scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

1998 ◽  
Vol 13 (11) ◽  
pp. 853-860 ◽  
Author(s):  
VINCENZO MAROTTA

We discuss a realization of stress–tensor for parafermion theories following a construction for higher level affine algebras, based on the projection of the standard level-one bosonic realization on the winding subalgebra. All the fields are obtained from rank free bosons compactified on torus, d. This gives an alternative realization of Virasoro algebra in terms of a nonlocal correction of a free field construction which does not fit the usual background charge of the Feigin–Fuchs approach.


2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenzo Bianchi ◽  
Adam Chalabi ◽  
Vladimír Procházka ◽  
Brandon Robinson ◽  
Jacopo Sisti

Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.


2021 ◽  
Vol 49 ◽  
Author(s):  
Sabrina Barros Araújo ◽  
Flávio Ribeiro Alves ◽  
Gerson Tavares Pessoa ◽  
Renan Paraguassu De Sá Rodrigues ◽  
Laecio Da Silva Moura ◽  
...  

Background: Veterinary Ophthalmology provides complementary information for the diagnosis of ocular pathologies. Studies in wild species are essential. Among the diagnostic techniques in ophthalmology, two-dimensional ultrasonography stands out. The agouti is a rodent belonging to the Dasyproctidae family that has been widely used as an experimental model. For these animals, sight is one of the crucial senses for their survival. The aim of this study was to evaluate the effectiveness of the two-dimensional ocular ultrasound technique to obtain anatomical measurements and the external ophthalmic artery resistivity index, presumably normal in the species Dasyprocta prymnolopha.Materials, Methods & Results: Forty eye bulbs of 20 adult rodents of the species were evaluated by ultrasonography. In these animals, B-mode echobiometry was performed using the transpalpebral approach and the hemodynamic study of the external ophthalmic artery using the color Doppler technique. All examinations were initiated by the left eye bulb and all measurements were performed by only one examiner. The collected data related to echobiometry were analyzed using Bioest 5.0 for Windows. Initially, normality was tested using the Shapiro-Wilk test for each parameter, then the paired t-test was performed, comparing right and left eyes, and a significance level of 5% (P < 0.05) was adopted. Based on the methodology used, the following values were obtained for the right and left eyeballs, respectively: anterior chamber thickness - mean of 1.28 ± 0.3 mm and 1.22 ± 0.1 mm; lens thickness - 8.27 ± 0.9 mm and 8.11 ± 0.9 mm; vitreous chamber thickness - 5.35 ± 0.48 mm and 5.30 ± 0.47 mm and axial length - 12.7 ± 0.9 mm and 13 ± 0.68 mm. The mean external ophthalmic artery resistivity values were 0.4305 ± 0.0390 and 0.4258 ± 0.0387 (right and left eye, respectively), characterizing a low resistance. There was no statistical difference between the right and left eyeballs in any of the studied parameters.Discussion: The use of the convex transducer was feasible, promoting adequate contact with the ocular surface and images of satisfactory quality for obtaining measurements, similar to what was observed in studies evaluating the ocular biometry of primates and dogs. The anterior chamber thickness values in this experiment did not differ statistically between the antimers, as well as observed for dogs. The data obtained for lens thickness did not differ statistically for antimers, like those obtained for other rodent species evaluated with the same methodology. The mean values of vitreous chamber thickness were like those observed in chinchillas but correspond to about half of that obtained for capybaras. In this study, the external ophthalmic artery was characterized in all animals, but obtaining the spectral tracing was difficult due to its fine caliber. In wild animals, and especially in wild rodents, there are few data reporting the resistivity of the ophthalmic artery, and there is a lack of studies, which can be explained by the behavioral characteristics of defense and by the high susceptibility to stress in capture, since the performing the technique requires, as in other procedures, the use of chemical containment.Keywords: Doppler flow, ultrasound, eye, agouti.


2019 ◽  
pp. 152-162
Author(s):  
Pavel Verheles ◽  
Natalya Pinchuk ◽  
Tatyana Kovalenko

The results of study of dynamics of quantity of the American white butterfly are reflected in the article, taking into account chronology of population density of districts of area. It is indicated on actuality of problematiki of adjusting of this dangerous quarantine wrecker, taking into account his harmfulness and wide specialization. The results of statistical account of quantity of wrecker are generalized as a quarantine object in the cut of districts of the Winnitca area. The division of character of settling of territory a wrecker is conducted in the variants of private land-tenure and different economies. On the basis of own researches the feed natural base of wrecker is appraised at the level of region and conclusions are done about the prospects of growth of his quantity in default of quarantine measures. The stages of development of wrecker are in detail analysed and confronted with the proper stages characteristic in general under conditions of the right-bank Forest-steppe of Ukraine. The conclusions about the general aspects of prevalence of wrecker and separate factors of optimization of defence of the fruit planting at the level of area awas done.


2016 ◽  
Vol 23 (4) ◽  
pp. 469-475
Author(s):  
Hafedh Bousbih ◽  
Mohamed Majdoub

AbstractThis paper focuses on the analysis of the stationary case of incompressible viscoelastic generalized Oldroyd-B fluids derived in [2] by Bejaoui and Majdoub. The studied model is different from the classical Oldroyd-B fluid model in having a viscosity function which is shear-rate depending, and a diffusive stress added to the equation of the elastic part of the stress tensor. Under some conditions on the viscosity stress tensor and for a large class of models, we prove the existence of weak solutions in both two-dimensional and three-dimensional bounded domains for shear-thickening flows.


1972 ◽  
Vol 62 (2) ◽  
pp. 453-470
Author(s):  
R. J. Scavuzzo ◽  
D. D. Raftopoulos ◽  
J. L. Bailey

abstract The interaction of lateral inertia forces of an N-mass structure with a base mass and lateral seismic motion of the foundation is formulated as an integral equation of the Volterra type. Flexibility of the foundation is based on the transient solution of a two-dimensional elastic half-space. Interaction effects are evaluated by comparing the response spectra of the free-field motion to that of the foundation motion. Results show that changes in the response spectra are significant for heavy, stiff structures such as a reactor-containment vessel.


Sign in / Sign up

Export Citation Format

Share Document