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The local-global property for G-invariant terms [article]

Alexandr Kazda, Michael Kompatscher
2021 arXiv   pre-print
In this paper we investigate the local-global property for the existence of a G-term, i.e. an n-ary term that is invariant under permuting its variables according to a permutation group G ≤ Sym(n).  ...  This local-global property is the main known source of tractability results for deciding Maltsev conditions.  ...  Acknowledgements We thank Matt Valeriote for suggesting the question of studying the conditions Σ .  ... 
arXiv:2109.02065v2 fatcat:sgqbk5xrw5ekldtopmf3wtgl34

Symmetries, Symmetry Breaking, Gauge Symmetries [article]

Franco Strocchi
2015 arXiv   pre-print
The topological invariants of a local gauge group define superselected quantum numbers, which account for the θ vacua.  ...  responsible for most distinctive physical properties of gauge quantum field theories.  ...  [11] ) not being implied by G invariance (e.g. in QEDψ(x) ψ(y) is invariant under G = U(1), but not under G and is not a local observable field).  ... 
arXiv:1502.06540v2 fatcat:vufwnadjzfcdnbvnfgsimkcbhq

Global Aspects of Symmetries in Sigma Models with Torsion [article]

G. Papadopoulos
1994 arXiv   pre-print
The associated anomaly is computed, and it is shown that it depends on the homotopy class of the topological sector of the theory and the group action on the sigma model manifold that generates the symmetries  ...  It is shown that non-trivial topological sectors can prevent the quantum mechanical implementation of the symmetries of the classical field equations of sigma models with torsion.  ...  The action I is either locally or globally defined depending on whether the WZ term b is a locally or globally defined form correspondingly.  ... 
arXiv:hep-th/9406176v1 fatcat:tn7l6yjwxnfpzczzhp7pefjfwq

Parametrization of cosets for AdS5xS5 superstring action [article]

W. Siegel
2015 arXiv   pre-print
A formulation recently proposed [arXiv:1506.07706] as an alternative to the usual coset PSU(2,2|4)/USp(2,2)USp(4) for the superspace geometry of the Type IIB superstring on an AdS5xS5 background is shown  ...  Thus the fermions θ are invariant under the local groups, while the bosonic local-group invariants are (in terms of the antisymmetric metric C of USp (2, 2) and USp(4))X = xCx T , Y = yCy T(2) Global  ...  One such factorization is [2] g ′ = a b c d g ⇒ θ ′ = (aθ + b)(d + cθ) −1 ,θ ′ = (dθ + c)(a + bθ) −1 The action can then be constructed as quadratic in the globally invariant currents J = g −1 dg (  ... 
arXiv:1506.08172v1 fatcat:fq3bitdy5jcgvbinvrtfwabeey

Global anomalies and effective field theory

Siavash Golkar, Savdeep Sethi
2016 Journal of High Energy Physics  
For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.  ...  As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient (up to an overall additive factor).  ...  We therefore list all the local terms that are local functionals of the background fields and have 3D Lorentz invariance.  ... 
doi:10.1007/jhep05(2016)105 fatcat:6ilg7ooqpjhy5jj2y2jhfwzl5e


Anton Tsitsulin, Davide Mottin, Panagiotis Karras, Alexander Bronstein, Emmanuel Müller
2018 Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining - KDD '18  
However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation.  ...  Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable.  ...  A representation σ is scaleadaptive iff it contains both local features σ i and global features σ j : • Local Feature: ∀G ∃f (·) : σ i = f (ξ (G)) • Global Feature: ∀G f (·) : σ j = f (ξ (G)) Size-invariance  ... 
doi:10.1145/3219819.3219991 dblp:conf/kdd/TsitsulinMKBM18 fatcat:jf2ownxrrfcu3fppip3kbks7c4

Renormalizability Properties of Supergravity

S. Deser, J. H. Kay, K. S. Stelle
1977 Physical Review Letters  
It also established the basic pattern for the corresponding 4-point finite corrections in string theory effective actions. We thank J Franklin for producing this arXiv version.  ...  Abstract The possible local counterterms in supergravity are investigated to all loop orders.  ...  For supergravity itself, it is excluded because the components [e.g., the Einstein pseudotensor or T µν (ψ)] lack local Lorentz and Abelian invariance, but it is permitted for the (1, 1/2) system.  ... 
doi:10.1103/physrevlett.38.527 fatcat:rczblvcpenb6lbuwmayu2lfmoe

Numerically stable formulations of convective terms for turbulent compressible flows

G. Coppola, F. Capuano, S. Pirozzoli, L. de Luca
2019 Journal of Computational Physics  
Local conservation of primary invariants, which is a fundamental property to build high-fidelity shock-capturing methods, is also discussed in the paper.  ...  Furthermore, the conservation properties yielded by different choices for the energy equation (i.e. total and internal energy, entropy) are analyzed thoroughly.  ...  In what follows, when a discretization reproduces the property that nonlinear terms do not contribute to the generalized global energy balance, we will term it a globally energy-preserving discretization  ... 
doi:10.1016/ fatcat:mwpl6fergfadvd5jpg2dx4esai

Weyl cohomology and the effective action for conformal anomalies

Pawel O. Mazur, Emil Mottola
2001 Physical Review D, Particles and fields  
The non-local action so obtained is unique up to the addition of trivial cocycles and Weyl invariant terms, both of which are insensitive to global Weyl rescalings.  ...  In the physical dimension the non-trivial cocycles generate covariant non-local action functionals characterized by sensitivity to global Weyl rescalings.  ...  Antoniadis in particular for his hospitality and for stimulating conversations at the outset of this work. The research of P. O.  ... 
doi:10.1103/physrevd.64.104022 fatcat:bhsmp3heifemlkvlmfrjblmlt4

Area Preserving Diffeomorphisms and 2-d Gravity [article]

HoSeong La
1995 arXiv   pre-print
The h-decomposition makes the conformal factor of a metric SDiffM-invariant and the rest of the metric invariant under conformal diffeomorphisms, whilst the g-decomposition makes the conformal factor a  ...  We find two classes of decompositions of a Riemannian metric, namely, h- and g-decomposition, that help to formulate a gravitational theory which is area preserving diffeomorphism (SDiffM-) invariant but  ...  Nelson for communications, R. Jackiw and B. Zwiebach for reading the manuscript.  ... 
arXiv:hep-th/9510147v1 fatcat:tb7sbtd2ofhwpjralnkkixhcze

Gradient-Like Observers for Invariant Dynamics on a Lie Group

C. Lageman, J. Trumpf, R. Mahony
2010 IEEE Transactions on Automatic Control  
We propose a design methodology for the innovation term based on gradient-like terms derived from invariant or non-invariant cost functions.  ...  The resulting nonlinear observers have strong (almost) global convergence properties and examples are used to demonstrate the relevance of the proposed approach.  ...  Furthermore, if Y → f (Y, e) is a Morse-Bott function such that e is the only local minimum and a global minimum, then Y →f (Y, e) has the same properties.  ... 
doi:10.1109/tac.2009.2034937 fatcat:vxtibs5w65fhpng3vh3pzw6i5a

Page 205 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 66, Issue 4 [page]

1960 American Mathematical Society. Bulletin of the American Mathematical Society  
It is the purpose of the present discussion to focus attention on properties which in general lie between the global and local, and which might therefore be termed medial.‘ For example, the property of  ...  These aspects would today be termed global and local, and those whose interests lay mainly in global properties of a space or configuration formed one school, while those whose chief interest lay in local  ... 

Invariants and nonlinear fields in Spinor Gravity [article]

2004 arXiv   pre-print
The vielbein and metric arise as composite objects. Due to the lack of local Lorentz-symmetry new invariants in the effective gravitational action lead to a modification of Einstein's equations.  ...  The effective gravitational field equations arise as solutions to the lowest order Schwinger-Dyson equation for spinor gravity.  ...  In terms ofQ (18) We can combine these transformation properties in order to find the change of global Lorentz invariants under local Lorentz transformations.  ... 
arXiv:gr-qc/0410132v1 fatcat:kvnkgorl7rcrtj65g4qjeuazxu

Lattice spinor gravity

C. Wetterich
2011 Physics Letters B  
The lattice construction can be employed for formulating models with local gauge symmetries purely in terms of fermions  ...  The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric arises as a composite field.  ...  For a formulation of a lattice gauge theory purely in terms of fermions the local Lorentz symmetry is not necessary -it is sufficient that the lattice action exhibits global Lorentz symmetry.  ... 
doi:10.1016/j.physletb.2011.09.059 fatcat:kfpmbl4xabc47gj2nr3vg2v7qu

Gauge-invariant matter field actions from iterative Nöther coupling [article]

Aniket Basu, Parthasarathi Majumdar, Indrajit Mitra
2018 arXiv   pre-print
This procedure is shown to yield precisely the same locally gauge invariant theory (with the non-Abelian group as the gauge group) as obtained by the usual minimal coupling prescription originating from  ...  Deser's work on pure SU(2) gauge theory, we consider scalar, spinor and vector matter fields transforming under arbitrary representations of a non-Abelian, compact, semisimple internal Lie group which is a global  ...  This term compensates for the difference in gauge transformation property of the field at two different (neighbouring) points.  ... 
arXiv:1711.05608v3 fatcat:3pu2ctf3njf3jcb77kfzddt5fu
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