arXiv subjects

Claudio Corianò

Publications and source records attributed to Claudio Corianò.

At least 37 records · Page 2Linked to original sources

arXiv2024

Semiclassical Lensing and Radiative Lens Equations

We analyze lensing of photons and neutrinos in a gravitational field, proposing a method to include radiative effects in classical lens equations. The study uses Schwarzschild and a Reissner-Nordstrom metrics expanded at second post Newtonian order in the Newtonian potential, employing a semiclassical approach to compare one-loop corrections from the Standard Model with Einstein's deflection formula via an impact parameter representation. We also explore the energy dependence of deflection due to quantum corrections and integrate these with classical lens equations.

gr-qc↗

arXiv2024

CFT Correlators and CP-Violating Trace Anomalies

We analyze the parity-odd correlators $\langle JJO\rangle_{odd}$, $\langle JJT\rangle_{odd}$, $\langle TTO\rangle_{odd}$ and $\langle TTT\rangle_{odd}$ in momentum space, constrained by conformal Ward identities, extending our former investigation of the parity-odd chiral anomaly vertex. We investigate how the presence of parity-odd trace anomalies affect such correlators. Motivations for this study come from holography, early universe cosmology and from a recent debate on the chiral trace anomaly of a Weyl fermion. In the current CFT analysis, $O$ can be either a scalar or a pseudoscalar operator and it can be identified with the trace of the stress energy tensor. We find that the $\langle JJO\rangle_{odd}$ and $\langle TTO\rangle_{odd}$ can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is $Δ_3=4$, as in the case of $O=T^μ_μ$. Moreover, if we assume the existence of parity-odd trace anomalies, the conformal $\langle JJT\rangle_{odd}$ and $\langle TTT\rangle_{odd}$ are nonzero. In particular, in the case of $\langle JJT\rangle_{odd}$ the transverse-traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole.

hep-th↗

arXiv2024

Axion-like Quasiparticles and Topological States of Matter: Finite Density Corrections of the Chiral Anomaly Vertex

We investigate the general structure of the chiral anomaly $AVV/AAA$ and $(LLL, RRR)$ vertices, in the presence of chemical potentials in perturbation theory. The study finds application in anomalous transport, whenever chirally unbalanced matter is present, with propagating external currents that are classically conserved. Examples are topological materials and the chiral magnetic effect in the plasma state of matter of the early universe. We classify the minimal number of form factors of the $AVV$ parameterization, by a complete analysis of the Schouten identities in the presence of a heat bath. We show that the longitudinal (anomaly) sector in the axial-vector channel, for on-shell and off-shell photons, is protected against corrections coming from the insertion of a chemical potential in the fermion loop. When the photons are on-shell, we prove that also the transverse sector, in the same channel, is $μ$-independent and vanishes. The related effective action is shown to be always described by the exchange of a massless anomaly pole, as in the case of vanishing chemical potentials. The pole is interpreted as an interpolating axion-like quasiparticle generated by the anomaly. In each axial-vector channel, it is predicted to be a correlated fermion/antifermion pseudoscalar (axion-like) quasiparticle appearing in the response function, once the material is subjected to an external chiral perturbation. The cancellation of the $μ$ dependence extends to any chiral current within the Standard Model, including examples like $B$ (baryon), $L$ (lepton), and $B-L$. This holds true irrespective of whether these currents exhibit anomalies.

hep-ph↗

arXiv2024

Nonlocal Gravity, Dark Energy and Conformal Symmetry: Testing the Hierarchies of Anomaly-Induced Actions

Conformal back-reaction generates cosmological models where the trace anomaly reflects the breaking of Weyl invariance. Analyzing these actions yields a dynamic approach to dark energy through anomaly-induced actions (AIAs), that are variational solutions of the trace anomaly functional constraint. Expanded around Minkowski space, they produce semiclassical correlators subject to hierarchical anomalous Ward identities, tied to conformal symmetry and diffeomorphism invariance. We focus on comparing the hierarchy of a specific 4-point function, particularly the 2-gravitons-2-photons correlator $(TTJJ)$, generated by AIAs, to free field theory realizations of the same correlator. We observe that the free field theory original hierarchy splits into one ordinary and one anomalous hierarchy, both satisfying the conservation Ward identities from diffeomorphism invariance. However, we find that the anomalous hierarchy derived from ordinary AIAs in both the Riegert or Fradkin-Vilkovisky gauges, are either affected by double poles or violate the hierarchy of the trace Ward identity, respectively. We show that correct forms of the anomalous hierarchies of 4-point functions (for the $TTTT$ and $TTJJ$), identified in a perturbative free field theory expansion around flat space, are characterised by anomaly poles, corresponding to a curvature expansion in $R\Box^{-1}$, together with Weyl invariant terms. We derive the effective action that generates the correct form of the hierarchy for the $TTJJ$.

hep-th↗

arXiv2024

Parity-Violating CFT and the Gravitational Chiral Anomaly

We illustrate how the Conformal Ward Identities (CWI) and the gravitational chiral anomaly completely determine the structure of the $\langle TTJ_{5}\rangle$ (graviton-graviton-chiral gauge current) correlator in momentum space. This analysis extends our previous results on the anomaly vertices $\langle AVV\rangle$ and $\langle AAA\rangle$, as well as the $\langle TJJ\rangle$ parity-odd conformal anomaly vertex in general CFTs. The $\langle TTJ_{5}\rangle$ plays a fundamental role in the analysis of the conformal backreaction in early universe cosmology, affecting the particle content and the evolution of the primordial plasma. Our approach is nonperturbative and not Lagrangian-based, requiring the inclusion of a single anomaly pole in the solution of the anomaly constraint. The pole and its residue, along with the CWIs, determine the entire correlator in all of its sectors (longitudinal/transverse), all of which are proportional to the same anomaly coefficient. The method does not rely on a specific expression of the CP-odd anomalous current, which in free field theory can be represented either by a bilinear fermion current or by a gauge-dependent Chern-Simons current; it relies solely on the symmetry constraints. We compute the correlator perturbatively at one-loop in free field theory and verify its exact agreement with the non-perturbative result. A comparison with the perturbative analysis confirms the presence of a sum rule satisfied by the correlator, similar to the parity-even $\langle TJJ\rangle$ and the chiral $\langle AVV\rangle$.

hep-th↗

arXiv2024

The Gravitational Chiral Anomaly at Finite Temperature and Density

We investigate the gravitational anomaly vertex $\langle TTJ_5\rangle$ (graviton - graviton - axial current) under conditions of finite density and temperature. Through a direct analysis of perturbative contributions, we demonstrate that neither finite temperature nor finite fermion density affects the gravitational chiral anomaly. These results find application in several contexts, from topological materials to the early universe plasma. They affect the decay of any axion or axion-like particle into gravitational waves, in very dense and hot environments.

hep-th↗

arXiv2024

The $SU(3)_C\times SU(3)_L\times U(1)_X$ (331) Model:Addressing the Fermion Families Problem within Horizontal Anomalies Cancellation

One of the most important and unanswered problems in particle physics is the origin of the three generations of quarks and leptons. The standard Model does not provide any hint regarding its sequential charge assignments, which remain a fundamental mystery of Nature. One possible solution of the puzzle is to look for charge assignments, in a given gauge theory, that are inter-generational, by employing the cancellation of the gravitational and gauge anomalies horizontally. The 331 model, based on an $SU(3)_C\times SU(3)_L \times U(1)_X$ does it in an economic way, and defines a possible extension of the Standard Model, where the number of families has to be necessarily three. We review the model in Frampton's formulation, that predicts the existence of bileptons. Another characteristics of the model is to unify the $SU(3)_C\times SU(2)_L \times U(1)_X$ into the 331 symmetry at a scale which is in the TeV range, and can be tested at the LHC. Expressions of the scalar mass eigenstates and of the renormalization group equations of the model are also presented.

hep-ph↗

arXiv2024

Axion-like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

We discuss fundamental aspects of chiral anomaly-driven interactions in conformal field theory (CFT) in four spacetime dimensions. They find application in very general contexts, from early universe plasma to topological condensed matter. We outline the key shared characteristics of these interactions, specifically addressing the case of chiral anomalies, both for vector currents and gravitons. In the case of topological materials, the gravitational chiral anomaly is generated by thermal gradients via the (Tolman-Ehrenfest) Luttinger relation. In the CFT framework, a nonlocal effective action, derived through perturbation theory, indicates that the interaction is mediated by an excitation in the form of an anomaly pole, which appears in the conformal limit of the vertex. To illustrate this, we demonstrate how conformal Ward identities (CWIs) in momentum space allow us to reconstruct the entire chiral anomaly interaction in its longitudinal and transverse sectors just by inclusion of a pole in the longitudinal sector. Both sectors are coupled in amplitudes with an intermediate chiral fermion or a bilinear Chern-Simons current with intermediate photons. In the presence of fermion mass corrections, the pole transforms into a cut, but the absorption amplitude in the axial-vector channel satisfies mass-independent sum rules related to the anomaly in any chiral interaction. The detection of an axion-like/quasiparticle in these materials may rely on a combined investigation of these sum rules, along with the measurement of the angle of rotation of the plane of polarization of incident light when subjected to a chiral perturbation. This phenomenon serves as an analogue of a similar one in ordinary axion physics, in the presence of an axion-like condensate, that we rederive using axion electrodynamics.

hep-ph↗

arXiv2023

Parity-Odd 3-Point Functions from CFT in Momentum Space and the Chiral Anomaly

We illustrate how the Conformal Ward Identities (CWI) in momentum space for parity-odd correlators determine the structure of a chiral anomaly interaction, taking the example of the VVA (vector/vector/axial-vector) and AAA correlators in momentum space. Only the conservation and the anomalous WIs, together with the Bose symmetry, are imposed from the outset for the determination of the correlators. We use a longitudinal/transverse decomposition of tensor structures and form factors. The longitudinal (L) component is fixed by the anomaly content and the anomaly pole, while in the transverse (T) sector we define a new parameterization. We relate the latter both to the Rosenberg original representation of the VVA and to the longitudinal/transverse (L/T) one, first introduced in the analysis of $g-2$ of the muon in the investigation of the diagram in the chiral limit of QCD. The correlators are completely identified by the conformal constraints whose solutions are fixed only by the anomaly coefficient, the residue of the anomaly pole. In both cases, our CFT result matches the one-loop perturbative expression, as expected. The CWIs for correlators of mixed chirality $J_L J J_R$ generate solutions in agreement with the all-orders nonrenormalization theorems of perturbative QCD and in the chiral limit.

hep-th↗

arXiv2023

Atmospheric Neutrino Octant from Flavour Symmetry

The binary tetrahedral group ($T^{'}$) has provided the most successful flavour symmetry in understanding simultaneously the three mixing angles both for quarks in the CKM matrix and for neutrinos in the PMNS matrix. One prediction, invariant under leptonic CP violation, relates the atmospheric and reactor neutrino mixings $θ_{23}$ and $θ_{13}$ respectively. We study sedulously this relation using the latest neutrino data. It is natural to focus on the frustrating experimental octant ambiguity of $θ_{23}$. We conclude that the flavour symmetry requires that $θ_{23}$ is in the second octant $θ> 45^0$, not in the first one $θ_{23}<45^0$, and eagerly await experimental confirmation of this prediction.

hep-ph↗

arXiv2023

Broken Scale Invariance and the Regularization of a Conformal Sector in Gravity with Wess-Zumino actions

We elaborate on anomaly induced actions of the Wess-Zumino (WZ) form and their relation to the renormalized effective action, which is defined by an ordinary path integral over a conformal sector, in an external gravitational background. In anomaly-induced actions, the issue of scale breaking is usually not addressed, since these actions are obtained only by solving the trace anomaly constraint and are determined by scale invariant functionals. We investigate the changes induced in the structure of such actions once identified in dimensional renormalization (DR) when the $ε= d-4 \to 0$ limit is accompanied by the dimensional reduction (DRed) of the field dependencies. We show that operatorial nonlocal modifications $(\sim\Box^ε)$ of the counterterms are unnecessary to justify a scale anomaly. In this case, only the ordinary finite subtractions play a critical role in the determination of the scale breaking. This is illustrated for the WZ form of the effective action and its WZ consistency condition, as seen from a renormalization procedure. Logarithmic corrections from finite subtractions are also illustrated in a pure $d=4$ (cutoff) scheme. The interplay between two renormalization schemes, one based on dimensional regularization (DR) and the second on a cutoff in $d=4$, illustrates the ambiguities of DR in handling the quantum corrections in a curved background. Therefore, using DR in a curved background, the scale and trace anomalies can both be obtained by counterterms that are Weyl invariant only at $d=4$.

hep-th↗

arXiv2023

$4d$ Einstein Gauss-Bonnet Gravity without a Dilaton

A nonlocal version of Einstein-Gauss Bonnet (EGB) gravity can be generated by a procedure that follows closely the steps of the derivation of the conformal anomaly effective action. The action is obtained using a Weyl decomposition of the metric, with the conformal factor removed by a finite renormalization of the topological term. We outline the mains steps in the derivation of this action, stressing on the analogies and differences respect to the anomaly action and to the ordinary $4d$ EGB theory formulated as a special version of dilaton gravity. These formulations allow a systematic investigation of the nonlocal $R\Box^{-1}$ corrections to General Relativity. In the case of conformal anomaly action they are motivated by the generation of a conformal backreaction, due to the breaking of conformal symmetry in the early universe.

hep-th↗

arXiv2023

Three-Wave and Four-Wave Interactions in the $4d$ Einstein Gauss-Bonnet (EGB) and Lovelock Theories

We derive the conformal constraints satisfied by classical vertices of a (Einstein) Gauss-Bonnet theory around flat space, in general dimensions and at $d=4$ (4d EGB). In $4d$ EGB they are obtained by a singular limit of the integral of the Euler-Poincarè density. Our analysis exploits the relation between this theory and the conformal anomaly action, which allows to uncover some interesting features of the GB vertex at cubic and quartic level. If we introduce a conformal decomposition of the metric, the resulting theory can be formulated in two different versions, which are regularization dependent, a local one which is quartic in the dilaton field, and a nonlocal one, with a quadratic dilaton. The nonlocal version is derived by a finite redefinition of the GB density with the inclusion of a $(d-4)R^2$ correction, before performing the singular $d\to 4$ limit. In the local version of the theory, we show how the independent dynamics of the metric and of the dilaton are interwinded by a classical trace identity. Three-gravitational wave interactions can be organised in a nontrivial way by using directly the nonlocal 4d EGB version of the theory. This is possible thanks to the consistency of such formulation - only up to 3-point functions - directly inherited from the conformal anomaly (Riegert) action. The constraints satisfied by the vertices are classical, hierarchical Ward identities. At quartic level, similar relations are derived, borrowing from the analysis of the counterterms of the 4T correlators of the conformal anomaly action, as defined by a perturbative expansion. For $d\neq 4$ these constraints hold also for Lovelock actions. They can be extended to higher order topological invariants in such class of theories.

hep-th↗

arXiv2023

Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ

We present an analysis of the perturbative realization of the $TTJJ$ correlator, with two stress energy tensors and two conserved currents, using free field theory realizations, integrating out conformal sectors in the quantum corrections. This allows defining, around flat space, an exact perturbative expansion of the complete anomaly effective action - up to 4-point functions - whose predictions can be compared against those of the anomaly induced action. The latter is a variational solution of the conformal anomaly constraint at $d=4$ in the form of a nonlocal Wess-Zumino action. The renormalization procedure and the degeneracies of the tensor structures of this correlator are discussed, valid for a generic conformal field theory, deriving its anomalous trace Ward identities (WIs). In this application, we also illustrate a general procedure that identifies the minimal number of tensorial structures and corresponding form factors for the $TTJJ$ and any $4$-point function. The result of the direct computation is compared against the expression of the same 4-point function derived from the nonlocal anomaly induced action. We show that the prediction for the anomalous part of the $TTJJ$ derived from such action, evaluated in two different conformal decompositions, the Riegert and Fradkin-Vilkovisky (FV) choices, differ from the anomaly part identified in the perturbative $TTJJ$, in the flat spacetime limit. The anomaly part of the correlator computed with the Riegert choice is affected by double poles, while the one computed with the FV choice does not satisfy the conservation WIs. We present the correct form of the expansion of the anomaly induced action at the second order in the metric perturbations around flat space that reproduces the perturbative result.

hep-th↗

arXiv2022

Topological Corrections and Conformal Backreaction in the Einstein Gauss-Bonnet/Weyl Theories of Gravity at D=4

We investigate the gravitational backreaction, generated by coupling a general conformal sector to external, classical gravity, as described by a conformal anomaly effective action. We address the issues raised by the regularization of the topological Gauss-Bonnet and Weyl terms in these actions and the use of dimensional regularization (DR). We discuss both their local and nonlocal expressions, as possible IR and UV descriptions of conformal theories, below and above the conformal breaking scale. Our discussion overlaps with several recent studies of dilaton gravities - obtained via a certain singular limit of the Einstein-Gauss-Bonnet (EGB) theory - originally introduced as a way to bypass Lovelock's theorem. We show that nonlocal, purely gravitational realizations of such EGB theories, quadratic in the dilaton field, beside their local quartic forms, are possible by a finite renormalization of the Euler density. Such nonlocal versions, which are deprived of any scale, can be expanded, at least around flat space, in terms of the combination $R \Box^{-1}$ times multiple variations of the anomaly functional, as pointed out in recent studies at $d=4$. Similar conclusions can be drawn for the proposed nonlocal EGB theory. The expansion emerges from previous investigations of the anomalous conformal Ward identities that constrain such theories around the flat spacetime limit in momentum space.

hep-th↗

arXiv2022

Quantum Field Theory and its Anomalies for Topological Matter

Topology enters in quantum field theory (qft) in multiple forms: one of the most important, in non-abelian gauge theories, being in the identification of the $θ$ vacuum in QCD. A very relevant aspect of this connection is through the phenomenon of chiral and conformal qft anomalies. It has been realized that a class of materials, comprising topological insulators and Weyl semimetals, also exhibit the phenomenon of anomalies, which are responsible for several exotic phenomena, such as the presence of edge currents, resilient under perturbations and scattering by impurities. Another example comes from the response functions of these materials under thermal and mechanical stresses, that may be performed using correlation functions of stress energy tensors in General Relativity. In this case the conformal anomaly plays an important role. We briefly illustrate some salient features of this correspondence, and the effective action describing the long-range interactions that may account for such topological effects.

hep-th↗

arXiv2022

An $SU(15)$ Approach to $B$ Anomalies

The most efficient way to extend the Standard Model of particle theory so that it accommodates the observed B anomalies is the hypothesis of a leptoquark which is a color-triplet weak-singlet boson with electric charge $Q=+\frac{2}{3}$. We point out that SU(15) grand unification with a scalar leptoquark in the adjoint representation gives a natural explanation for the violation of lepton flavour universality. We briefly discuss biquarks and bileptons.

hep-ph↗

arXiv2022

Dimensional Regularization of Topological Terms in Dilaton Gravity

The possibility of evading Lovelock's theorem at $d=4$, via a singular redefinition of the dimensionless coupling of the Gauss-Bonnet term, has been extensively discussed in the cosmological context. The term is added as a quadratic contribution of the curvature tensor to the Einstein-Hilbert action, originating theories of "Einstein Gauss-Bonnet" (EGB) type. These studies are interlaced with those of the conformal anomaly effective action. We review some basic results concerning the structure of these actions, their conformal constraints around flat space and their relation to EGB theories. The local and nonlocal formulations of such effective actions are illustrated. This class of theories find applications in the seemingly unrelated context of topological materials, subjected to thermal and mechanical stress.

hep-th↗