arXiv subjects

Loriano Bonora

Publications and source records attributed to Loriano Bonora.

At least 19 recordsLinked to original sources

arXiv2026

Conformal symmetry, SM and Gravity

This paper is a bottom up attempt to incorporate the standard model and general relativity in a unique quantum field theory. The tentative model presented here in particular is free of chiral gauge and gravitational anomalies that appear in the divergence of currents, and in the divergence and trace of the energy-momentum tensor when the SM matter couples to gravity. The fermion spectrum is composed of two multiplets, the SM (left) multiplet and a mirror copy (right) with opposite handedness. The right multiplet is interpreted as describing the dark matter world. The natural symmetry of the theory is enlarged to incorporate also Weyl invariance, by introducing one or more dilaton fields. After the cosmological and theoretical motivations, the necessary formalism is introduced for algebraic renormalization: gauge fixings, ghosts, propagators and vertices and their interplay in guaranteeing the conditions for convergence of the subtracted amplitudes according to the BPHZL scheme, the Slavnov-Taylor identity and the relevant enlarged BRST symmetry. The corresponding (conformal) cohomology is analyzed and found to be trivial: there are no non-trivial even trace anomalies in theories with dilatons, but there are plenty of trivial ones, which require corresponding counterterms in the effective action. It is shown that such counterterms can play an important role in freeing the theory of unphysical particles.

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arXiv2026

A fermion primer

This is a review paper intended to illustrate a few critical issues concerning Dirac, Weyl and Majorana fermions and their differences. The first part consists in basic introductions to fermions, and more in detail to fermions in 4d, focusing in particular in what differentiate the three type of fermions: chirality, helicity, mass, field equations, properties under discrete symmetry transformations, Actions, Observables. On this basis we tackle a series of challenging and sometime controversial problems: the non-existence of Weyl fermion propagators, and the ways to circumvent it; the regularizations for Weyl fermion amplitudes, in particular the appropriateness of using the PV regularization; the definition of a functional integral for Weyl fermion, the difference between Weyl and massless Majorana fermions and the difference between the Dirac and Majorana mass terms. Most notably we come to the conclusion that the trick of replacing the non-existing Weyl fermion propagator with a massless Dirac one, although it may yield in some cases correct results, is flawed at the very origin by a logical loophole. We then show which is the correct way to proceed in this case. We consider also the topic of applying the Wick rotation at the classical Action level for Weyl fermions and conclude that this procedure leads to a nonequivalent theory. Finally, although anomalies are not the central focus here, we have deemed it useful to summarily review the relation, and its cohomological basis, that exists between the lack of a Weyl fermion propagator (non-invertibility of the Weyl-Dirac operator) and the appearance of dangerous anomalies in the theory.

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arXiv2026

Anomaly footprints in SM+Gravity

This is a follow-up of arXiv:2412.07470 [hep-th]. A simplified version of the SM plus gravity, put forward there, is presented here and some of its aspects delved into. The basic structure consists of two sectors, left and right, with chirally mirror fermions and scalars, as well as $SU(3)$ and $U(1)$ gauge fields, while the $SU(2)$ gauge fields as well as the metric are in common to both sectors. This structure is dictated by the request to cancel all dangerous anomalies. The left sector consists of the fermion, gauge and scalar fields of the SM, now minimally coupled to gravity. The right sector is a mirror image of the left, with distinct fields, except the metric and the $SU(2)$ gauge potentials. The first new aspect is the proposed and motivated interpretation of the right sector as the dark matter one. The second new subject covered here is Weyl symmetry and its possible application to cosmology and its theoretical fallout on unitarity and renormalization of the model. A background solution of the Weyl invariant theory is derived, which may apply to the very early stages of the universe. This solution also suggests interesting applications to the cosmological constant problem. On the quantum field theory side the subject of Weyl symmetry and Weyl anomalies is reviewed and, among other things, an application of the WZ terms is illustrated to the problem of one-loop quantization of the model which may avoid negative norm states.

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arXiv2025

Something Anomalies can tell about SM and Gravity

This ia a review/research paper on anomalies applied to a bottom-up approach to standard model and gravity. It is divided in two parts. The first consists in a review proper of anomalies in quantum field theories. Anomalies are analyzed according to three different methods: a perturbative one based on Feynman diagram, a non-perturbative one relying on the Schwinger-DeWitt approach and, third, the one hinging on the Atiyah-Singer family's index theorem. The three methods are applied both to chiral gauge anomalies and trace anomalies. The fundamental distinction that our presentation leads to is between obstructive (O) and non-obstructive (NO) anomalies. The former are tied to the non-existence of fermion propagators, which fatally maim the corresponding theory. In the second part we apply this analysis to the SM and various of its extensions immersed in a gravitational background, and find that they all are plagued by a residual chiral trace anomaly. To completely eliminate all kind of dangerous anomalies in SM-like theories we propose a somewhat unconventional scheme, and exemplify it by means of an explicit model. The latter is a left-right symmetric model. We embed it in a Weyl geometry to render it conformal invariant. We then deal with some of its quantum aspects, in particular its even (NO) trace anomalies and the means to preserve its confomal invariance at the quantum level. We briefly review renormalization and unitarity in the framework of similar models discussed in the existing literature. Finally we present a possible (conjectural) application of the model to describe the junction between cosmology and quantum field theory.

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arXiv2023

Addendum: Weyl cocycles, (Class.Quantum Grav. 3 (1986) 635)

Weyl 0- and 1-cocycles of canonical dimension 6 in six dimensions, which were computed earlier in ref.\cite{bonorabregolapasti1986}, are recalculated from scratch. The analysis yields five Weyl invariants (0-cocycles), instead of four, and the same four non-trivial 1-cocycles (possible trace anomalies), like in that reference (up to the correction of one typo)

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arXiv2021

Perturbative and non-pertrubative trace anomalies

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach.

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arXiv2020

Supersymmetric HS Yang-Mills-like models

We introduce the supersymmetric version of YM-like theories with infinitely many spin fields in 4 dimension. The construction is carried out via the superfield method. The surprising feature of these models is that they describe in particular gauge and gravity in a supersymmetric form with no need of supergravity.

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arXiv2020

On the trace anomaly for Weyl fermions

This note is a comment on some recent papers that have raised a controversy about the existence of the odd-parity trace anomaly in a four-dimensional theory of Weyl fermions. Without going into too technical details we explain why the methods employed in those papers cannot detect it.

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arXiv2016

Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories

We derive formulas for the classical Chern-Simons invariant of irreducible $SU(n)$-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.

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arXiv2016

Pure contact term correlators in CFT

We discuss the case of correlators in CFT made of pure contact terms, without a corresponding bare part. We show two examples. The first is provided by the conformal limits of a free massive fermion theory in 3d. We show that the (conserved) current correlators are in one-to-one correspondence with the terms of the 3d gauge CS action. The second is the Pontryagin trace anomaly. The corresponding 3-point correlator is nonvanishing even though the corresponding untraced correlator vanishes.

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arXiv2015

Regularization of energy-momentum tensor correlators and parity-odd terms

We discuss the problem of regularizing correlators in conformal field theories. The only way to do it in coordinate space is to interpret them as distributions. Unfortunately except for the simplest cases we do not have tabulated mathematical results. The way out we pursue here is to go to momentum space and use Feynman diagram techniques and their regularization methods. We focus on the energy-momentum tensor correlators and, to gain insight, we compute and regularize 2-point functions in 2d with various techniques both in coordinate space and in momentum space, obtaining the same results. Then we do the same for 2-point functions in 4d. Finally we turn to 3-point function in 4d, and concentrate on the parity-odd part. We derive in particular the regularized trace and divergence of the energy-momentum tensor in a chiral fermion model. We discuss the problems related to the parity-odd trace anomaly.

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arXiv2014

Comments on lump solutions in SFT

We analyze a recently proposed scheme to construct analytic lump solutions in open SFT. We argue that in order for the scheme to be operative and guarantee background independence it must be implemented in the same 2D conformal field theory in which SFT is formulated. We outline and discuss two different possible approaches. Next we reconsider an older proposal for analytic lump solutions and implement a few improvements. In the course of the analysis we formulate a distinction between regular and singular gauge transformations and advocate the necessity of defining a topology in the space of string fields.

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arXiv2014

Trace anomalies in chiral theories revisited

Motivated by the search for possible CP violating terms in the trace of the energy-momentum tensor in theories coupled to gravity we revisit the problem of trace anomalies in chiral theories. We recalculate the latter and ascertain that in the trace of the energy-momentum tensor of theories with chiral fermions at one-loop the Pontryagin density appears with an imaginary coefficient. We argue that this may break unitarity, in which case the trace anomaly has to be used as a selective criterion for theories, analogous to the chiral anomalies in gauge theories. We analyze some remarkable consequences of this fact, that seem to have been overlooked in the literature.

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arXiv2013

Generalized states in SFT

The search for analytic solutions in open string fields theory à la Witten often meets with singular expressions, which need an adequate mathematical formalism to be interpreted. In this paper we discuss this problem and propose a way to resolve the related ambiguities. Our claim is that a correct interpretation requires a formalism similar to distribution theory in functional analysis. To this end we concretely construct a locally convex space of test string states together with the dual space of functionals. We show that the above suspicious expressions can be identified with well defined elements of the dual.

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arXiv2013

Symmetries and gravitational Chern-Simons Lagrangian terms

We consider some general consequences of adding pure gravitational Chern-Simons term to manifestly diff-covariant theories of gravity. Extending the result of a previous paper we enlarge the class of metrics for which the inclusion of a gCS term in the action does not affect solutions and corresponding physical quantities. In the case in which such solutions describe black holes (of general horizon topology) we show that the black hole entropy is also unchanged. We arrive at these conclusions by proving three general theorems and studying their consequences. One of the theorems states that the contribution of the gravitational Chern-Simons to the black hole entropy is invariant under local rescaling of the metric.

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arXiv2013

Stationary rotating black holes in theories with gravitational Chern-Simons Lagrangian term

We study the effects of introducing purely gravitational Chern-Simons Lagrangian terms in ordinary Einstein gravity on stationary rotating black hole solutions and on the associated thermodynamical properties, in a generic number of dimensions which support these terms (i.e. in D = 4k-1). We analyze the conditions, namely the number of vanishing angular momenta, under which the contributions of the Chern-Simons term to the equations of motion and the black hole entropy vanish. The particular case of a 7-dimensional theory in which a purely gravitational Chern-Simons term is added to the Einstein-Hilbert Lagrangian in D=7 dimensions is investigated in some detail. As we have not been able to find exact analytic solutions in nontrivial cases, we turn to perturbation theory and calculate the first-order perturbative correction to the Myers-Perry metric in the case where all angular momenta are equal. The expansion parameter is a dimensionless combination linear in the Chern-Simons coupling constant and the angular momentum. Corrections to horizon and ergosurface properties, as well as black hole entropy and temperature, are presented.

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arXiv2012

String Partition Functions, Hilbert Schemes, and Affine Lie Algebra Representations on Homology Groups

This review paper contains a concise introduction to highest weight representations of infinite dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in the paper is to be found in a very important feature of the theory of infinite dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated $q$-series. For mathematicians, elliptic genera are commonly associated to new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function (therefore they are applicable, for instance, to topological Casimir effect calculations). We show that elliptic genera can be conveniently transformed into product expressions which can then inherit the homology properties of appropriate polygraded Lie algebras.

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arXiv2012

Gravitational Chern-Simons Lagrangian terms and spherically symmetric spacetimes

We show that for general spherically symmetric configurations, contributions of general gravitational and mixed gauge-gravitational Chern-Simons terms to the equations of motion vanish identically in $D>3$ dimensions. This implies that such terms in the action do not affect Birkhoff's theorem or any previously known spherically symmetric solutions. Furthermore, we investigate the thermodynamical properties using the procedure described in an accompanying paper. We find that in $D>3$ static spherically symmetric case Chern-Simons terms do not contribute to the entropy either. Moreover, if one requires only for the metric tensor to be spherically symmetric, letting other fields unrestricted, the results extend almost completely, with only one possible exception --- Chern-Simons Lagrangian terms in which the gravitational part is just the $n=2$ irreducible gravitational Chern-Simons term.

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