Logarithmic exotic conformal Galilean algebras

Henkel, Malte; Hosseiny, Ali; Rouhani, S.

doi:10.1016/j.nuclphysb.2013.12.009

Cited by 10 publications

(16 citation statements)

References 70 publications

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“…In this way we have achieved the tensor density construction of the superalgebra sg ℓ : 15) where ⊕ denotes the direct sum of vector spaces. In order to discuss coadjoint representations, we would like to introduce the algebraic dual of sg ℓ .…”

Section: Tensor Density Module Construction Of Sg ℓ and Regular Dualmentioning

confidence: 99%

“…The same algebra appears in non-relativistic analogue of AdS/CFT correspondence and called infinite dimensional Galilean conformal algebra (GCA) [10,11,12,13,14,15] (see also [16,17,18,19,20,21] for some varieties of the algebra). The same algebra also appears in cosmological topologically massive gravity [22,2] and bosonic string theory [23,24].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Tensor Density Module Construction Of Sg ℓ and Regular Dualmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

Aizawa

Segar

2016

Journal of Mathematical Physics

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“…Analogous representations can also be considered for the Schrödinger and conformal Galilean algebras and their sub-algebras. Then, it becomes necessary to consider simultaneously the scaling dimensions x, ξ and the rapidities γ as matrices [41,42,43,57,37]. From the Lie algebra commutators it can then be shown that these characteristic elements of the scaling operators are simultaneously Jordan [37].…”

Section: Examplementioning

confidence: 99%

“…Then, it becomes necessary to consider simultaneously the scaling dimensions x, ξ and the rapidities γ as matrices [41,42,43,57,37]. From the Lie algebra commutators it can then be shown that these characteristic elements of the scaling operators are simultaneously Jordan [37]. Several applications to non-equilibrium relaxation phenomena have been explored in the literature [34,35,44,22], see [36] for a review.…”

Section: Examplementioning

confidence: 99%

Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

Henkel

2015

Symmetry

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Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal invariance has led to enormous progress in equilibrium phase transitions, especially in two dimensions. Non-equilibrium phase transitions can arise in much larger portions of the parameter space than equilibrium phase transitions. The state of the art of recent attempts to generalise conformal invariance to a new generic symmetry, taking into account the different scaling behaviour of space and time, will be reviewed. Particular attention will be given to the causality properties as they follow for co-variant n-point functions. These are important for the physical identification of n-point functions as responses or correlators.

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“…Such co-variant n-point functions arise for example in several distinct non-relativistic versions of the AdS/CFT correspondence, see e.g. [5,3,4,13,27,11,12,33,6,1,28,14,7,22] and refs. therein.…”

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confidence: 99%

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

Henkel

Stoimenov

2016

J. Phys. A: Math. Theor.

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The covariant two-point functions, derived from Ward identities in direct space, can be affected by consistency problems and can become unbounded for large time-or spaceseparations. This difficulty arises for several extensions of dynamical scaling, for example Schrödinger-invariance, conformal Galilei invariance or meta-conformal invariance, but not for standard ortho-conformal invariance. For meta-conformal invariance in (1 + 1) dimensions, which acts as a dynamical symmetry of a simple advection equation, these difficulties can be cured by going over to a dual space and an extension of these dynamical symmetries through the construction of a new generator in the Cartan sub-algebra. This provides a canonical interpretation of meta-conformally covariant two-point functions as correlators. Galilei-conformal correlators can be obtained from meta-conformal invariance through a simple contraction. In contrast, by an analogus construction, Schrödinger-covariant two-point functions are causal response functions. All these two-point functions are bounded at large separations, for sufficiently positive values of the scaling exponents.

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Logarithmic exotic conformal Galilean algebras

Cited by 10 publications

References 70 publications

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

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

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