arXiv subjects

Matteo Maria Maglio

Publications and source records attributed to Matteo Maria Maglio.

At least 19 recordsLinked to original sources

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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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.

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arXiv2023

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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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 $d=4$.

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arXiv2023

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 $\Delta_3=4$, as in the case of $O=T^\mu_\mu$. 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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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.

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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.

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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.

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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.

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arXiv2022

Gravitational coupling of QED and QCD: 3- and 4- point functions in momentum space

Conformal symmetry has important consequences for strong interactions at short distances and provides powerful tools for practical calculations. Even if the Lagrangians of Quantum Chromodynamics (QCD) and Electrodynamics (QED) are invariant under conformal transformations, this symmetry is broken by quantum corrections. The signature of the symmetry breaking is encoded in the presence of massless poles in correlators involving stress-energy tensors. We present a general study of the correlation functions $\langle TJJ\rangle$ and $\langle TTJJ\rangle$ of conformal field theory (CFT) in the flat background limit in momentum space, following a reconstruction method for tensor correlators. Furthermore, our analysis also focuses on studying the dimensional degeneracies of the tensor structures related to these correlators.

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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.

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arXiv2022

Einstein Gauss-Bonnet Theories as Ordinary, Wess-Zumino Conformal Anomaly Actions

Recently, 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 very 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. We point out that the action obtained by the dimensional regularization procedure, implemented with the extraction of a single conformal factor, correspond just to an ordinary Wess-Zumino anomaly action, even though it is deprived of the contribution from the Weyl tensor. We also show that a purely gravitational version of the EGB theory can be generated by allowing a finite renormalization of the Gauss-Bonnet topological contribution at $d= 4 + ε$, as pointed out by Mazur and Mottola. The result is an effective action which is quadratic, rather then quartic, in the dilaton field, and scale free, compared to the previous derivations. The dilaton, in this case can be removed from the spectrum, leaving a pure gravitational theory, which is nonlocal. We comment on the physical meaning of the two types of actions, which may be used to describe such topological terms both below and above the conformal breaking scale.

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arXiv2021

Conformal field theory in momentum space and anomaly actions in gravity:The analysis of three- and four-point functions

After a brief outline of general aspects of conformal field theories in coordinate space, in a first part we review the solution of the conformal constraints of three- and four-point functions in momentum space in dimensions $d\geq 2$, in the form of conformal Ward identities (CWI's). We center our discussion on the analysis of correlators containing stress-energy tensors $(T)$, conserved currents $(J)$, and scalar operators $(O)$. For scalar four-point functions, we briefly discuss our method for determining the dual conformal solutions of such equations, identified only by the CWI's, and related to the conformal Yangian symmetry, introduced by us in previous work. In correlation functions with $T$ tensors, evaluated around a flat spacetime, the conformal anomaly is characterized by the (non-local) exchange of massless poles in specific form factors, a signature that has been investigated both in free field theory and non-perturbatively, by solving the conformal constraints. We discuss the anomaly effective action, and illustrate the derivation of the CWI's directly from its path integral definition and its Weyl symmetry, which is alternative to the standard operatorial approach used in conformal field theories in flat space. For two- and three-point functions, we elaborate on the matching of these types of correlators to free-field theories. Perturbative realizations of CFTs at one-loop provide the simplest expressions of the general solutions identified by the CWI's, for generic operators $T$, $J$, and scalars of specific scaling dimensions, by an appropriate choice of their field content. In a technical appendix we offer details on the reconstruction of the $TTO$ and $TTT$ correlators in the approach of Bzowski, McFadden and Skenderis, and specifically on the secondary Ward identities of the method, in order to establish a complete match with the perturbative description.

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arXiv2021

The Conformal Anomaly Action to Fourth Order (4T) in $d=4$ in Momentum Space

We elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations $(h)$ of the background metric, in the flat spacetime limit. For this purpose we discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions with the goal of identifying the structure of the anomaly action. We focus on a separation of the correlator into its transverse/traceless and longitudinal components, applied to the trace and conservation Ward identities (WI) in momentum space. These are sufficient to identify, from their hierarchical structure, the anomaly contribution, without the need to proceed with a complete determination of all of its independent form factors. Renormalization induces sequential bilinear graviton-scalar mixings on single, double and multiple trace terms, corresponding to $R\square^{-1}$ interactions of the scalar curvature, with intermediate virtual massless exchanges. These dilaton-like terms couple to the conformal anomaly, as for the chiral anomalous WIs. We show that at 4T level a new traceless component appears after renormalization. We comment on future extensions of this result to more general backgrounds, with possible applications to non local cosmologies.

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arXiv2021

TTT in CFT: Trace Identities and the Conformal Anomaly Effective Action

Stress-energy correlation functions in a general Conformal Field Theory (CFT) in four dimensions are described in a fully covariant approach, as metric variations of the quantum effective action in an arbitrary curved space background field. All Conservation, Trace and Conformal Ward Identities (CWIs), including contact terms, are completely fixed in this covariant approach. The Trace and CWIs are anomalous. Their anomalous contributions may be computed unambiguously by metric variation of the exact 1PI quantum effective action determined by the conformal anomaly of $\left\langle T^{μν}\right\rangle$ in $d = 4$ curved space. This action implies the existence of massless propagator poles in three and higher point correlators of $T^{μν}$ . The metric variations of the anomaly effective action in its local form in terms of a scalar conformalon field are carried out explicitly for the case of the correlator of three CFT stress-energy tensors, and the result is shown to coincide with the algebraic reconstruction of $\left\langle TTT\right\rangle$ from its transverse, tracefree parts, determined independently by the solution of the CWIs in d dimensional flat space in the momentum representation. This demonstrates that the specific analytic structure and massless poles predicted by the general curved space anomaly effective action are in fact a necessary feature of the exact solution of the anomalous CWIs in any $d = 4$ CFT.

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arXiv2021

Conformal Symmetry in Momentum Space and Anomaly Actions in Gravity

In this thesis we study the momentum space approach to the solution of the CWI's of CFT's in higher dimensions. Our work's goal is to illustrate the essential steps needed to build tensor correlators starting from the scalar solutions, for 3-point functions. In the case of 4-point functions, our attention is centred around scalar correlators for which the CWI's are sufficient to isolate the unique solution if we enhance the symmetry with the addition of a dual conformal symmetry. Dual conformal symmetry in momentum space is obtained once the momentum variables are rewritten in a dual form, as the difference of coordinate-like variables and treated as ordinary correlators in such variables, mirroring the action of coordinate space. This enhancement of the symmetry is sufficient to fix the solutions also for such correlators. The solution of the conformal constraints are given in terms of triple-$K$ integrals and are expressed in terms of a set of constants, specific for each correlator and spacetime dimension. We present a discussion of the intermediate steps in the description of two nontrivial correlators, the $TTO$ and the $TTT$, in a more pedagogical way, offering details that could help extend such methods to higher point function.

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arXiv2020

Dark Matter with Light and Ultralight Stückelberg Axions

Scenarios with axion-like particles of variable masses, from the milli-eV range to ultralight, can be generated in a natural way in the context of effective field theory models with anomalous $U(1)$ gauge symmetries. They include dimension-5 operators which define a coupling of the axion to the gauge anomaly. They provide a realization, in the domain of ordinary gauge theories, of models for such particles, which evade the usual mass/coupling constraint of ordinary (Peccei-Quinn) axions and are natural dark matter candidates. As an illustration of these models, we present an overview of two of these scenarios. One of them is built around the next-to-minimal MSSM (NMSSM), a model called the USSM-A, which illustrates how the Stückelberg supermultiplet can be used to generate two dark matter candidates, a neutralino containing an axino component coming from the Stückelberg sector, plus the axion ($\textrm{Im}\, b$). The real component of the complex Stückelberg field carries dilaton-like ($\textrm{Re}\, b\, FF$) interactions. In a second model, non-supersymmetric, the Stückelberg scale is raised up to the GUT epoch. In this case the axion mass can be ultralight ($\sim 10^{-20}$ eV). The periodic potential generated at the GUT phase transition and the corresponding oscillations are related to a particle whose De Broglie wavelength can be sub-galactic. A similar analysis is also possible for the supersymmetric scenario.

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arXiv2020

The Generalized Hypergeometric Structure of the Ward Identities of CFT's in Momentum Space in $d > 2$

We review the emergence of hypergeometric structures (of $F_4$ Appell functions) from the conformal Ward identities (CWIs) in conformal field theories (CFTs) in dimensions $d > 2$. We illustrate the case of scalar 3- and 4-point functions. 3-point functions are associated to hypergeometric systems with 4 independent solutions. For symmetric correlators they can be expressed in terms of a single 3K integral - functions of quadratic ratios of momenta - which is a parametric integral of three modified Bessel $K$ functions. In the case of scalar 4-point functions, by requiring the correlator to be conformal invariant in coordinate space as well as in some dual variables (i.e. dual conformal invariant), its explicit expression is also given by a 3K integral, or as a linear combination of Appell functions which are now quartic ratios of momenta. Similar expressions have been obtained in the past in the computation of an infinite class of planar ladder (Feynman) diagrams in perturbation theory, which, however, do not share the same (dual conformal/conformal) symmetry of our solutions. We then discuss some hypergeometric functions of 3 variables, which define 8 particular solutions of the CWIs and correspond to Lauricella functions. They can also be combined in terms of 4K integral and appear in an asymptotic description of the scalar 4-point function, in special kinematical limits.

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