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A bstract We use the numerical S-matrix bootstrap method to obtain bounds on the two leading Wilson coefficients (or low energy constants) of the chiral lagrangian controlling the low-energy dynamics of massless pions. This provides a proof of concept that the numerical S-matrix bootstrap can be used to derive non-perturbative bounds on massless EFTs in more than two spacetime dimensions.

A bstract Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.

A bstract The worldsheet axion plays a crucial role in the dynamics of the Yang-Mills confining flux tubes. According to the lattice measurements, its mass is of order the string tension and its coupling is close to a certain critical value. Using the S-matrix Bootstrap, we construct non-perturbative 2 → 2 branon scattering amplitudes which also feature a weakly coupled axion resonance with these properties. We study the extremal bootstrap amplitudes in detail and show that the axion plays a dominant role in their UV completion in two distinct regimes, in one of which it cannot be considered a parametrically light particle. We conjecture that the actual flux tube amplitudes exhibit a similar behavior.

A bstract We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ϵ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O ( N )-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.

A bstract We study effective actions for simultaneous breaking of space-time and internal symmetries. Novel features arise due to the mixing of Goldstone modes under the broken symmetries which, in contrast to the usual Adler’s zero, leads to non-vanishing soft limits. Such scenarios are common for spontaneously broken SCFT’s. We explicitly test these soft theorems for N = 4 sYM in the Coulomb branch both perturbatively and non-perturbatively. We explore the soft constraints systematically utilizing recursion relations. In the pure dilaton sector of a general CFT, we show that all amplitudes up to order s n ∼ ∂ 2 n are completely determined in terms of the k -point amplitudes at order s k with k ≤ n . Terms with at most one derivative acting on each dilaton insertion are completely fixed and coincide with those appearing in the conformal DBI, i.e. DBI in AdS. With maximal supersymmetry, the effective actions are further constrained, leading to new non-renormalization theorems. In particular, the effective action is fixed up to eight derivatives in terms of just one unknown four-point coefficient and one more coefficient for ten-derivative terms. Finally, we also study the interplay between scale and conformal invariance in this context.

A bstract Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α ′ expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to O α ′ 6 . Thus the massless S-matrix of string theory “knows” about the presence of D-branes.

In this article, we discuss some applications of the construction of the Apéry set of a good semigroup in N d given in (Commun Algebra 49(10):4136–4158, 2021). In particular, we study the duality of a symmetric and almost symmetric good semigroup, the Apéry set of non-local good semigroups and the Apéry set of value semigroups of plane curves.

The review of all available contemporary documents, i.e., technical and photographic reports, newspapers, and other archive material, of the 1908, M 7.1, Messina–Reggio Calabria earthquake has allowed to recognize and classify a large number (365) of independent environmental effects of the earthquake and the subsequent tsunami. The effects have been categorized as slope movement, ground settlement, ground vertical movement and coastal retreat, liquefaction, ground crack, hydrological anomaly, gas emission, light, and rumble. No undisputable evidence of surface faulting has been pointed out. Nevertheless, the widespread and rather homogeneous subsidence of the coastal area of Messina (40–70 cm) might have been caused by slip along a NNE–SSW-trending, east-dipping fault, corresponding to the here proposed Messina Lineament. Likewise, slips along the Reggio Calabria, Armo and Motta San Giovanni faults, suggested by coastal subsidence and slides, ground cracks, and leveling data, cannot be ruled out. A large part of the achieved information has allowed to evaluate the epicentral intensity and local intensities at 74 sites, by applying the environmental seismic intensity scale ESI 2007. This study has led to the most comprehensive picture of the distribution and characteristics of coseismic environmental effects of that earthquake, a crucial knowledge to better estimate the future impact of a similar earthquake on a region that has seen a broad, and often poorly concerned, urban and infrastructural development since then.

On 6 April 2009, a moderate earthquake (Mw = 6.3; Ml = 5.8) struck the Abruzzo region in central Italy, causing more than 300 fatalities and heavy damage to L'Aquila and surrounding villages. Coseismic surface effects have been thoroughly documented by timely field surveys as well as by remote sensing analyses of satellite images. The outstanding quality of geological, seismological, geodetic, and interferometric synthetic aperture radar (InSAR) information arguably represents the best ever data set made available immediately after a moderate seismic event. Based on this data set, we aim at testing the capability of coupled geological and InSAR data to map surface faulting patterns associated with moderate earthquakes. Coseismic ground ruptures have been mapped at a scale of 1:500 in the whole epicentral area. Traces of surface ruptures have been inferred from linear phase discontinuities identified in the interferogram. A very good agreement between the two methods resulted in the characterization of the main surface rupture along the Paganica fault. The same approach applied to ground ruptures hypothesized along other capable fault segments provided more questionable results. Thus, the combined field and InSAR approach appeared useful for detecting continuous surface ruptures exceeding 1 km in length and showing displacements greater than a few centimeters. These are the typical faulting parameters for moderate earthquakes (6.0 < Mw < 6.5) in central Apennines. For continuous ground cracks shorter than a few hundred meters and/or that show displacements smaller than 1–2 cm, the described approach may be less helpful, most probably due to the limited resolution of the data.

A new procedure is presented for simultaneous estimation of SO2 and ash abundance in a volcanic plume, using thermal infrared (TIR) MODIS data. Plume altitude and temperature are the only two input parameters required to run the procedure, while surface emissivity, temperature, atmospheric profiles, ash optical properties, and radiative transfer models are not necessary to perform the atmospheric corrections. The procedure gives the most reliable results when the surface under the plume is uniform, for example above the ocean, but still produces fairly good estimates in more challenging and not easily modelled conditions, such as above land or meteorological cloud layers. The developed approach was tested on the Etna volcano. By linearly interpolating the radiances surrounding a detected volcanic plume, the volcanic plume removal (VPR) procedure described here computes the radiances that would have been measured by the sensor in the absence of a plume, and reconstructs a new image without plume. The new image and the original data allow computation of plume transmittance in the TIR-MODIS bands 29, 31, and 32 (8.6, 11.0 and 12.0 μm) by applying a simplified model consisting of a uniform plume at a fixed altitude and temperature. The transmittances are then refined with a polynomial relationship obtained by means of MODTRAN simulations adapted for the geographical region, ash type, and atmospheric profiles. Bands 31 and 32 are SO2 transparent and, from their transmittances, the effective ash particle radius (Re ), and aerosol optical depth at 550 nm (AOD550) are computed. A simple relation between the ash transmittances of bands 31 and 29 is demonstrated and used for SO2 columnar content (cs ) estimation. Comparing the results of the VPR procedure with MODTRAN simulations for more than 200 000 different cases, the frequency distribution of the differences shows the following: the Re error is less than ±0.5 μm in more than 60% of cases; the AOD550 error is less than ±0.125 in 80% of cases; the cs error is less than ±0.5 g m-2 in more than 60% of considered cases. The VPR procedure was applied in two case studies of recent eruptions occurring at the Mt Etna volcano, Italy, and successfully compared with the results obtained from the established SO2 and ash assessments based on look-up tables (LUTs). Assessment of the sensitivity to the plume altitude uncertainty is also made. The VPR procedure is simple, extremely fast, and can be adapted to other ash types and different volcanoes.