicitly discussed our results in the context of the de Sitter spacetime, although our calculations are valid for any non-singular curved spacetime. We show that, in contrast to the perturbative results, SSB is possible with a vanishing non-minimal coupling. These results are further extended to the case of an $O(N)$ symmetric scalar field theory. Restoration of the broken symmetry in the thermal case is also briefly discussed.

gr-qc↗

arXiv2024

Resummation of local and non-local scalar self energies via the Schwinger-Dyson equation in de Sitter spacetime

We consider a massless and minimally coupled self interacting quantum scalar field in the inflationary de Sitter spacetime. The scalar potential is taken to be a hybrid, $V(ϕ)= λϕ^4/4!+βϕ^3/3!$ ($λ>0$). Compared to the earlier well studied $β=0$ case, the present potential has a rolling down effect due to the $ϕ^3$ term, along with the usual bounding effect due to the $ϕ^4$ term. We begin by constructing the Schwinger-Dyson equation for the scalar Feynman propagator up to two loop, at ${\cal O}(λ)$, ${\cal O}(β^2)$, ${\cal O}(λ^2)$ and ${\cal O}(λβ^2)$. We consider first the local part of the scalar self energy and compute the rest mass squared of the scalar field, dynamically generated via the late time non-perturbative secular logarithms, by resumming the daisy-like graphs. The logarithms associated here are sub-leading, compared to those associated with the non-local, leading terms. We also argue that unlike the quartic case, considering merely the one loop results for the purpose of resummation does not give us any sensible result here. We next construct the non-perturbative two particle irreducible effective action up to three loop and derive from it the Schwinger-Dyson equation once again. This equation is satisfied by the non-perturbative Feynman propagator. By series expanding this propagator, the resummed local part of the self energy is shown to yield the same dynamical mass as that of the above. We next use this equation to resum the effect of the non-local part of the scalar self energy, and show that even though the perturbatively corrected propagator shows secular growth at late times, there exists one resummed solution which is vanishing for large spatial separations, in qualitative agreement with that of the stochastic formalism.

hep-th↗