Four-Dimensional Yang-Mills Theory as a Deformation of Topological BF Theory

The classical action for pure Yang--Mills gauge theory can be formulated as a deformation of the topological $BF$ theory where, beside the two-form field $B$, one has to add one extra-field $\eta$ given by a one-form which transforms as the difference of two connections. The ensuing action functional gives a theory that is both classically and quantistically equivalent to the original Yang--Mills theory. In order to prove such an equivalence, it is shown that the dependency on the field $\eta$ can be gauged away completely. This gives rise to a field theory that, for this reason, can be considered as semi-topological or topological in some but not all the fields of the theory. The symmetry group involved in this theory is an affine extension of the tangent gauge group acting on the tangent bundle of the space of connections. A mathematical analysis of this group action and of the relevant BRST complex is discussed in details.Comment: 74 pages, LaTeX, minor corrections; to be published in Commun. Math. Phy

Romanesque and territory. The construction materials of Sardinian medieval churches: new approaches to the valorization, conservation and restoration

This paper is intended to illustrate a multidisciplinary research project devoted to the study of the constructive materials of the Romanesque churches in Sardinia during the “Giudicati” period (11th -13th centuries). The project focuses on the relationship between a selection of monuments and their territory, both from a historical-architectural perspective and from a more modern perspective addressing future restoration works. The methodologies of the traditional art-historical research (study of bibliographic, epigraphic and archival sources, formal reading of artifacts) are flanked by new technologies: digital surveys executed with a 3D laser-scanner, analyses of the materials (stones, mortars, bricks) with different instrumental methods: X-ray fluorescence (XRF) and inductively coupled mass spectrometry (ICP-MS) for chemical composition, X-ray diffractometer (XRD) to determine the alteration phases (e.g., soluble salts), optical microscopy and electronic (SEM) to study textures, mineral assemblages and microstructures, termogravimetric/differential scanning, calorimetric analysis (TG/DTA) for the composition of the binder mortars. This multidisciplinary approach allows the achieving of important results in an archaeometric context: 1) from a historical point of view, with the possible identification of ancient traffics, trade routes, sources of raw materials, construction phases, wall textures; 2) from a conservative point of view, by studying chemical and physical weathering processes of stone materials compatible for replacement in case of future restoration works. Sardinian Romanesque architectural heritage is particularly remarkable: about 200 churches of different types and sizes, with the almost exclusive use of cut stones. Bi- or poly-chromy, deriving from the use of different building materials, characterizes many of these monuments, becoming also a vehicle for political and cultural meanings. The paper will present some case studies aimed to illustrate the progress of the project and the results achieved

Looking for the right balance between human and economic costs during COVID-19 outbreak

Since the beginning of Coronavirus 2019 (COVID-19) disease outbreak, there has been a heated debate about public health measures, as they can presumably reduce human costs in the short term but can negatively impact economies and well-being over a longer period. Materials and methods: To study the relationship between health and economic impact of COVID-19, we conducted a secondary research on Italian regions, combining official data (mortality due to COVID-19 and contractions in value added of production for a month of lockdown). Then, we added the tertiles of the number of people tested for COVID-19 and those of health aids to evaluate the correspondence with the outcome measures. Results: Five regions out of 20, the most industrialized northern regions, which were affected both earlier and more severely by the outbreak, registered both mortality and economic value loss above the overall medians. The southern regions, which were affected later and less severely, had low mortality and less economic impact. Conclusions: Our analysis shows that considering health and economic outcomes in the assessment of response to pandemics offers a bigger picture perspective of the outbreak and could allow policymakers and health managers to choose systemic, 'personalized' strategies, in case of a feared second epidemic wave

Nonrenormalization theorems for N=2 Super Yang-Mills

The BRST algebraic proofs of the the nonrenormalization theorems for the beta functions of N=2 and N=4 Super Yang-Mills theories are reviewed.Comment: 3 pages, contribution to SUSY 2000 Encyclopedi

Simulating H/V spectral ratios (HVSR) of ambient vibrations: a comparison among numerical models

The use of H/V spectral ratios (HVSR) of ambient vibrations to constrain the local seismo-stratigraphical configuration relies on numerical forward models able to connect observations with subsoil seismic properties. Several models were proposed to this purpose in the last decades, which are based on different assumptions about the nature of the ambient vibration wavefield. Performances of nine numerical tools implementing these models have been checked by considering 1600 realistic 1-D subsoil configurations mostly relative to A, B and C Eurocode8 soil classes. Resultant HVSR curves predicted by the models are quite similar both in their general shape and in predicting the resonant soil frequencies, possibly because all of them share the same basic representation of the subsoil as a 1-D stack of flat uniform viscoelastic layers. The common sensitivity to transmission/reflection matrices resulting from that representation explains the well-known correspondence of HVSR maxima to 1-D resonance frequency estimates, regardless of the physical assumptions (about source distribution, radiation pattern, dominating seismic phases, etc.) behind the computational model adopted for simulating HVSR curves. On the other hand, the computational models here considered provide quite different amplitudes for HVSR values corresponding to the resonance frequencies. However, since experimental HVSR amplitudes at the same site are affected by an inherent variability (e.g. due to the possible lack of ergodicity of the ambient vibration stochastic wavefield, non-ideal experimental settings, etc.) and uncertainty about the local seismo-stratigraphical profile (attenuation, 2-D/3-D effects, etc.) observations cannot be used for general scoring of the considered computational models on empirical basis. In this situation, the ‘optimal’ numerical tool to be considered for the forward HVSR modelling must be defined case by case

Topological Gravity versus Supergravity on Manifolds with Special Holonomy

We construct a topological theory for euclidean gravity in four dimensions, by enforcing self-duality conditions on the spin connection. The corresponding topological symmetry is associated to the SU(2) X diffeomorphism X U(1) invariance. The action of this theory is that of d=4, N=2 supergravity, up to a twist. The topological field theory is SU(2) invariant, but the full SO(4) invariance is recovered after untwist. This suggest that the topological gravity is relevant for manifolds with special holonomy. The situation is comparable to that of the topological Yang-Mills theory in eight dimensions, for which the SO(8) invariance is broken down to Spin(7), but is recovered after untwisting the topological theory.Comment: LateX file, 19 page

The action of N=4 Super Yang-Mills from a chiral primary operator

Using the Vafa-Witten twisted version of N=4 Super Yang-Mills a subset of the supercharges actually relevant for the nonrenormalization properties of the theory is identified. In particular, a relationship between the gauge-fixed action and the chiral primary operator tr(\phi)^2 is worked out. This result can be understood as an off-shell extension of the reduction formula introduced by Intriligator.Comment: 1+15 pages, LaTeX2e, one reference changed, a footnote adde

Algebraic renormalization of the BF Yang-Mills Theory

We discuss the quantum equivalence, to all orders of perturbation theory, between the Yang-Mills theory and its first order formulation through a second rank antisymmetric tensor field. Moreover, the introduction of an additional nonphysical vector field allows us to interpret the Yang-Mills theory as a kind of perturbation of the topological BF model.Comment: 14 pages, some references and acknowledgments added, version to appear in Phys.Lett.

General Solution Of Linear Vector Supersymmetry

We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example.Comment: 18 pages, LaTeX, no figure