Conformal Invariance of the Newtonian Weyl Tensor

AbstractIt is well-known that the conformal structure of a relativistic spacetime is of profound physical and conceptual interest. In this note, we consider the analogous structure for Newtonian theories. We show that the Newtonian Weyl tensor is an invariant of this structure.

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SUPERCONFORMAL GEOMETRY FROM THE GRASSMANN AND HARMONIC ANALYTICITIES II: THE N=4 SU(2) CONFORMAL CASE

International Journal of Modern Physics A ◽

10.1142/s0217751x91001544 ◽

1991 ◽

Vol 06 (18) ◽

pp. 3175-3200 ◽

Cited By ~ 9

Author(s):

E.H. SAIDI ◽

M. ZAKKARI

Keyword(s):

Conformal Invariance ◽

Conformal Structure ◽

Harmonic Superspace

N=4 SU(2) conformal invariance is studied in the harmonic superspace. It is shown that the N=4 SU(2) conformal structure is equivalent to the harmonic analyticity. The solutions to the superconformal constraints are worked out in detail and the conformal properties of all objects of interest are given. A realization of the N=4 current in terms of the free (F.S.) hypermultiplet is obtained.

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Effective String Description of the Confining Flux Tube at Finite Temperature

Universe ◽

10.3390/universe7060170 ◽

2021 ◽

Vol 7 (6) ◽

pp. 170

Author(s):

Michele Caselle

Keyword(s):

Flux Tube ◽

Dimensional Reduction ◽

Conformal Invariance ◽

Finite Temperature ◽

Gauge Theories ◽

Linear Increase ◽

General Introduction ◽

Interquark Potential ◽

Effective String Theory ◽

Good Agreement

In this review, after a general introduction to the effective string theory (EST) description of confinement in pure gauge theories, we discuss the behaviour of EST as the temperature is increased. We show that, as the deconfinement point is approached from below, several universal features of confining gauge theories, like the ratio Tc/σ0, the linear increase of the squared width of the flux tube with the interquark distance, or the temperature dependence of the interquark potential, can be accurately predicted by the effective string. Moreover, in the vicinity of the deconfinement point the EST behaviour turns out to be in good agreement with what was predicted by conformal invariance or by dimensional reduction, thus further supporting the validity of an EST approach to confinement.

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Integrability and conformal invariance

Nuclear Physics B - Proceedings Supplements ◽

10.1016/0920-5632(91)90117-w ◽

1991 ◽

Vol 18 (2) ◽

pp. 10-15

Author(s):

O. Babelon ◽

L. Bonora

Keyword(s):

Conformal Invariance

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Two-dimensional fractal geometry, critical phenomena and conformal invariance

Physics Reports ◽

10.1016/0370-1573(89)90042-2 ◽

1989 ◽

Vol 184 (2-4) ◽

pp. 229-257 ◽

Cited By ~ 29

Author(s):

Bertrand Duplantier

Keyword(s):

Critical Phenomena ◽

Conformal Invariance ◽

Fractal Geometry ◽

Two Dimensional

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SURPRISING TRACE ANOMALY FROM FREAKOLOGRAPHY

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194513009410 ◽

2013 ◽

Vol 21 ◽

pp. 63-76 ◽

Cited By ~ 1

Author(s):

YU NAKAYAMA

Keyword(s):

Weyl Tensor ◽

Ricci Scalar ◽

Field Theories ◽

Conformal Field Theories ◽

Conformal Field ◽

Trace Anomaly

I will discuss how an unexpected form of trace anomaly can be obtained from holographic models with no simple string interpretation. In addition to the usual trace anomaly, Euler density and Weyl tensor squared, we pursue the possibility that it is given by Ricci scalar and Hirzebruch-Pontryagin density. It has a deep connection with scale but non-conformal field theories and their holographic dual. I would like to urge you to judge whether such holographic theories are consistent or pathological.

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Conformal invariance and Bjorken scaling

Physics Letters B ◽

10.1016/0370-2693(72)90454-6 ◽

1972 ◽

Vol 41 (2) ◽

pp. 169-172 ◽

Cited By ~ 1

Author(s):

E. Etim

Keyword(s):

Conformal Invariance ◽

Bjorken Scaling

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Regularity of the m-symphonic map

SN Partial Differential Equations and Applications ◽

10.1007/s42985-021-00074-y ◽

2021 ◽

Vol 2 (2) ◽

Author(s):

Masashi Misawa ◽

Nobumitsu Nakauchi

Keyword(s):

Critical Points ◽

Conformal Invariance ◽

Hölder Continuity ◽

Energy Functional ◽

Higher Dimension ◽

Holder Continuity ◽

New Energy ◽

Symphonic Map

AbstractWe introduce a new energy functional of conformal invariance and consider its critical points, named the m-symphonic map. We study a Hölder continuity of m-symphonic maps from domains of $$\mathbb {R}^m$$ R m into the spheres in the higher dimension $$m \ge 4$$ m ≥ 4 .

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Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816500158 ◽

2016 ◽

Vol 13 (02) ◽

pp. 1650015 ◽

Cited By ~ 9

Author(s):

Carlo Alberto Mantica ◽

Young Jin Suh

Keyword(s):

Symmetric Space ◽

Weyl Tensor ◽

Killing Vector ◽

Complete Classification ◽

Space Time ◽

Conformal Killing ◽

Conformally Flat ◽

Conformal Curvature ◽

Wave Space ◽

Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

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