arXiv subjects

D. M. Ghilencea

Publications and source records attributed to D. M. Ghilencea.

At least 19 recordsLinked to original sources

arXiv2026

Weyl conformal geometry vs Riemannian geometry of Weyl gauge invariant (dressed) metric

Weyl conformal geometry is the natural underlying geometry of gauge theories of Weyl group (of dilatations and Poincaré symmetry), such as Weyl quadratic gravity and its generalisation, Weyl-Dirac-Born-Infeld action (WDBI). These are local, Weyl-anomaly free (quantum) gauge theories of gravity. We describe Weyl gauge symmetry from a more familiar Riemannian view of Weyl gauge invariant dressed fields by the Wilson line of dilatations. Weyl geometry can then be seen as Riemannian geometry of non-local dressed metric ($g_{μν}^*$), at the "cost" of (gauge-induced) non-commutativity in the UV, due to Wilson line. Then Weyl quadratic gravity and WDBI actions of Weyl geometry, which are Weyl gauge invariant in $d$ dimensions, have the same expression in Riemannian geometry defined by $g^*_{μν}$. This is a non-local map and dual description of the two geometries and actions in the symmetric phase. Unlike for the metric, the equation of motion of Weyl gauge field ($ω_μ$) does not commute with the dressing of the metric. Quantum non-locality, in particular entanglement, and non-commutativity are (gauge-invariant) physical artefacts of "translating" (local) Weyl geometry and Weyl gauge covariance into our real-world Riemannian geometry of Weyl gauge invariant observables, and they are evidence of Weyl gauge symmetry. At lower energies, $ω_μ$ becomes massive, can decouple and Einstein-Hilbert action and commutativity are recovered. The case of a light $ω_μ$ is also discussed.

hep-th↗

arXiv2026

Weyl gauge symmetry at LIGO-Virgo-KAGRA

With current advances in gravitational wave (GW) detection made by the worldwide LIGO-Virgo-KAGRA (LVK) network of detectors, ever-more sensitive tests of gravity in the strong-field regime are now possible. This enables one to test gauge theories beyond Einstein-Hilbert action, such as Weyl gauge theories of gravity. The only anomaly-free (quantum) gauge theory of a space-time symmetry beyond Poincaré is based on Weyl gauge group (of dilatations and Poincaré symmetry) with Weyl conformal geometry as its natural underlying geometry. This gauge theory has spontaneous breaking of Weyl gauge symmetry to Einstein-Hilbert and Proca actions, plus a positive cosmological constant. We investigate the GW polarisation modes of Weyl (quadratic) gauge theory of gravity in Weyl geometry and compare our findings to the most recent experimental data. We show how the geodesic deviation equation from Riemannian geometry translates to Weyl geometry, and explain why it is crucial to perform the analysis around de Sitter background, which is the correct low-energy limit of Weyl quadratic gravity, to not alter the GW content, and then compute the polarisation modes. In addition to the two transverse-traceless tensor modes predicted by Einstein-Hilbert action, we find two additional vector modes induced by the transverse fluctuations of the Weyl gauge field. If detected, these vectors modes would be important evidence for Weyl gauge symmetry.

gr-qc↗

arXiv2026

The fall and the rise of Weyl gauge theory

In 1918 Weyl introduced Weyl conformal geometry and its associated quadratic action which was the first gauge theory, of the Weyl group (of dilatations and Poincaré symmetry). The initial physical interpretation of his theory was however short-lived and led to the downfall of Weyl geometry as a physical theory. We review how this action was re-born into a physical Weyl quadratic gauge theory of gravity. This is the only (quadratic) gauge theory of a spacetime symmetry with a physical gauge boson, is Weyl anomaly-free, has {\it exact} geometric interpretation, with all scales of geometric origin, and generates Einstein-Hilbert action and a positive cosmological constant in its Stueckelberg broken phase. A more fundamental Weyl gauge theory is the Weyl-Dirac-Born-Infeld (WDBI) action of Weyl geometry, that is Weyl gauge invariant in arbitrary $d$ dimensions and that does not need a UV regulator (!), of which the (geometrically regularised) Weyl quadratic gauge theory is the leading order. For $d=4$ the WDBI action can include SM operators alongside gravitational terms into a unified description, both geometric and by the gauge principle, of SM and Einstein-Hilbert gravity, which are recovered in the leading order of this action.

gr-qc↗

arXiv2025

Unification of Gravity and Standard Model: Weyl-Dirac-Born-Infeld action

We construct a unified (quantum) description, by the gauge principle, of gravity and Standard Model (SM), that generalises the Dirac-Born-Infeld action to the SM and Weyl geometry, hereafter called Weyl-Dirac-Born-Infeld action (WDBI). The theory is formulated in $d =4-2ε$ dimensions. The WDBI action is a general gauge theory of SM and Weyl group (of dilatations and Poincaré symmetry), in the Weyl gauge covariant (metric!) formulation of Weyl geometry. The theory is SM and Weyl gauge invariant in $d=4-2ε$ dimensions and there is no Weyl anomaly. The WDBI action has the unique elegant feature, not present in other gauge theories or even in string theory, that it is mathematically well-defined in $d=4-2ε$ dimensions with no need to introduce in the action a UV regulator scale or field. This action actually {\it predicts} that gravity, through (Weyl covariant) space-time curvature $\hat R$, acts as UV regulator of both SM and gravity in $d=4$. A series expansion of the WDBI action (in dimensionless couplings) recovers in the leading order a Weyl gauge invariant version of SM and the Weyl (gauge theory of) quadratic gravity. The SM and Einstein-Hilbert gravity are recovered in the Stueckelberg broken phase of Weyl gauge symmetry, which restores Riemannian geometry below Planck scale. Sub-leading orders are suppressed by powers of (dimensionless) gravitational coupling ($ξ$) of Weyl quadratic gravity.

hep-ph↗

arXiv2025

Quantum gravity from Weyl conformal geometry

We review recent developments in physical implications of Weyl conformal geometry. The associated Weyl quadratic gravity action is a gauge theory of the Weyl group of dilatations and Poincaré symmetry. Weyl conformal geometry is defined by equivalence classes of the metric and Weyl gauge field ($ω_μ$), related by Weyl gauge transformations. Weyl geometry can be seen as a covariantised version of Riemannian geometry with respect to Weyl gauge symmetry (of dilatations). This Weyl gauge-covariant formulation of Weyl geometry is metric, which avoids century-old criticisms on the physical relevance of this geometry, that ignored its gauge symmetry. Weyl quadratic gravity and its geometry have interesting properties: a) Weyl gauge symmetry is spontaneously broken and Einstein-Hilbert gravity and Riemannian geometry are recovered, with $Λ>0$; b) this is the only true gauge theory of a space-time symmetry i.e. with a physical (Weyl) gauge boson ($ω_μ$); c) all fields and masses have geometric origin (with no added scalar fields); d) the theory has a Weyl gauge invariant geometric regularisation (by $\hat R$) in $d$ dimensions and it is Weyl-anomaly free; this anomaly is recovered in the broken phase after massive $ω_μ$ decouples; e) the theory is the leading order of the general Weyl gauge invariant Dirac-Born-Infeld (WDBI) action of Weyl conformal geometry in $d$ dimensions; f) in the limit of vanishing Weyl gauge current, one obtains conformal gravity; g) finally, Standard Model (SM) has a natural embedding in conformal geometry with no new degrees of freedom, with successful Starobinsky-Higgs inflation. Briefly, Weyl conformal geometry generates a (quantum) gauge theory of gravity, given by Weyl quadratic gravity, and leads to a unified description, by the gauge principle, of Einstein-Hilbert gravity and SM interactions.

hep-th↗

arXiv2025

Conformal geometry as a gauge theory of gravity: covariant equations of motion & conservation laws

We study Weyl conformal geometry as a general gauge theory of the Weyl group (of Poincaré and dilatations symmetries) in a manifestly Weyl gauge covariant formalism in which this geometry is automatically metric and physically relevant. This gives a realistic (quadratic) gauge theory of gravity, with Einstein-Hilbert gravity recovered in its spontaneously broken phase, motivating our interest in this geometry. For the most general action we compute the manifestly Weyl gauge covariant equations of motion and present the conservation laws for the energy-momentum tensor and Weyl gauge current. These laws are valid both in Weyl conformal geometry (with respect to the Weyl gauge covariant derivative) but also in the Riemannian geometry equivalent picture (with respect to its associated covariant derivative). This interesting result is a consequence of gauged diffeomorphism invariance of the former versus usual diffeomorphism invariance of the latter. These results are first derived in $d=4$ dimensions. We then successfully derive the conservation laws and equations of motion in Weyl conformal geometry in arbitrary $d$ dimensions, while maintaining manifest Weyl gauge invariance/covariance. The results are useful in physical applications with this symmetry.

hep-th↗

arXiv2025

Weyl gauge invariant DBI action in conformal geometry

We construct the analogue of the Dirac-Born-Infeld (DBI) action in Weyl conformal geometry in $d$ dimensions and obtain a general theory of gravity with Weyl gauge symmetry of dilatations (Weyl-DBI). This is done in the Weyl gauge covariant formulation of conformal geometry in $d$ dimensions, suitable for a gauge theory, in which this geometry is metric. The Weyl-DBI action is a special gauge theory in that it has the same gauge invariant expression with dimensionless couplings in any dimension $d$, with no need for a UV regulator (be it a DR subtraction scale, field or higher derivative operator) for which reason we argue it is Weyl-anomaly free. For $d=4$ dimensions, the leading order of a series expansion of the Weyl-DBI action recovers the gauge invariant Weyl quadratic gravity action associated to this geometry, that is Weyl anomaly-free; this is broken spontaneously and Einstein-Hilbert gravity is recovered in the broken phase, with $Λ>0$. All the remaining terms of this series expansion are of non-perturbative nature but can, in principle, be recovered by (perturbative) quantum corrections in Weyl quadratic gravity in $d=4$ in a gauge invariant (geometric) regularisation, provided by the Weyl-DBI action. If the Weyl gauge boson is not dynamical the Weyl-DBI action recovers in the leading order the conformal gravity action. All fields and scales have geometric origin, with no added matter, scalar field compensators or UV regulators.

hep-th↗

arXiv2025

Weyl conformal geometry vs Weyl anomaly

Weyl conformal geometry is a gauge theory of scale invariance that naturally brings together the Standard Model (SM) and Einstein gravity. The SM embedding in this geometry is possible without new degrees of freedom beyond SM and Weyl geometry, while Einstein gravity is generated by the broken phase of this symmetry. This follows a Stueckelberg breaking mechanism in which the Weyl gauge boson becomes massive and decouples, as discussed in the past (arXiv:1812.08613, 1904.06596, 2104.15118). However, Weyl anomaly could break explicitly this gauge symmetry, hence we study it in Weyl geometry. We first note that in Weyl geometry {\it metricity} can be restored with respect to a new differential operator ($\hat \nabla$) that also enforces a Weyl-covariant formulation. This leads to a metric-like Weyl gauge invariant formalism that enables one to do quantum calculations directly in Weyl geometry, rather than use a Riemannian (metric) geometry picture. The result is the Weyl-covariance in $d$ dimensions of all geometric operators ($\hat R$, etc) {\it and} of their derivatives ($\hat\nabla_μ\hat R$, etc), including the Euler-Gauss-Bonnet term. A natural, Weyl-invariant dimensional regularisation of quantum corrections exists and Weyl gauge symmetry is then maintained and manifest at the quantum level, in $d$ dimensions. This is related to a non-trivial current of this symmetry, the divergence of which cancels the trace of the energy-momentum tensor. The "usual" Weyl anomaly and Riemannian geometry are recovered in the (spontaneously) broken phase. The relation to holographic Weyl anomaly is discussed.

hep-th↗

arXiv2024

Weyl quadratic gravity as a gauge theory and non-metricity vs torsion duality

We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation, generates Einstein gravity in its spontaneously broken phase and is anomaly-free, is that of Weyl gauge symmetry (of dilatations). Gauging the full conformal group does not generate a true gauge theory of physical (dynamical) associated gauge bosons. Regarding the Weyl gauge symmetry, it is naturally realised in Weyl conformal geometry, where it admits two different but equivalent geometric formulations, of same quadratic action: one non-metric but torsion-free, the other Weyl gauge-covariant and metric (with respect to a new differential operator). To clarify the origin of this intriguing result, a third equivalent formulation of this gauge symmetry is constructed using the standard, modern approach on the tangent space (uplifted to space-time by the vielbein), which is metric but has vectorial torsion. This shows an interesting duality vectorial non-metricity vs vectorial torsion of the corresponding formulations, related by a projective transformation. We comment on the physical meaning of these results.

hep-th↗

arXiv2024

Non-metric geometry as the origin of mass in gauge theories of scale invariance

We discuss gauge theories of scale invariance beyond the Standard Model (SM) and Einstein gravity. A consequence of gauging this symmetry is that their underlying 4D geometry is non-metric ($\nabla_μg_{αβ}\not=0$). Examples of such theories are Weyl's {\it original} quadratic gravity theory and its Palatini version. These theories have spontaneous breaking of the gauged scale symmetry to Einstein gravity. All mass scales have a geometric origin: the Planck scale ($M_p$), cosmological constant ($Λ$) and the mass of the Weyl gauge boson ($ω_μ$) of scale symmetry are proportional to a scalar field vev that has an origin in the (geometric) $\tilde R^2$ term in the action. With $ω_μ$ of non-metric geometry origin, the SM Higgs field also has a similar origin, generated by Weyl boson fusion in the early Universe. This appears as a microscopic realisation of "matter creation from geometry" discussed in the thermodynamics of open systems applied to cosmology. Unlike in local scale invariant theories (no $ω_μ$ present) with an underlying pseudo-Riemannian geometry, in our case: 1) there are no ghosts and no additional fields beyond the SM and underlying Weyl or Palatini geometry, 2) the cosmological constant is positive and is small because gravity is weak, 3) the Weyl or Palatini connection shares the Weyl (gauge) symmetry of the action, and: 4) there exists a non-trivial, conserved Weyl current of this symmetry. An intuitive picture of non-metricity and its relation to mass generation is also provided from a solid state physics perspective where it is common and is associated with point defects (metric anomalies) of the crystalline structure.

hep-th↗

arXiv2024

Standard Model in conformal geometry: local vs gauged scale invariance

We discuss comparatively local versus gauged Weyl symmetry beyond Standard Model (SM) and Einstein gravity and their geometric interpretation. The SM and Einstein gravity admit a natural embedding in Weyl integrable geometry which is a special limit of Weyl conformal (non-metric) geometry. The theory has a {\it local} Weyl scale symmetry but no associated gauge boson. Unlike previous models with such symmetry, this embedding is truly minimal i.e. with no additional fields beyond SM and underlying geometry. This theory is compared to a similar minimal embedding of SM and Einstein gravity in Weyl conformal geometry (SMW) which has a full {\it gauged} scale invariance, with an associated Weyl gauge boson. At large field values, both theories give realistic, Starobinsky-Higgs like inflation. The broken phase of the current model is the decoupling limit of the massive Weyl gauge boson of the broken phase of SMW, while the local scale symmetry of the current model is part of the larger gauged scale symmetry of SMW. Hence, the current theory has a gauge embedding in SMW. Unlike in the SMW, we note that in models with local scale symmetry the associated current is trivial, which is a concern for the physical meaning of this symmetry. Therefore, the SMW is a more fundamental UV completion of SM in a full gauge theory of scale invariance that generates Einstein gravity in the (spontaneously) broken phase, as an effective theory.

hep-th↗

arXiv2022

Standard Model in Weyl conformal geometry

We study the Standard Model (SM) in Weyl conformal geometry. This embedding is natural and truly minimal {\it with no new fields} required beyond the SM spectrum and Weyl geometry. The action inherits a gauged scale symmetry $D(1)$ (known as Weyl gauge symmetry) from the underlying geometry. The associated Weyl quadratic gravity undergoes spontaneous breaking of $D(1)$ by a geometric Stueckelberg mechanism in which the Weyl gauge field ($ω_μ$) acquires mass by "absorbing" the spin-zero mode ($ϕ_0$) of the $\tilde R^2$ term in the action. This mode also generates the Planck scale and the cosmological constant. The Einstein-Proca action of $ω_μ$ emerges in the broken phase. In the presence of the SM, this mechanism receives corrections (from the Higgs) and it can induce electroweak (EW) symmetry breaking. The EW scale is proportional to the vev of the Stueckelberg field ($ϕ_0$). The Higgs field ($σ$) has direct couplings to the Weyl gauge field, and its mass may be protected at quantum level by the D(1) symmetry. The SM fermions can acquire couplings to $ω_μ$ only in the special case of a non-vanishing kinetic mixing of the gauge fields of $D(1)\times U(1)_Y$. If this mixing is indeed present, part of $Z$ boson mass is not due to the Higgs mechanism, but to its mixing with massive $ω_μ$. Precision measurements of $Z$ mass then set lower bounds on the mass of $ω_μ$ which can be light (few TeV). In the early Universe the Higgs field can have a {\it geometric} origin, by Weyl vector fusion, and the Stueckelberg-Higgs potential can drive inflation. The dependence of the tensor-to-scalar ratio $r$ on the spectral index $n_s$ is similar to that in Starobinsky inflation but shifted to lower $r$ by the Higgs non-minimal coupling to Weyl geometry.

hep-ph↗

arXiv2022

Cosmological evolution in Weyl conformal geometry

We discuss the cosmological evolution of the Weyl conformal geometry and its associated Weyl quadratic gravity. The Einstein gravity (with a positive cosmological constant) is recovered in the spontaneously broken phase of Weyl gravity; this happens after the Weyl gauge field ($ω_μ$) of scale symmetry, that is part of the Weyl geometry, becomes massive by Stueckelberg mechanism and then decouples. This breaking is a natural result of the cosmological evolution of Weyl geometry, in the absence of matter. Of particular interest in the analysis is the special limiting case of Weyl integrable geometry. Both this case and the general one provide an accelerated expansion of the Universe, controlled by the scalar mode of the $\tilde R^2$ term in the action and by $ω_0$. Their comparison to the $Λ$CDM model shows a very good agreement to this model for the (dimensionless) Hubble function $h(z)$ and the deceleration $q(z)$ for redshift $z\leq 3$. Therefore, the Weyl conformal geometry and its associated Weyl quadratic gravity provide an interesting alternative to the $Λ$CDM model and to the Einstein gravity.

gr-qc↗

arXiv2021

Gauging scale symmetry and inflation: Weyl versus Palatini gravity

We present a comparative study of inflation in two theories of quadratic gravity with {\it gauged} scale symmetry: 1) the original Weyl quadratic gravity and 2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field ($w_μ$) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of $w_μ$), Planck scale and metricity emerge in the broken phase after $w_μ$ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($ϕ_1$), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their $R^2$ term, both theories have a small tensor-to-scalar ratio ($r\sim 10^{-3}$), larger in Palatini case. For a fixed spectral index $n_s$, reducing the non-minimal coupling ($ξ_1$) increases $r$ which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $ξ_1\leq 10^{-3}$, unlike the Palatini version, Weyl theory gives a dependence $r(n_s)$ similar to that in Starobinsky inflation, while also protecting $r$ against higher dimensional operators corrections.

hep-th↗

arXiv2020

Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

We study quadratic gravity $R^2+R_{[μν]}^2$ in the Palatini formalism where the connection and the metric are independent. This action has a {\it gauged} scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field $v_μ= (\tildeΓ_μ-Γ_μ)/2$, with $\tildeΓ_μ$ ($Γ_μ$) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the $R_{[μν]}^2$ term acting as a gauge kinetic term for $v_μ$. We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field ($ϕ$) is not added ad-hoc to this purpose but is "extracted" from the $R^2$ term. The gauge field becomes massive by absorbing the derivative term $\partial_μ\lnϕ$ of the Stueckelberg field ("dilaton"). In the broken phase one finds the Einstein-Proca action of $v_μ$ of mass proportional to the Planck scale $M\sim \langleϕ\rangle$, and a positive cosmological constant. Below this scale $v_μ$ decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio $0.007\leq r \leq 0.01$ for current spectral index $n_s$ (at $95\%$CL) and N=60 efolds. This value of $r$ is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.

hep-th↗

arXiv2019

Stueckelberg breaking of Weyl conformal geometry with applications to gravity

Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian geometry after a Weyl gauge transformation (of "gauge fixing") while Stueckelberg mechanism re-arranges the degrees of freedom, conserving their number ($n_{df}$). The Weyl gauge field ($ω_μ$) of local scale transformations acquires a mass after absorbing a compensator (dilaton), decouples, and Weyl connection becomes Riemannian. Mass generation has thus a dynamic origin, as a transition from Weyl to Riemannian geometry. We show that a "gauge fixing" symmetry transformation of the original Weyl quadratic gravity action in its Weyl geometry formulation immediately gives the Einstein-Proca action for the Weyl gauge field and a positive cosmological constant, plus matter action (if present). As a result, the Planck scale is an {\it emergent} scale, where Weyl gauge symmetry is spontaneously broken and Einstein action is the broken phase of Weyl action. This is in contrast to local scale invariant models (no gauging) where a negative kinetic term (ghost dilaton) remains present and $n_{df}$ is not conserved when this symmetry is broken. The mass of $ω_μ$, setting the non-metricity scale, can be much smaller than $M_\text{Planck}$, for ultraweak values of the coupling ($q$). If matter is present, a positive contribution to the Planck scale from a scalar field ($ϕ_1$) vev induces a negative (mass)$^2$ term for $ϕ_1$ and spontaneous breaking of the symmetry under which it is charged. These results are immediate when using a Weyl geometry formulation of an action instead of its Riemannian picture. Briefly, Weyl gauge symmetry is physically relevant and its role in high scale physics should be reconsidered.

hep-th↗

arXiv2019

Weyl $R^2$ inflation with an emergent Planck scale

We study inflation in Weyl gravity. The original Weyl quadratic gravity, based on Weyl conformal geometry, is a theory invariant under Weyl symmetry of (gauged) local scale transformations. In this theory Planck scale ($M$) emerges as the scale where this symmetry is broken spontaneously by a geometric Stueckelberg mechanism, to Einstein-Proca action for the Weyl "photon" (of mass near $M$). With this action as a "low energy" broken phase of Weyl gravity, century-old criticisms of the latter (due to non-metricity) are avoided. In this context, inflation with field values above $M$ is natural, since this is just a phase transition scale from Weyl gravity (geometry) to Einstein gravity (Riemannian geometry), where the massive Weyl photon decouples. We show that inflation in Weyl gravity coupled to a scalar field has results close to those in Starobinsky model (recovered for vanishing non-minimal coupling), with a mildly smaller tensor-to-scalar ratio ($r$). Weyl gravity predicts a specific, narrow range $0.00257 \leq r\leq 0.00303$, for a spectral index $n_s$ within experimental bounds at $68\%$CL and e-folds number $N=60$. This range of values will soon be reached by CMB experiments and provides a test of Weyl gravity. Unlike in the Starobinsky model, the prediction for $(r, n_s)$ is not affected by unknown higher dimensional curvature operators (suppressed by some large mass scale) since these are forbidden by the Weyl gauge symmetry.

gr-qc↗

arXiv2019

Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation

We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the Standard Model (SM) and inflation. In models with non-minimal couplings of the scalar fields to the Ricci scalar, that are conformal invariant, the spontaneous generation by a scalar field(s) vev of a positive Newton constant demands a negative kinetic term for the scalar field, or vice-versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field $ω_μ$ couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field $ω_μ$ undergoes a Stueckelberg mechanism and becomes massive after "eating" the (radial mode) would-be-Goldstone field (dilaton $ρ$) in the scalar sector. Before the decoupling of $ω_μ$, the dilaton can act as UV regulator and maintain the Weyl symmetry at the {\it quantum} level, with relevance for solving the hierarchy problem. After the decoupling of $ω_μ$, the scalar potential depends only on the remaining (angular variables) scalar fields, that can be the Higgs field, inflaton, etc. We show that successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with $ω_μ$ introduced to avoid ghosts, the natural framework is that of Weyl geometry which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.

hep-th↗