arXiv subjects

Stefano Lionetti

Publications and source records attributed to Stefano Lionetti.

25 records · Page 2Linked to original sources

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

$4d$ 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↗

arXiv2022

Asymptotic symmetries and soft theorems in higher-dimensional gravity

Soft theorems can be recast as Ward identities of asymptotic symmetries. We review such relation for the leading and subleading soft graviton theorems in arbitrary even dimensions. While soft theorems are trivially generalized to dimensions higher than four, the charges of asymptotic symmetries are plagued by divergences requiring a renormalization. We argue that the renormalized charges of these symmetries can be determined by rewriting soft theorems as Ward identities. In order to show that the charges of such identities generate asymptotic symmetries, we propose a suitable commutation relation among certain components of the metric fields

hep-th↗

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↗

arXiv2022

Asymptotic symmetries and subleading soft graviton theorem in higher dimensions

We investigate the relation between the subleading soft graviton theorem and asymptotic symmetries in gravity in even dimensions $d=2+2m$ higher than four. After rewriting the subleading soft graviton theorem as a Ward identity, we argue that the charges of such identity generate Diff$(S^{2m})$. In order to show that, we propose suitable commutation relation among certain components of the metric fields. As a result, all Diff$(S^{2m})$ transformations are symmetries of gravitational scattering.

hep-th↗