arXiv subjects

Stefano Lionetti

Publications and source records attributed to Stefano Lionetti.

At least 19 recordsLinked to original sources

arXiv2026

From chiral to conformal anomalies: a double copy perspective for CFT correlators

We uncover a double-copy relation between chiral and conformal anomalies in four-dimensional conformal field theory. We show that this relation extends from local anomaly structures to complete momentum-space three-point correlators and, through their flat-space limits, to five-dimensional scattering amplitudes. In particular, the parity-odd current correlators associated with the chiral anomaly reduce, in the flat-space limit, to a universal amplitude generated by a Chern--Simons interaction. Squaring these anomalous current correlators reproduces the contribution to the stress-tensor three-point function $\langle TTT\rangle$, controlled by the conformal anomaly, thereby establishing a direct link between chiral- and conformal-anomaly structures.

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arXiv2026

Anomaly-mediated Scalar Gravitational Interactions and the Coupling of Conformal Sectors

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in General Relativity, the conformalon mode, directly at the level of $2\to2$ scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons $(TTT)$ and Abelian gauge currents $(TJJ)$, through single-graviton exchange derived from the quadratic expansion of the Einstein--Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behaviour arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in de Donder gauge. The resulting anomaly-mediated $4$-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated $2\to2$ graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

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arXiv2026

Dilaton Sum Rules of Gravitational Form Factors in QCD at Order $α_s$

We formulate a partonic description of hadronic gravitational form factors within QCD, focusing on the three-point function of the energy-momentum tensor and two gluon currents. Despite the lack of exact conformal symmetry in QCD, the correlator may be organized around the conformal limit through momentum-space CFT methods, suitably adjusted for gauge-fixing effects. This yields a tensor decomposition into spin-2, spin-1, and spin-0 sectors, with the spin-0 contribution governed by the conformal anomaly. The corresponding anomaly form factor satisfies a mass-independent dispersive sum rule and allows a dilaton-like interpretation. In the light-cone limit, this term and an additional traceless structure become dominant, indicating an effective anomaly-mediated description relevant to hadronic gravitational form factors.

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arXiv2025

Anomalies and Parity-Violating Interactions: From Conformal to Thermal Field Theory

Chiral and conformal anomalies are fundamental phenomena that span multiple disciplines, including high-energy physics, condensed matter theory and cosmology. These anomalies play a crucial role in understanding fundamental interactions and manifest themselves through divergences and traces of correlation functions. In this thesis, we investigate these phenomena within the framework of conformal field theory, elucidating their intricate structure and physical implications. Our primary focus is on the role of conformal Ward identities in fully characterizing parity-odd interactions associated with chiral and conformal anomalies in momentum space. Furthermore, we explore mechanisms that lead to the breaking of conformal invariance, such as finite-temperature and finite-density effects or the presence of a fermion mass, and examine how parity-odd anomalous interactions behave under these conditions. By analyzing these phenomena through the lens of conformal and thermal field theories, we obtain deeper insights into their mathematical structure and their significance across a wide range of physical contexts.

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arXiv2025

A Dilaton Sum Rule for the Conformal Anomaly Form Factor in QCD at Order $α_s$

We present an off-shell dispersive analysis of the graviton-gluon-gluon ($TJJ$) vertex, extending previous investigations carried out in both QED and QCD. Within the framework of a non-Abelian gauge theory, we extract the conformal anomaly form factor from the trace component of the correlator and demonstrate that it satisfies a one-loop sum rule, valid under the most general kinematic conditions. Analogously to the chiral and chiral-gravitational cases, a spectral flow emerges in which the exchanged intermediate state becomes localized at zero invariant mass along the graviton line as the quark mass approaches zero. The total integral of the spectral density precisely reproduces the anomaly. We examine how the behaviour of these spectral densities evolves as the system approaches the conformal limit with on-shell gluons. The perturbative analysis reveals that such sum rules are fundamental dynamical features of anomaly-induced interactions. In particular, the appearance or absence of associated dilaton poles is closely tied to whether the sum rule is saturated by a pole contribution or by a dispersive continuum. In the conformal, on-shell limit, the particle-pole interaction yields a nonlocal S-matrix element entirely supported on the light-cone.

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arXiv2025

Topological Sum Rules and Spectral Flows of Chiral and Gravitational Axion-like Interactions

We examine the structure of off-shell effective actions arising from chiral and gravitational anomalies, focusing on the $JJJ_A$ (axial-vector/vector/vector) and $J_A TT $ (axial-vector/stress-energy tensors) correlators, relevant in the analysis of anomaly-driven interactions in perturbation theory. Our approach relies on conformal field theory in momentum space, extended to chiral anomalies. The analysis centers on the presence of both particle poles and anomaly poles within these interactions, characterizing their behavior both in the conformal and non conformal limits. Through explicit computations, we show that universal sum rules in the longitudinal sector regulate these interactions for all kinematic conditions, extending previous analysis, and we discuss the resulting spectral flow, an area law of the absorptive part of the anomaly form factors as one moves away from or returns to the conformal point. These features are absent in the local effective action of anomaly interactions, commonly used in the description of axion-like particles. The spectral densities in both cases are shown to be self-similar. Our results further show that anomaly poles correspond to true particle poles only in the conformal limit, when the interaction describes a massless S-matrix process supported on a null-surface. Under these conditions, they can be effectively described by two kinetically mixed pseudoscalar fields propagating on the light-cone. These studies find application in polarized deeply inelastic scattering, axion-like dark matter and analogue systems such as topological materials.

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arXiv2025

Gravitational Form Factors and the QCD Dilaton at Large Momentum Transfer

We investigate the hard scatterings of hadronic matrix elements corresponding to hadronic gravitational form factors (GFFs) of the pion and proton using QCD factorization, applying conformal field theory (CFT) tools. These GFFs are key to understanding quark and gluon angular momentum via their connection to DVCS moments. The core object is the non-Abelian $ TJJ $ 3-point function, which shows an anomaly-induced dilaton exchange in the $ t $-channel. We analyze quark, ghost, and gauge-fixing effects through a CFT-based decomposition and propose a parameterization useful for future DVCS studies at the Electron-Ion Collider. The dilaton interaction is interpolated by a conformal anomaly form factor, defined in the nonconformal case, which is constrained by a (dilaton) sum rule.

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arXiv2025

The Gravitational Form Factors of Hadrons from CFT in Momentum Space and the Dilaton in Perturbative QCD

We analyze the hard scattering amplitude of the gravitational form factors (GFFs) of hadrons at one-loop, in relation to their conformal field theory (CFT) description, within the framework of QCD factorization for hard exclusive processes at large momentum transfers. These form factors play an essential role in studying the quark and gluon angular momentum of the hadrons due to their relation to the Mellin moments of the Deeply Virtual Compton Scattering (DVCS) invariant amplitudes. Our analysis is performed using a diffeomorphism invariant approach, applying the formalism of the gravitational effective action and conformal symmetry in momentum space for the discussion of the quark and gluon contributions. The interpolating correlator in the hard scattering of any GFF is the non-Abelian $TJJ$ (stress-energy/gluon/gluon) 3-point function at $O(α_s^2)$, revealing an effective dilaton interaction in the $t$-channel due to the trace anomaly, in the form of a massless anomaly pole in the QCD hard scattering. We investigate the role of quarks, gauge-fixing and ghost contributions in the reconstruction of the hard scattering amplitude mediated by this interaction, performed in terms of its transverse traceless, longitudinal, and trace decomposition, as identified from CFT in momentum space (CFT$_p$). We present a convenient parameterization of the hard scattering amplitude relevant for future experimental investigations of the DVCS/GFF amplitudes at the Electron-Ion Collider at BNL.

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arXiv2024

CFT Constraints on Parity-odd Interactions with Axions and Dilatons

We illustrate how the conformal Ward identities (CWIs) in momentum space completely determine the structure of a parity-odd 3-point correlator involving currents, energy momentum tensors and at least one scalar operator in $d=4$. Conformal invariance fixes almost all such possible correlators to vanish. The only exceptions are given by the $\langle JJO\rangle_{odd}$ and the $\langle TTO \rangle_{odd}$ which in momentum-space are protected by chiral and conformal anomalies. Specifically, one can obtain a non-vanishing solution by considering scalar operators such as $O=\nabla \cdot J_A$, $O=g_{μν}T^{μν}$ or their shadow transforms. We comment on the implications of these results that constrain the coupling of axions and dilatons in a conformal phase of the early universe.

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arXiv2024

The Gravitational Form Factor of the Pion and Proton and the Conformal Anomaly

We analyze the hard scattering amplitude of gravitational form factors (GFFs) of hadrons within QCD factorization at large momentum transfers, focusing on their conformal field theory (CFT) description. These form factors are key to studying quark and gluon angular momentum in hadrons, connected to Mellin moments of Deeply Virtual Compton Scattering (DVCS). The analysis uses diffeomorphism invariance and conformal symmetry in momentum space. A non-Abelian $TJJ$ 3-point function at $O(α_s^2)$ reveals a dilaton interaction in the $t$-channel. We present a parameterization relevant for future DVCS/GFF experiments at the Electron-Ion Collider.

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arXiv2024

Conformal Backreaction, Chiral and Conformal Anomalies in the Early Universe

The backreaction of a conformal matter sector and its associated conformal anomaly on gravity can be systematically studied using the formalism of the anomaly effective action. This action, defined precisely in flat spacetime within ordinary quantum field theory, can be analyzed perturbatively in terms of external graviton insertions. The expansion coefficients correspond to correlation functions of the stress-energy tensor, which are renormalized through two key counterterms: the square of the Weyl tensor $(C^2)$ and the Gauss-Bonnet term $(E)$. Anomalous conformal Ward identities impose hierarchical constraints on this expansion, revealing that the anomaly's contribution arises from bilinear mixings of the form $R \Box^{-1} E$ and $R \Box^{-1} C^2$, supplemented by local Weyl-invariant terms. These mixings reflect the non-local structure of the anomaly. The precise form of the effective action, however, may vary depending on the regularization scheme used, with potential differences manifesting through additional Weyl-invariant terms. These actions encapsulate the breaking of Weyl invariance in the early universe, with implications that are particularly relevant during the inflationary epoch. For chiral and gravitational anomalies, we demonstrate that the corresponding effective actions exhibit similar structures, influencing the evolution of chiral asymmetries in the early universe plasma.

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arXiv2024

Quantum Anomalies and Parity-odd CFT Correlators for Chiral States of Matter

Chiral currents influence the parity-odd sector of CFT correlators in momentum space, playing a crucial role in the evolution of the quark-gluon plasma in the early universe. We demonstrate that these parity-odd interactions, which couple quarks and gluons to gravitons, can be fully determined in terms of their anomaly content by solving the conformal constraints in momentum space. This process involves a single nonlocal, massless axion-like interaction in the longitudinal channel, which remains protected against thermal and finite density effects.

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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.

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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.

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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 $TTJJ$.

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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 $\langle AVV\rangle$.

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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.

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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.

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