arXiv subjects

Matteo Maria Maglio

Publications and source records attributed to Matteo Maria Maglio.

27 records · Page 2Linked to original sources

arXiv2020

Anomalous Gravitational TTT Vertex, Temperature Inhomogeneity, and Pressure Anisotropy

The conformal anomaly in curved spacetime generates a nontrivial anomalous vertex, given by the three-point correlation function $TTT$ of the energy-momentum tensor $T^{μν}$. We show that a temperature inhomogeneity in a gas of charged massless particles generates, via the $TTT$ vertex, a pressure anisotropy with respect to the axis of the temperature variation. This very particular signature may provide an experimental access to the elusive gravitational coefficient $b$ which determines the anomaly contribution of the Weyl tensor to the trace of the energy-momentum tensor in curved spacetime. We present an estimate of the pressure anisotropy both for fermionic quasiparticles in the solid-state environment of Dirac semimetals as well as for a quark-gluon plasma in relativistic heavy-ion collisions. In both cases, the pressure anisotropy is small compared to the mean thermal pressure.

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arXiv2019

Four-Point Functions in Momentum Space: Conformal Ward Identities in the Scalar/Tensor case

We derive and analyze the conformal Ward identities (CWI's) of a tensor 4-point function of a generic CFT in momentum space. The correlator involves the stress-energy tensor $T$ and three scalar operators $O$ ($TOOO$). We extend the reconstruction method for tensor correlators from 3- to 4-point functions, starting from the transverse traceless sector of the $TOOO$. We derive the structure of the corresponding CWI's in two different sets of variables, relevant for the analysis of the 1-to-3 (1 graviton $\to$ 3 scalars) and 2-to-2 (graviton + scalar $\to$ two scalars) scattering processes. The equations are all expressed in terms of a single form factor. In both cases, we discuss the structure of the equations and their possible behaviors in various asymptotic limits of the external invariants. A comparative analysis of the systems of equations for the $TOOO$ and those for the $OOOO$, both in the general (conformal) and dual-conformal/conformal (dcc) cases, is presented. We show that in all the cases the Lauricella functions are homogenous solutions of such systems of equations, also described as parametric 4K integrals of modified Bessel functions.

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arXiv2019

On Some Hypergeometric Solutions of the Conformal Ward Identities of Scalar 4-point Functions in Momentum Space

We discuss specific hypergeometric solutions of the conformal Ward identities (CWI's) of scalar 4-point functions of primary fields in momentum space, in $d$ spacetime dimensions. We determine such solutions using various dual conformal ansätze (DCA's). We start from a generic dual conformal correlator, and require it to be conformally covariant in coordinate space. The two requirements constrain such solutions to take a unique hypergeometric form. They describe correlators which are at the same time conformal and dual conformal in any dimension. These specific ansätze also show the existence of a link between 3- and 4-point functions of a CFT for such class of exact solutions, similarly to what found for planar ladder diagrams. We show that in $d=4$ only the box diagram and its melonic variants, in free field theory, satisfies such conditions, the remaining solutions being nonperturbative. We then turn to the analysis of some approximate high energy fixed angle solutions of the CWI's which also in this case take the form of generalized hypergeometric functions. We show that they describe the behaviour of the 4-point functions at large energy and momentum transfers, with a fixed $-t/s$. The equations, in this case, are solved by linear combinations of Lauricella functions of 3 variables and can be rewritten as generalized 4K integrals. In both cases the CWI's alone are sufficient to identify such solutions and their special connection with generalized hypergeometric systems of equations.

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arXiv2019

Exact Correlators from Conformal Ward Identities in Momentum Space and Perturbative Realizations

The general solution of the conformal Ward identities (CWI's) in momentum space, and their matching to perturbation theory, allows to uncover some specific characteristics of the breaking of conformal symmetry, induced by the anomaly. It allows to compare perturbative features of the 1-particle irreducible (1PI, nonlocal) anomaly action with the prediction of a similar (but exact) nonlocal action identified by the CWI's. The two predictions can be exactly matched at the level of 3-point functions. The analysis of the $TJJ$ and $TTT$ shows that both approaches - based either on 1PI or on the exact solutions of the CWI's - predict massless (dynamical) scalar exchanges in 3-point functions as the signature of the conformal anomaly. In a local formulation such 1PI actions exhibit a ghost in the spectrum which may induce ghost condensation. We also discuss alternative approaches, which take to Wess-Zumino forms of the action with an asymptotic dilaton, which should be considered phenomenological alternatives to the exact nonlocal action. If derived by a Weyl gauging, they also include a ghost in the spectrum. The two formulations, nonlocal and of WZ type, can be unified under the assumption that they describe the same anomaly phenomenon at two separate (UV/IR) ends of the renormalization group flow, possibly separated by a vacuum rearrangement at an intermediate scale. A similar analysis is presented for an $\mathcal{N}=1$ supersymmetric Yang-Mills theory. We comment on the possibile cosmological implications of such quasi Nambu-Goldstone modes as ultralight dilatons and axions.

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arXiv2018

Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative $TJJ$ Vertex

We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example. We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conformal equations in the reconstruction method of BMS, originally formulated using a minimal tensor basis in the transverse traceless sector. A careful comparison with a second basis introduced in previous studies shows that this correlator is affected by one anomaly pole in the graviton (T) line, induced by renormalization. The result shows that the origin of the anomaly, in this correlator, should be necessarily attributed to the exchange of a massless effective degree of freedom. Our results are then exemplified in massless QED at one-loop in $d$-dimensions, expressed in terms of perturbative master integrals. An independent analysis of the Fuchsian character of the solutions, which bypasses the 3K integrals, is also presented. We show that the combination of field theories at one-loop - with a specific field content of degenerate massless scalar and fermions - is sufficient to generate the complete non-perturbative solution, in agreement with a previous study in coordinate space. The result shows that free conformal field theories, in specific dimensions, arrested at one-loop, reproduce the general result for the $TJJ$. Analytical checks of this correspondence are presented in $d=3,4$ and $5$ spacetime dimensions[..].

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arXiv2018

The General 3-Graviton Vertex ($TTT$) of Conformal Field Theories in Momentum Space in $d=4$

We present a study of the correlation function of three stress-energy tensors in $d$ dimensions using free field theory realizations, and compare them to the exact solutions of their conformal Ward identities (CWI's) obtained by a general approach in momentum space. The identification of the corresponding form factors is performed within a reconstruction method, based on the identification of the transverse traceless components $(A_i)$ of the same correlator. The solutions of the primary CWI' s are found by exploiting the universality of the Fuchsian indices of the conformal operators and a re-arrangement of the corresponding inhomogenous hypergeometric systems. We confirm the number of constants in the solution of the primary CWI's of previous analysis. In our comparison with perturbation theory, we discuss scalar, fermion and spin 1 exchanges at 1-loop in dimensional regularization. Explicit checks in $d=3$ and $d=5$ prove the consistency of this correspondence. By matching the 3 constants of the CFT solution with the 3 free field theory sectors available in d=4, the general solutions of the conformal constraints is expressed just in terms of ordinary scalar 2- and 3-point functions $(B_0,C_0)$. We show how the renormalized $d=4$ TTT vertex separates naturally into the sum of a traceless and an anomaly part, the latter determined by the anomaly functional and generated by the renormalization of the correlator in dimensional regularization. The result confirms the emergence of anomaly poles and effective massless exchanges as a specific signature of conformal anomalies in momentum space, directly connected to the renormalization of the corresponding gravitational vertices, generalizing the behaviour found for the $TJJ$ vertex in previous works.

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arXiv2018

Conformal Ward Identities and the Coupling of QED and QCD to Gravity

We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent works. We investigate and detail the structure of the CWIs and their non-perturbative solutions, and compare them to perturbation theory, taking QED and QCD as examples. Exact solutions of CFT's in the flat background limit in momentum space are matched by the perturbative realizations in free field theories, showing that the origin the conformal anomaly is related to efffective scalar interactions, generated by the renormalization of the longitudinal components of the corresponding operators.

hep-ph↗

arXiv2018

Renormalization, Conformal Ward Identities and the Origin of a Conformal Anomaly Pole

We investigate the emergence of a conformal anomaly pole in conformal field theories in the case of the $TJJ$ correlator. We show how it comes to be generated in dimensional renormalization, using a basis of 13 form factors (the $F$-basis), where only one of them requires renormalization $(F_{13})$, extending previous studies. We then combine recent results on the structure of the non-perturbative solutions of the conformal Ward identities (CWI's) for the $TJJ$ in momentum space, expressed in terms of a minimal set of 4 form factors ($A-$ basis), with the properties of the $F$-basis, and show how the singular behaviour of the corresponding form factors in both basis can be related. The result proves the centrality of such massless effective interactions induced by the anomaly, which have recently found realization in solid state, in the theory of topological insulators and of Weyl semimetals. This pattern is confirmed in massless abelian and nonabelian theories (QED and QCD) investigated at one-loop.

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arXiv2015

Electroweak Corrections to Photon Scattering, Polarization and Lensing in a Gravitational Background and the Near Horizon Limit

We investigate the semiclassical approach to the lensing of photons in a spherically symmetric gravitational background, starting from Born level and include in our analysis the radiative corrections obtained from the electroweak theory for the graviton/photon/photon vertex. In this approach, the cross section is related to the angular variation of the impact parameter ($b$), which is then solved for $b$ as a function of the angle of deflection, and measured in horizon units ($b_h\equiv b/(2 G M)$). Exact numerical solutions for the angular deflection are presented. The numerical analysis shows that perturbation theory in a weak background agrees with the classical Einstein formula for the deflection already at distances of the order of $20$ horizon units ($\sim 20\, b_h$) and it is optimal in the description both of very strong and weak lensings. We show that the electroweak corrections to the cross section are sizeable, becoming very significant for high energy gamma rays. Our analysis covers in energy most of the photon spectrum, from the cosmic microwave background up to very high energy gamma rays, and scatterings with any value of the photon impact parameter. We also study the helicity-flip photon amplitude, which is of $O(α^2)$ in the weak coupling $α$, and its massless fermion limit, which involves the exchange of a conformal anomaly pole. The corresponding cross section is proportional to the Born level result and brings to a simple renormalization of Einsten's formula.

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