Meta-conformal invariance and the boundedness of two-point correlation functions

Henkel, Malte; Stoimenov, Stoimen

doi:10.1088/1751-8113/49/47/47lt01

Cited by 11 publications

(26 citation statements)

References 51 publications

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“…The conformal galilean generator Y 0 = −t∂ r − γ ∈ cga(1) is distinct from the ordinary Galilei generator Y 1/2 = −t∂ r − Mr ∈ sch(1) of the Schrödinger algebra, as these imply distinct transformations of the scaling operators.3 For the Schrödinger group, an analogous construction shows that the two-point functions are response functions[56,60,61,62]. The scaling form (1.15) of the meta-conformal correlator is the same as the special case z = 1 for the conformally co-variant two-time response function G(t, r) [21, eq.…”

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confidence: 99%

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Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions

Henkel¹,

Stoimenov²

2019

J. Stat. Mech.

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Meta-conformal transformations are constructed as sets of time-space transformations which are not angle-preserving but contain time-and space translations, time-space dilatations with dynamical exponent z = 1 and whose Lie algebras contain conformal Lie algebras as sub-algebras. They act as dynamical symmetries of the linear transport equation in d spatial dimensions. For d = 1 spatial dimensions, meta-conformal transformations constitute new representations of the conformal Lie algebras, while for d = 1 their algebraic structure is different. Infinite-dimensional Lie algebras of meta-conformal transformations are explicitly constructed for d = 1 and d = 2 and they are shown to be isomorphic to the direct sum of either two or three centre-less Virasoro algebras, respectively. The form of co-variant two-point correlators is derived. An application to the directed Glauber-Ising chain with spatially long-ranged initial conditions is described.1 In memoriam Vladimir Rittenberg "Whenever you have to do with a structure-endowed entity, try to determine its group of automorphisms. You can expect to gain a deep insight." H. Weyl, Symmetry, Princeton University Press (1952) 1 See [81] and refs. therein for the considerable recent interest into the case r ∈ R d with d > 2.

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“…We did not yet carry out explicitly the full algebraic procedure which should in the t ≫ z,z limit produce the non-diverging behaviour F ∼ t −2δ1 exp −2βγ 1 z+z t , see[62].…”

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confidence: 99%

Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions

Henkel¹,

Stoimenov²

2019

J. Stat. Mech.

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“…6 The names are motivated by the greek prefixes o̺θo: right, standard and µετ α: of secondary rank. 7 Our results on the dynamical symmetries of the dle process, see propositions 3 and 4, require us to present here a more flexible definition than given in [34,35]. Table 2: Comparison of local ortho-conformal, conformal galilean and meta-1 conformal invariance, in (1 + 1)D. The non-vanishing Lie algebra commutators, the defining equation of the generators, the invariant differential operator S and the covariant two-point function is indicated, where applicable.…”

Section: Local Conformal Invariancementioning

confidence: 99%

“…The formulation of the meta-1 conformal Ward identities does require some care, since already the two-point function turns out to be a non-analytic function of the time-and space-coordinates. It can be shown that the covariant two-point correlator is [35]…”

Section: Local Conformal Invariancementioning

confidence: 99%

Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain

Henkel

2016

Symmetry

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Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent z = 1, none of the known variants of conformal invariance can act as its dynamical symmetry. In d = 1 spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.

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“…Readers may refer the recent works [71,72] (and references therein) for a detailed study of two-point functions.…”

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Aspects of infinite dimensional ℓ-super Galilean conformal algebra

Aizawa

Segar

2016

Journal of Mathematical Physics

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In this work we construct a infinite dimensional ℓ-super Galilean conformal algebra, which is a generalization of the ℓ = 1 algebra found in the literature. We give a classification of central extensions, the vector field representation, the coadjoint representation and the operator product expansion of the infinite dimensional ℓ-super Galilean conformal algebra, keeping possible applications in physics and mathematics in mind.

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Meta-conformal invariance and the boundedness of two-point correlation functions

Cited by 11 publications

References 51 publications

Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions

Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions

Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

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