Logarithmic correlators in nonrelativistic conformal field theory

Hosseiny, Ali; Rouhani, S.

doi:10.1063/1.3482008

Cited by 18 publications

(22 citation statements)

References 55 publications

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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%

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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Section: Examplementioning

confidence: 99%

Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

Henkel

2015

Symmetry

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“…Replacing in the generators (4) the scaling dimension x by a 2 × 2 Jordan matrix, the Schrödinger Ward identities (or co-variance conditions) can be written down for the three two-point functions (12). The result is, in d ≥ 1 dimensions [28]…”

Section: Schrödinger Algebramentioning

confidence: 99%

Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

Henkel

Stoimenov

2014

Springer Proceedings in Mathematics &Amp; Statistics

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Indecomposable but reducible representations of several Lie algebras of local scale-transformations, including the Schrödinger and conformal Galilean algebras, and their applications in physical ageing are reviewed. The physical requirement of the decay of co-variant two-point functions for large distances is related to analyticity properties in the coordinates dual to the physical masses or rapidities.

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“…The best-known special cases of such symmetry algebras are the Schrödinger algebra and the conformal Galilei algebra (CGA), both to be defined below. The natural question arises as to whether logarithmic correlators may be found for such NRCFTs [19][20][21], for a recent review see [22]. The answer is affirmative.…”

Section: Introductionmentioning

confidence: 99%

“…In 1 + 1 dimensions, CGA is even more special since it has an infinite-dimensional extension (which is called 'full CGA/altern-Virasoro algebra' in the literature, contains a Virasoro sub-algebra and admits two independent central charges [38]) which in turn can be obtained fully from contraction [39,40]. This infinite-dimensional extension of the CGA is almost solvable [41], a property which helps to investigate logarithmic representations and holographic realisation easily [19,20].…”

Section: Introductionmentioning

confidence: 99%

Logarithmic exotic conformal Galilean algebras

Henkel¹,

Hosseiny²,

Rouhani³

2014

Nuclear Physics B

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International audienceLogarithmic representations of the conformal Galilean algebra (CGA) and the Exotic Conformal Galilean algebra (EcGA) are constructed. This can be achieved by non-decomposable representations of the scaling dimensions or the rapidity indices, specific to conformal Galilean algebras. Logarithmic representations of the non-exotic CGA lead to the expected constraints on scaling dimensions and rapidities and also on the logarithmic contributions in the co-variant two-point functions. On the other hand, the ECG A admits several distinct situations which are distinguished by different sets of constraints and distinct scaling forms of the two-point functions. Two distinct realisations for the spatial rotations are identified as well. This is the first concrete example of a reducible, but non-decomposable representation, without logarithmic terms. Such cases had been anticipated before

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Logarithmic correlators in nonrelativistic conformal field theory

Cited by 18 publications

References 55 publications

Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

Logarithmic exotic conformal Galilean algebras

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