arXiv subjects

César Riquelme

Publications and source records attributed to César Riquelme.

7 recordsLinked to original sources

arXiv2026

New constraints on modified gravity with dimension-six operators from gravitational waves

The present article deals with gravitational-wave propagation affected by higher-derivative terms that break spacetime symmetries. Two dimension-6 contributions of the gravitational Standard-Model Extension pose our starting point. A linearization of the action implies a wave equation that contains additional terms with spacetime-constant background fields. The modified dispersion relations in covariant form for gravitational waves are derived, where we distinguish between nonbirefringent and birefringent sectors. A classification of the coefficients in terms of sets with index structures resembling those of the electromagnetic fields has proven to be valuable. We constrain the nonbirefringent coefficients based on the measured arrival time difference between the gravitational wave and photons from the events GW170817 and GRB 170817A, respectively. Bounds on the birefringent coefficients result from the absence of a perceivable separation of the two modes in the event GW150914. These findings quantify the extent to which standard linearized gravity is valid based on the modifications considered.

gr-qc↗

arXiv2026

Dipole ghosts and spontaneous symmetry breaking in higher-order Chern-Simons theory

In this work, we investigate the emergence of dipole ghost structures in gauge theories at both the classical and quantum levels. Traditionally, dipole ghosts are introduced through an auxiliary field $χ$ satisfying $\Box^2χ=0$, whose presence is reflected in the appearance of double poles in the propagator. We show that such dipole ghost sectors can instead be understood as a consequence of the multiplicity of solutions of the classical equations of motion. To establish this connection, we develop a constructive method and first apply it to covariant Maxwell theory in $(2+1)$ dimensions, where the essential ingredients can be identified in a transparent manner. We then extend the analysis to the constrained higher-order Chern-Simons theory, demonstrating that the same mechanism gives rise to dipole ghost sectors and associated double poles in the propagator. Our results provide a unified perspective on the origin of dipole ghosts, relating them directly to the degeneracy structure of the underlying classical dynamics. As a physical application, we investigate spontaneous symmetry breaking and compute the one-loop effective potential. We show that symmetry breaking removes the degeneracy underlying the dipole ghost sector, leading to a spectrum of ordinary massive gauge excitations that determine the quantum vacuum structure of the theory.

hep-th↗

arXiv2026

Gödel-symmetric backgrounds and explicit spacetime symmetry breaking

Explicit breaking of diffeomorphism symmetry with nondynamical background fields in gravitational theories can lead to inconsistencies between the equations of motion and the underlying pseudo-Riemannian geometry. These theories produce a constraint equation that follows from the modified Einstein's equations and the contracted Bianchi identity which has no simple solution and raises questions about the consistency of backgrounds structures in extensions to general relativity. In contrast, spontaneous symmetry breaking where fields acquire a vacuum expectation value are shown to avoid these problems. Nevertheless, there are some approaches that consistently implement explicit diffeomorphism breaking by: i) introducing geometrical restrictions which may dynamically restore diffeomorphism invariance, ii) using the Stückelberg formalism where auxiliary scalar fields can carry degrees of freedom associated to spontaneously broken symmetries, and more recently by iii) exploiting the isometries of a given gravitational configuration in the presence of a background; which ultimately requires the background fields to be Lie-dragged along the Killing vectors. In this work, we further develop and apply the latter approach focusing on a concrete example involving the Gödel metric and the minimal gravitational Standard-Model Extension. We show that the resulting dynamics is fully consistent with the constraint equation and produce new Noether's identities. Furthermore we investigate causality violations by analyzing the critical radius, which is found to depend explicitly on the background fields. This dependence allows for the emergence of both causal and non-causal regions in spacetime.

gr-qc↗

arXiv2025

Higher-order Chern-Simons extensions to QED in $2+1$ dimensions

In this work, we investigate radiative corrections in the higher-order extension of the Maxwell-Chern-Simons model coupled to standard spinor matter in $2+1$ dimensions. We begin analyzing the higher-order gauge sector, where we find the modes and the polarizations vectors associated to a massive photon and ghost field. The higher-order gauge model is canonically quantized and as expected the resulting algebra of creation and annihilation operators corresponds to an indefinite metric in Hilbert space. Subsequently, we compute all relevant one-loop diagrams in the modified QED starting with the fermion self-energy. We show that the induced corrections to the fermion two-point function produce two independent fermionic degrees of freedom, which can be included in a redefined Lagrangian describing two decoupled fermions fields, one corresponding to a physical particle and the other to a negative-norm ghost state. We take advantage of this decomposition to compute the photon polarization operator and the vertex correction, both of which are found to be finite. Finally, we analyze the causal behavior of the model by computing the commutator of gauge fields at different spacetime points, and found that microcausality is preserved.

hep-th↗

arXiv2025

Reduced geometry and its role in explicit spacetime symmetry violation

The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an approach proposed originally by Stückelberg and the latter is to restrict spacetime geometry via the dynamical field equations and the second Bianchi identities. Moreover, a third technique is introduced in this work, which relies on isometries of a gravitational system. Our conclusion is that an SME background field configuration compatible with Riemannian geometry is more likely to be determined the more diffeomorphisms are isometries of the particular system. The proposal is demonstrated to work for cosmological time evolution with the SME backgrounds $u$ and $s^{μν}$ present. This finding has the potential to provide an alternative treatment of explicit spacetime symmetry violation in gravity.

gr-qc↗

arXiv2024

Cosmology with explicit and spontaneous background fields

We study a general class of effective backgrounds that break diffeomorphism invariance and their potential roles in cosmology. Specifically, we examine both explicit and spontaneous background fields which display distinct transformation properties and are characterized with different dynamics. For explicit breaking, we focus on the $t$-sector of the minimal gravitational Standard-Model Extension (SME) and for spontaneous breaking on a vector field called the bumblebee model. In both cases, we derive the modified Friedmann equations and find a configuration of the background fields that preserve isotropy and homogeneity. We show that the explicit $t$-sector admits phases of accelerated expansion of the universe with standard matter.

gr-qc↗

arXiv2023

Perturbative S-matrix unitarity and higher-order Lorentz violation

We investigate the preservation of unitarity in a Lorentz and CPT-violating QED model containing higher-order operators. In particular, we consider modifications in the fermion sector with dimension-five operators. The higher-order operators lead to an indefinite metric and a pseudo-unitarity relation for the $S$-matrix. However, we show that the pseudo-unitarity condition can be promoted to a genuine unitarity relation by i) restricting the energies to the effective region far below the Planck mass and ii) considering stable particles to have positive metric. In the context of the optical theorem, we focus on the one-loop Bhabha and Compton scattering processes. We show that no ghost states get propagated through the cuts, thus satisfying the unitarity condition. Further, we show that discontinuities of propagators are equivalent to replacing physical Dirac functionals in the cutting equation. The physical Dirac functionals are defined to select only mode solutions of stable particles. The provided extension of Cutkosky rule may be helpful for analyzing perturbative unitarity in higher-order diagrams.

hep-th↗