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Luigi Delle Rose

Publications and source records attributed to Luigi Delle Rose.

At least 91 records · Page 5Linked to original sources
arXiv2013

The Dilaton Wess-Zumino Action in 6 Dimensions from Weyl Gauging: Local Anomalies and Trace Relations

We extend a previous analysis on the derivation of the dilaton Wess-Zumino (WZ) action in $d=4$, based on the method of Weyl gauging, to $6$ dimensions. As in the previous case, we discuss the structure of the same action in dimensional regularization using 6-dimensional Weyl invariants, extracting the dilaton interactions in the most general scheme, with the inclusion of the local anomaly terms. As an application, we present the WZ action for the (2,0) tensor multiplet, which has been investigated in the past in the context of the $AdS_7/CFT_6$ holographic anomaly matching. We then extend to $d=6$ the investigation of fully traced correlation functions of EMT's, formerly presented in $d=4$, showing that their hierarchy is functionally related only to the first 6 correlators. We give the explicit expressions of these in the most general scheme, up to rank-4.

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arXiv2013

The Standard Model in a Weak Gravitational Background. Dilatons, Scale Anomalies and Conformal Methods

The principal goal of the physics of the fundamental interactions is to provide a consistent description of the nature of the subnuclear forces, which manifest in our universe, together with the gravitational force, in a unified framework. This attempt, which is far from being complete, is characterized by two milestones, the Standard Model of the elementary particles and the Einstein's theory of General Relativity. The coupling of a quantum field theory, such as the Standard Model, to a weak gravitational background provides significant information concerning the coupling of matter to gravity and allows to study in a systematic way the origin of the conformal anomaly. For this reason, the computation of correlation functions in a weak gravitational background is of remarkable interest and the consequences of this analysis are also of phenomenological relevance. For instance, they concern the appearance in the spectrum of the theory of a composite state, the dilaton, which is identified, in perturbation theory, by an infrared coupled anomaly pole. The study of some applications of the methods discussed so far is presented in the second part of this thesis. In particular it is shown that the analysis of the classical metric perturbations in gravity can be related to some specific field theories via a holographic mapping. This requires the computation of correlators of energy-momentum tensors in $d=3$ dimensions and plays a role in the study of the non-gaussianities of the cosmic background radiation in the early universe. Finally, we mention an application in momentum space of the constraints derived from the conformal symmetry in the characterization of some correlation functions. This relies on the solution of a system of second order partial differential equations for a certain class of generalized hypergeometric functions of two variables.

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arXiv2013

Conformal Trace Relations from the Dilaton Wess-Zumino Action

We use the method of Weyl-gauging in the determination of the Wess-Zumino conformal anomaly action, to show that in any even ($d = 2 k$) dimensions all the hierarchy of correlation functions involving traces of the energy-momentum tensor is determined in terms of those of lower orders, up to $2 k$. We work out explicitly the case $d=4$, and show that in this case in any conformal field theory only the first 4 traced correlators are independent. All the remaining correlators are recursively generated by the first 4. The result is a consequence of the cocycle condition which defines the Wess-Zumino action and of the finite order of its dilaton interactions.

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arXiv2013

Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals

We investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for arbitrary scalar operators. We show that the differential equations generated by the requirement of symmetry under special conformal transformations coincide with those satisfied by generalized hypergeometric functions (Appell's functions). Combined with the position space expression of this correlator, whose Fourier transform is given by a family of generalized Feynman (master) integrals, the method allows to derive the expression of such integrals in a completely independent way, bypassing the use of Mellin-Barnes techniques, which have been used in the past. The application of the special conformal constraints generates a new recursion relation for this family of integrals.

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arXiv2013

Dilaton Interactions and the Anomalous Breaking of Scale Invariance of the Standard Model

We discuss the main features of dilaton interactions for fundamental and effective dilaton fields. In particular, we elaborate on the various ways in which dilatons can couple to the Standard Model and on the role played by the conformal anomaly as a way to characterize their interactions. In the case of a dilaton derived from a metric compactification (graviscalar), we present the structure of the radiative corrections to its decay into two photons, a photon and a $Z$, two $Z$ gauge bosons and two gluons, together with their renormalization properties. We prove that, in the electroweak sector, the renormalization of the theory is guaranteed only if the Higgs is conformally coupled. For such a dilaton, its coupling to the trace anomaly is quite general, and determines, for instance, an enhancement of its decay rates into two photons and two gluons. We then turn our attention to theories containing a non-gravitational (effective) dilaton, which, in our perturbative analysis, manifests as a pseudo-Nambu Goldstone mode of the dilatation current ($J_D$). The infrared coupling of such a state to the two-photons and to the two-gluons sector, and the corresponding anomaly enhancements of its decay rates in these channels, is critically analyzed.

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arXiv2013

Mass Corrections to Flavor-Changing Fermion-Graviton Vertices in the Standard Model

In a previous study, the flavor-changing fermion-graviton interactions have been analyzed in the framework of the standard model, where analytical results for the relevant form factors were obtained at the leading order in the external fermion masses. These interactions arise at one-loop level by the charged electroweak corrections to the fermion-graviton vertex, when the off-diagonal flavor transitions in the corresponding charged weak currents are taken into account. Due to the conservation of the energy-momentum tensor, the corresponding form factors turn out to be finite and gauge invariant when external fermions are on-shell. Here we extend this previous analysis by including the exact dependence on the external fermion masses. Complete analytical results are provided for all the relevant form factors to the flavor-changing fermion-graviton transitions.

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arXiv2013

One loop Standard Model corrections to flavor diagonal fermion-graviton vertices

We extend a previous analysis of flavor-changing fermion-graviton vertices, by adding the one-loop SM corrections to the flavor diagonal fermion-graviton interactions. Explicit analytical expressions taking into account fermion masses for the on-shell form factors are computed and presented. The infrared safety of the fermion-graviton vertices against radiative corrections of soft photons and gluons is proved, by extending the ordinary infrared cancellation mechanism between real and virtual emissions to the gravity case. These results can be easily generalized to fermion couplings with massive gravitons, graviscalar, and dilaton fields, with potential phenomenological implications to new physics scenarios with low gravity scale.

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arXiv2012

Three and Four Point Functions of Stress Energy Tensors in D=3 for the Analysis of Cosmological Non-Gaussianities

We compute the correlation functions of 3 and 4 stress energy tensors $(T)$ in D=3 in free field theories of scalars, abelian gauge fields, and fermions, which are relevant in the analysis of cosmological non-gaussianities. These correlators appear in the holographic expressions of the scalar and tensor perturbations derived for holographic cosmological models. The result is simply adapted to describe the leading contributions in the gauge coupling to the same correlators also for a non abelian SU(N) gauge theory. In the case of the bispectrum, our results are mapped and shown to be in full agreement with the corresponding expressions given in a recent holographic study by Bzowski, McFadden and Skenderis. In the 4-T case we present the completely traced amplitude plus all the contact terms. These are expected to appear in a fourth order extension of the holographic formulas for the 4-point functions of scalar metric perturbations.

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arXiv2012

Massless Scalar Degrees of Freedom in QCD and in the Electroweak Sector from the Trace Anomaly

The interaction of QCD and electroweak sector with gravity is characterized by the generation of a massless pole in a specific form factor present in the 1-loop effective action. We briefly illustrate how to single out this behaviour in perturbation theory, by taking as an example the $TJJ$ vertex, with $T$ denoting the energy momentum tensor of the Standard Model. The breaking of scale invariance, due to the trace anomaly, is then related to the appearance of a local degree of freedom in the effective action, which is of dilaton type.

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arXiv2012

Dilaton Interactions in QCD and in the Electroweak Sector of the Standard Model

We overview the structure of the effective action involving a dilaton and a Higgs in the Standard Model, which has been computed recently for the neutral currents sector. We discuss the role of the dilatation current ($J_D$) and of an effective degree of freedom appearing in the $J_D V V'$ correlator, with $V$ any neutral current, which can be interpreted as a Nambu-Goldstone mode generated by the anomalous breaking of the dilatation symmetry.

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arXiv2012

Higher Order Dilaton Interactions in the Nearly Conformal Limit of the Standard Model

We investigate the Standard Model in the nearly conformal limit, in which conformal symmetry is broken only by the dilatation anomaly, through a hierarchy of anomalous Ward identities for the divergence of its dilatation current. In this approximation, the identities allow to extract the coupling of the dilaton to the trace anomaly, which we compute up to the quartic order in the conformal breaking scale. Our approach can be easily extended to discuss the anomaly contributions to the dilaton effective action to an arbitrarily high order. They allow to make a distinction between the Higgs and a dilaton at a phenomenological level.

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arXiv2012

Graviton Vertices and the Mapping of Anomalous Correlators to Momentum Space for a General Conformal Field Theory

We investigate the mapping of conformal correlators and of their anomalies from configuration to momentum space for general dimensions, focusing on the anomalous correlators $TOO$, $TVV$ - involving the energy-momentum tensor $(T)$ with a vector $(V)$ or a scalar operator ($O$) - and the 3-graviton vertex $TTT$. We compute the $TOO$, $TVV$ and $TTT$ one-loop vertex functions in dimensional regularization for free field theories involving conformal scalar, fermion and vector fields. Since there are only one or two independent tensor structures solving all the conformal Ward identities for the $TOO$ or $TVV$ vertex functions respectively, and three independent tensor structures for the $TTT$ vertex, and the coefficients of these tensors are known for free fields, it is possible to identify the corresponding tensors in momentum space from the computation of the correlators for free fields. This works in general $d$ dimensions for $TOO$ and $TVV$ correlators, but only in 4 dimensions for $TTT$, since vector fields are conformal only in $d=4$. In this way the general solution of the Ward identities including anomalous ones for these correlators in (Euclidean) position space, found by Osborn and Petkou is mapped to the ordinary diagrammatic one in momentum space. We give simplified expressions of all these correlators in configuration space which are explicitly Fourier integrable and provide a diagrammatic interpretation of all the contact terms arising when two or more of the points coincide. We discuss how the anomalies arise in each approach [...]

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arXiv2011

Gravity and the Neutral Currents: Effective Interactions from the Trace Anomaly

We present a complete study of the one graviton-two neutral gauge bosons vertex at 1-loop level in the electroweak theory. This vertex provides the leading contribution to the interaction between the Standard Model and gravity, mediated by the trace anomaly, at first order in the inverse Planck mass and at second order in the electroweak expansion. At the same time, these corrections are significant for precision studies of models with low scale gravity at the LHC. We show, in analogy with previous results in the QED and QCD cases, that the anomalous interaction between gravity and the gauge current of the Standard Model, due to the trace anomaly, is mediated, in each gauge invariant sector, by effective massless scalar degrees of freedom. We derive the Ward and Slavnov-Taylor identities characterizing the vertex. Our analysis includes the contributions from the improvements of the scalar sector, induced by a conformally coupled Higgs sector in curved space.

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arXiv2011

Comments on Anomaly Cancellations by Pole Subtractions and Ghost Instabilities with Gravity

We investigate some aspects of anomaly cancellation realized by the subtraction of an anomaly pole, stressing on some of its properties in superspace. In a local formulation these subtractions can be described in terms of a physical scalar, an axion and related ghosts. They appear to be necessary for the unitarization of the theory in the ultraviolet, but they may generate an infrared instability of the corresponding effective action, signalled by ghost condensation. In particular the subtraction of the superanomaly multiplet by a pole in superspace is of dubious significance, due to the different nature of the chiral and conformal anomalies. In turn, this may set more stringent constraints on the coupling of supersymmetric theories to gravity.

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arXiv2011

The Conformal Anomaly and the Neutral Currents Sector of the Standard Model

We elaborate on the structure of the graviton-gauge-gauge vertex in the electroweak theory, obtained by the insertion of the complete energy-momentum tensor ($T$) on 2-point functions of neutral gauge currents ($VV'$). The vertex defines the leading contribution to the effective action which accounts for the conformal anomaly and related interaction between the Standard Model and gravity. The energy momentum tensor is derived from the curved spacetime Lagrangian in the linearized gravitational limit, and with the inclusion of the term of improvement of a conformally coupled Higgs sector. As in the previous cases of QED and QCD, we find that the conformal anomaly induces an effective massless scalar interaction between gravity and the neutral currents in each gauge invariant component of the vertex. This is described by the exchange of an anomaly pole. We show that for a spontaneously broken theory the anomaly can be entirely attributed to the poles only for a conformally coupled Higgs scalar. In the exchange of a graviton, the trace part of the corresponding interaction can be interpreted as due to an effective dilaton, using a local version of the effective action. We discuss the implications of the anomalous Ward identity for the $TVV'$ correlator for the structure of the gauge/gauge/ effective dilaton vertex in the effective action. The analogy between these effective interactions and those related to the radion in theories with large extra dimensions is pointed out.

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arXiv2010

The Trace Anomaly and the Gravitational Coupling of an Anomalous U(1)

We extend a previous computation of the TJJ correlator, involving the energy-momentum tensor of an abelian gauge theory and two vector currents, to the case of mixed axial-vector/vector currents. The study is performed in analogy to the case of the $AVV$ vertex for the chiral anomaly. We derive the general structure of the anomalous Ward identities and provide explicit tests of their consistency using Dimensional Reduction. Mixed massive correlators of the form $TJ_V J_A$ are shown to vanish both by Ward identities and by C-invariance. The result is characterized by the appearance of massless scalar degrees of freedom in the coupling of chiral and vector theories to gravity, affecting both the soft and the ultraviolet region of the vertex. This is in agreement with previous studies of the effective action of gauge and conformal anomalies in QED and QCD.

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arXiv2010

Trace Anomaly, Massless Scalars and the Gravitational Coupling of QCD

The anomalous effective action describing the coupling of gravity to a non-abelian gauge theory can be determined by a variational solution of the anomaly equation, as shown by Riegert long ago. It is given by a nonlocal expression, with the nonlocal interaction determined by the Green's function of a conformally covariant operator of fourth order. In recent works it has been shown that this interaction is mediated by a simple pole in an expansion around a Minkowski background, coupled in the infrared in the massless fermion limit. This result relies on the local formulation of the original action in terms of two auxiliary fields, one physical scalar and one ghost, which take the role of massless composite degrees of freedom. In the gravity case, the two scalars have provided ground in favour of some recent proposals of an infrared approach to the solution of the dark energy problem, entirely based on the behaviour of the vacuum energy at the QCD phase transition. As a test of this general result, we perform a complete one-loop computation of the effective action describing the coupling of a non-abelian gauge theory to gravity. We confirm the appearance of an anomaly pole which contributes to the trace part of the $TJJ$ correlator and of extra poles in its trace-free part, in the quark and gluon sectors, describing the coupling of the energy momentum tensor ($T$) to two non abelian gauge currents ($J$).

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