scholarly journals Omega vs. pi, and 6d anomaly cancellation

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Joe Davighi ◽  
Nakarin Lohitsiri

Abstract In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘global’) gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of πd(G) is neither a necessary nor a sufficient condition for there being a possible global anomaly in a d-dimensional chiral gauge theory with gauge group G. To showcase the failure of sufficiency, we revisit ‘global anomalies’ that have been previously studied in 6d gauge theories with G = SU(2), SU(3), or G2. Even though π6(G) ≠ 0, the bordism groups $$ {\Omega}_7^{\mathrm{Spin}}(BG) $$ Ω 7 Spin BG vanish in all three cases, implying there are no global anomalies. In the case of G = SU(2) we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.

Author(s):  
Yasunori Lee ◽  
Yuji Tachikawa

Abstract Global gauge anomalies in 6d associated with non-trivial homotopy groups π6(G) for G = SU(2), SU(3), and G2 were computed and utilized in the past. In the modern bordism point of view of anomalies, however, they come from the bordism groups Ω7spin (BG), which are in fact trivial and therefore preclude their existence. Instead, it was noticed that a proper treatment of the 6d Green-Schwarz mechanism reproduces the same anomaly cancellation conditions derived from π6(G). In this paper, we revisit and clarify the relation between these two different approaches.


Human Ecology ◽  
2021 ◽  
Author(s):  
Adam Pain ◽  
Kristina Marquardt ◽  
Dil Khatri

AbstractWe provide an analytical contrast of the dynamics of secondary forest regeneration in Nepal and Peru framed by a set of common themes: land access, boundaries, territories, and rights, seemingly more secure in Nepal than Peru; processes of agrarian change and their consequences for forest-agriculture interactions and the role of secondary forest in the landscape, more marked in Peru, where San Martín is experiencing apparent agricultural intensification, than in Nepal; and finally processes of social differentiation that have consequences for different social groups, livelihood construction and their engagement with trees, common to both countries. These themes address the broader issue of the necessary conditions for secondary forest regeneration and the extent to which the rights and livelihood benefits of those actively managing it are secured.


Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 280
Author(s):  
Loriano Bonora ◽  
Rudra Prakash Malik

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.


2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ferruccio Feruglio

Abstract The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Riccardo Argurio ◽  
Matteo Bertolini ◽  
Sebastián Franco ◽  
Eduardo García-Valdecasas ◽  
Shani Meynet ◽  
...  

Abstract We study 4d$$ \mathcal{N} $$ N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.


2014 ◽  
Vol 25 (8) ◽  
pp. 1135-1147 ◽  
Author(s):  
Joao Quariguasi-Frota-Neto ◽  
Andrew Reade ◽  
Azadeh Dindarian ◽  
Andrew Gibson

Purpose – In 2011, a governmental initiative driven by the Department for Business Innovation and Skills invited the British Standards Institute (BSI) to write and publish a publicly available specification (PAS) for the reuse of waste electrical and electronic equipment entitled PAS 141. The specification's ambitious goals, chief among them to reduce the amount of e-waste generated in the UK, has prompted debate as to whether they are realistic and the extent to which they can be influenced by the certification. The purpose of this paper is to propose a comprehensive framework that can be used in future research to enhance understanding of the mechanisms by which the introduction of PAS 141 certification could lead to the fulfillment of its goals, that is, successful uptake. The authors believe this framework can serve as a roadmap for those interested in the investigation of this novel certification and its effect on the market for reusable electrical and electronic products. Design/methodology/approach – This paper is based on interviews with reuse organizations and first hand experience as a participant in the steering group that elaborated the certification being investigated, i.e. PAS 141. Findings – It is uncertain whether PAS 141 will fulfill its promises, which are, in the view of the authors, rather ambitious, e.g. reduce e-waste. Furthermore, more research is needed to examine the effect that the introduction of the certification has on the materialization of its goals, and on the complex inter-relationship that exist between the goals and what the authors define as intermediary necessary conditions. Research limitations/implications – This is the first attempt the outline the research needs that arise from the introduction of PAS-141, and the authors believe that there are other equally important questions that are yet to be presented and examined. Practical implications – This paper proposes 28 hypotheses which will help future work to empirically establish: the possibility of PAS-141 attaining its goals and the main necessary conditions for that to happen. This information is pivotal to determine whether the certification is working and to pinpoint opportunities for improvement. Social implications – This works contributes to the understanding of the role of certification on the market of reused products, which employs a large number of people, and in particular, whose coming from disadvantaged backgrounds. Originality/value – Although certification in general has been widely investigated in prior research, scant attention has been paid to certification in the context of electronic products. To the best of the knowledge, this is the first paper of its kind, as it is the first to examine certification in that context.


2007 ◽  
Vol 656 (1-3) ◽  
pp. 145-151 ◽  
Author(s):  
M. Gomes ◽  
T. Mariz ◽  
J.R. Nascimento ◽  
A.Yu. Petrov ◽  
A.J. da Silva ◽  
...  

2019 ◽  
pp. 35-51
Author(s):  
Vsevolod Skvortsov

In the last decade, the functions of the chief nurse have not only changed but they have become more complex, more diverse, patient-oriented and personal-oriented. The main duties of the Chief Medical Nurse today are to create the necessary conditions for the effective work of the middle and junior staff, to develop the necessary instructions and guidelines, to plan the budget, and to train and increase the professionalism of employees.


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