Self-interacting Field Research Articles

Fixing the dynamical evolution of self-interacting vector fields

Fixing the dynamical evolution of self-interacting vector fields

Quantum field theories of relativistic Luttinger fermions

We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using the spin-base invariant formalism. The corresponding minimal spinor has 32 complex components, matching with the degrees of freedom of a standard-model generation including a right-handed neutrino. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories. In particular, new asymptotically free self-interacting field theories can be constructed, representing first examples of high-energy complete quantum field theories based on pure matter degrees of freedom. Gauge theories with relativistic Luttinger fermions exhibit a strong paramagnetic dominance, requiring large non-Abelian gauge groups to maintain asymptotic freedom. We comment on the possibility to use Luttinger fermions for particle physics model building and the expected naturalness properties of such models. Published by the American Physical Society 2024

Generalized Brans-Dicke cosmology, noether symmetries and quantization

A generalized Brans-Dicke theory of gravitation is applied to investigate a cosmological model for a primordial universe that includes a self-interacting bosonic field as source. This model permits, initially, to consider an arbitrary ω function, not usual for BD formulations. The imposition of Noether symmetries conditions identifies a reduced space for the ω function. This model is shown to present a variety of behaviors consistent with a primordial era, depending on the parameters chosen. We find that the bosonic field is capable of promoting a transition from an initially accelerated to a decelerated regime. The self-interaction potential is also restricted by the Noether conditions, and can be interpreted as a vacuum energy contribution. The model also permits a quantization process, going through a hamiltonian formulation and recognizing the presence of cyclic variables. The Bohm approach shows as result a consistent model with a smooth classical limit as the Universe leaves the Planck era.

Hubble tension and gravitational self-interaction

One of the most important problems vexing the ΛCDM cosmological model is the Hubble tension. It arises from the fact that measurements of the present value of the Hubble parameter performed with low-redshift quantities, e.g. the Type IA supernova, tend to yield larger values than measurements from quantities originating at high-redshift, e.g. fits of cosmic microwave background radiation. It is becoming likely that the discrepancy, currently standing at 5σ, is not due to systematic errors in the measurements. Here we explore whether the self-interaction of gravitational fields in General Relativity, which are traditionally neglected when studying the evolution of the Universe, can contribute to explaining the tension. We find that with field self-interaction accounted for, both low- and high-redshift data are simultaneously well-fitted, thereby showing that gravitational self-interaction yield consistent H 0 values when inferred from SnIA and cosmic microwave background observations. Crucially, this is achieved without introducing additional parameters.

Vacuum zero point energy of self-interacting quantum fields in dS background

Vacuum zero point energy of self-interacting quantum fields in dS background

New boundary conditions in Einstein-scalar gravity in three dimensions

We analyze the backreaction of a class of scalar field self-interactions with the possibility of evolving from an AdS vacuum to a fixed point where the scalar field potential vanishes. Exact solutions which interpolate between these regions, ranging from stationary black hole to dynamical spacetimes are constructed. Their surface charges are finite but non-integrable. We study the properties of these charges on the solutions. In particular, we show that the integrable part of the charges provides a realization of the conformal algebra by means of a modification of the Dirac bracket proposed by Barnich and Troessaert. The latter construction allows for a field dependent central extension, whose value tends to the Brown-Henneaux central charge at late times.

The mass of simple and higher-order networks

We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu–Jona-Lasinio model. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry. Due to the breaking of the matter–antimatter symmetry observed for the harmonic modes of the discrete topological Dirac operator, two possible definitions of the network mass can be given. For both possible definitions, the mass of the network comes from a gap equation with the difference among the two definitions encoded in the value of the bare mass. Indeed, the bare mass can be determined either by the Betti number β 0 or by the Betti number β 1 of the network. We provide numerical results on the mass of different networks, including random graphs, scale-free, and real weighted collaboration networks. We also discuss the generalization of these results to higher-order networks, defining the mass of simplicial complexes. The observed dependence of the mass of the considered topological Dirac field with the topology and geometry of the network could lead to interesting physics in the scenario in which the considered Dirac field is coupled with a dynamical evolution of the underlying network structure.

Bootstrapping gravity and its extension to metric-affine theories

In this work we study diffeomorphism-invariant metric-affine theories of gravity from the point of view of self-interacting field theories on top of Minkowski spacetime (or other background). We revise how standard metric theories couple to their own energy-momentum tensor, and discuss the generalization of these ideas when torsion and nonmetricity are also present. We review the computation of the corresponding currents through the Hilbert and canonical (Noether) prescriptions, emphasizing the potential ambiguities arising from both. We also provide the extension of this consistent self-coupling procedure to the vielbein formalism, so that fermions can be included in the matter sector. In addition, we clarify some subtle issues regarding previous discussions on the self-coupling problem for metric theories, both General Relativity and its higher derivative generalizations. We also suggest a connection between Lovelock theorem and the ambiguities in the bootstrapping procedure arising from those in the definition of conserved currents.

Pervasiveness of the breakdown of self-interacting vector field theories

Various groups recently argued that self-interacting vector field theories lack a well-defined time evolution when the field grows to large amplitudes, which has drastic consequences for models in gravity and high energy theory. Such field amplitudes can be a result of an external driving mechanism, or occur intrinsically, due to large values of the field and its derivatives in the initial data. This brings a natural question: Is small amplitude initial data guaranteed to evolve indefinitely in these theories in the absence of an outside driving term? We answer this question in the negative, demonstrating that arbitrarily low amplitude initial data can still lead to the breakdown of the theory. Namely, ingoing spherically symmetric wave packets in more than one spatial dimensions grow as an inverse power of the radius, and their amplitudes can generically reach high enough values where time evolution ceases to exist. This simple example further establishes the pervasiveness of the pathology of self-interacting vector field theories.

Some disquisitions on cosmological 2-form dualities

In this work we study different aspect of self-interacting 2-form fields with special emphasis in their cosmological applications. We provide the explicit construction of how massless 2-forms are compatible with the cosmological principle without resorting to the dual scalar field formulation. In terms of the 2-form, the residual Euclidean group is non-trivially realised by means of a combination of external spatial translations and internal gauge transformations. After presenting the general discussion of the dualities in cosmological scenarios, we analyse particular examples for some singular models and discuss in some detail the dual descriptions of the DBI, the cuscuton and the ghost condensate as well as the role of the duality in the effective field theories of cosmological perturbations. We then proceed to analysing scenarios with several self-interacting massless 2-forms and we show that they naturally provide the dual description of a solid. We then show how the perfect fluid and superfluids can be obtained by taking the appropriate limits in the dual formulations. We finally consider the case of massive 2-forms and their duals and briefly discuss their potential signatures in gravitational waves astronomy.

Characterizing the post-inflationary reheating history. Part II. Multiple interacting daughter fields

We characterize the post-inflationary dynamics of an inflaton ϕ coupled to multiple interacting daughter fields Xn (n = 1, … Nd ) through quadratic-quadratic interactions gn 2 ϕ 2 Xn 2. We assume a monomial inflaton potential V(ϕ) ∝ |ϕ| p (p ≥ 2) around the minimum. By simulating the system in 2+1-dimensional lattices, we study the post-inflationary evolution of the energy distribution and equation of state, from the end of inflation until a stationary regime is achieved. We show that in this scenario, the energy transferred to the daughter field sector can be larger than 50%, surpassing this way the upper bound found previously for single daughter field models. In particular, for p ≥ 4 the energy at very late times is equally distributed between all fields, and only 100/(Nd + 1) % of the energy remains in the inflaton. We also consider scenarios in which the daughter fields have scale-free interactions λnmXn 2 Xm 2, including the case of quartic daughter field self-interactions (for n = m). We show that these interactions trigger a resonance process during the non-linear regime, which in the single daughter field case already allows to deplete more than 50% of the energy from the inflaton for p ≥ 4.

Coordinate Singularities of Self-Interacting Vector Field Theories.

Self-interacting vectors are seeing a burst of interest where various groups demonstrated that the field evolution ends in finite time. Two nonequivalent criteria have been offered to identify this breakdown: (i)the vector constraint equation cannot be satisfied beyond a point where the breakdown occurs, (ii)the dynamics is governed by an effective metric that becomes singular at the breakdown. We show that (i)identifies a coordinate singularity, and can be removed by a change of coordinates. Hence, it does not signify a physical problem, and cannot determine the validity of a theory.

Fermionic tachyons as a source of dark energy

We investigate a model for the universe based on the self-interacting fermionic tachyon field. We have shown that by devising a self-interaction potential of a proper form, the fermionic tachyon field is capable of producing an accelerating expansion. At late times, this potential tends to a constant value; this behavior is consistent with the cosmological constant. In this way, the introduced fermionic tachyon field can be interpreted as the source of dark energy.

The well-posedness of the Cauchy problem for self-interacting vector fields

We point out that the initial-value (Cauchy) problem for self-interacting vector fields presents the same well-posedness issues as for first-order derivative self-interacting scalar fields (often referred to as k-essence). For the latter, suitable strategies have been employed in the last few years to successfully evolve the Cauchy problem at the level of the infrared theory, without the need for an explicit ultraviolet completion. We argue that the very same techniques can also be applied to self-interacting vector fields, avoiding a number of issues and “pathologies” recently found in the literature.

Resolving the pathologies of self-interacting Proca fields: A case study of Proca stars

It has been argued that a self-interacting massive vector field is pathological due to a dynamical formation of a singular effective metric of the vector field, which is the onset of a gradient or ghost instability. We discuss that this singularity formation is not necessarily a fundamental problem but a breakdown of the effective field theory (EFT) description of the massive vector field. By using a model of ultraviolet (UV) completion of the massive vector field, we demonstrate that a Proca star, a self-gravitating condensate of the vector field, continues to exist even after the EFT suffers from a gradient instability without any pathology at UV, in which the EFT description is still valid and the gradient instability in EFT may be interpreted as a standard dynamical instability of a high-density boson star from the UV perspective. On the other hand, we find that the EFT description is broken before the ghost instability appears. This suggests that a heavy degree of freedom may be spontaneously excited to cure the pathology of the EFT as the EFT dynamically tends to approach the onset of the ghost instability.

Intrinsic Pathology of Self-Interacting Vector Fields.

We show that self-interacting vector field theories exhibit unphysical behavior even when they are not coupled to any external field. This means any theory featuring such vectors is in danger of being unphysical, an alarming prospect for many proposals in cosmology, gravity, high energy physics, and beyond. The problem arises when vector fields with healthy configurations naturally reach a point where time evolution is mathematically ill defined. We develop tools to easily identify this issue, and provide a simple and unifying framework to investigate it.

Ghost Instabilities in Self-Interacting Vector Fields: The Problem with Proca Fields.

Massive vector fields feature in several areas of particle physics, e.g., as carriers of weak interactions, dark matter candidates, or an effective description of photons in a plasma. Here, we investigate vector fields with self-interactions by replacing the mass term in the Proca equation with a general potential. We show that this seemingly benign modification inevitably introduces ghost instabilities of the same kind as those recently identified for vector-tensor theories of modified gravity (but in this simpler, minimally coupled theory). It has been suggested that nonperturbative dynamics may drive systems away from such instabilities. We demonstrate that this is not the case by evolving a self-interacting Proca field on a Kerr background, where it grows due to the superradiant instability. The system initially evolves as in the massive case, but instabilities are triggered in a finite time once the self-interaction becomes significant. These instabilities have implications for the formation of condensates of massive, self-interacting vector bosons, the possibility of spin-one bosenovae, vector dark matter models, and effective models for interacting photons in a plasma.

The self-interacting Dirac fields in FLRW spacetime

We prove the existence of global in time solution with the small initial data for the semilinear equation of the spin-\(\frac{1}{2}\) particles in the Friedmann–Lemaître–Robertson–Walker spacetime. Moreover, we also prove that if the initial function satisfies the Lochak–Majorana condition, then the global solution exists for arbitrary large initial value. The solution scatters to free solution for large time. The mass term is assumed to be complex-valued. The conditions on the imaginary part of mass are discussed by proving nonexistence of the global solutions if certain relation between scale function and the mass are fulfilled.

Subnucleon fluctuations in coherent and incoherent ultra-peripheral AA collisions at LHC and RHIC with the Sartre event generator

Sartre~has been extensively used for describing photon-nuclei processes at the electron-ion collider (EIC) as well as ultra-peripheral collisions (UPC) at LHC and RHIC. Sartre is an event generator which implements the dipole model for DIS, and models the transverse geometry of the target nucleus or proton in coordinate space. It uses the Good-Walker mechanism for simulating fluctuations which contribute to the incoherent cross section for which the target breaks up after the interaction. With improved precision of UPC measurements in the last years, a detailed test of the dipole model has become possible, and Sartre's model was found lacking. In these proceedings we add subnucleon fluctuations to the nucleus and show that this is sufficient for describing the vast majority of the present measurements. We also find that for larger momentum transfers in the nucleus, which probes gluon fluctuations at higher resolution, the current complexity of the model may not suffice. Future measurements at the LHC, RHIC and especially the EIC has the potential to reveal these gluon vacuum fluctuations and glean novel insights into the self-interacting quantum field of QCD.

Effect of the field self-interaction of General Relativity on the cosmic microwave background anisotropies

Field self-interactions are at the origin of the non-linearities inherent to General Relativity. We study their effects on the cosmic microwave background (CMB) anisotropies. We find that they can reduce or alleviate the need for dark matter and dark energy in the description of the CMB power spectrum.