Modular discretization of the AdS2/CFT1 holography

Axenides, Minos; Floratos, E.G.; Nicolis, Stam

doi:10.1007/jhep02(2014)109

Cited by 24 publications

(44 citation statements)

References 66 publications

(92 reference statements)

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“…As D is inversely proportional to the resistivity, systems saturating the above bound would display linear resistivity behavior 18 . 17 In systems of units where and k B are not equal to one, the bound on the Lyapunov exponent reads λ L ď 2πk B β . 18 See [110] for a recent successful holographic description of linear resistivity at high-temperature.…”

Section: Chaos and Hydrodynamicsmentioning

confidence: 99%

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Recent Developments in the Holographic Description of Quantum Chaos

Jahnke

2019

Advances in High Energy Physics

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Section: Chaos and Hydrodynamicsmentioning

confidence: 99%

“…Another interesting perspective on the characterization of chaos in the context of (regularized) AdS 2 {CF T 1 is provided by[17][18][19].…”

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confidence: 99%

Recent Developments in the Holographic Description of Quantum Chaos

Jahnke

2019

Advances in High Energy Physics

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“…Putting then for simplicity u = 1, v = 0, w = σ −2 , we reduce (3.14) to the relation 1 2 σH g = J 0 that shows that Hamiltonian (3.7) is the generator of rotations in (2 + 1)-dimensional Minkowski space with coordinates J µ . According to Dirac [60,61], H g and H g provide us with different forms of relativistic dynamics on the upper sheet of two-sheeted hyperboloid in (2 + 1)dimensional Minkowski space, which by means of solutions (3.4) and (3.13) are projected to configuration spaces with coordinates q and y, and are described by evolution parameters t and τ , respectively.…”

Section: Aff Conformal Mechanics Modelmentioning

confidence: 99%

Klein four-group and Darboux duality in conformal mechanics

Inzunza

Plyushchay

2019

Phys. Rev. D

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We study the Klein four-group (K 4 ) symmetry of the time-dependent Schrödinger equation for the conformal mechanics model of de Alfaro-Fubini-Furlan (AFF) with confining harmonic potential and coupling constant g = ν(ν + 1) ≥ −1/4. We show that it undergoes a complete or partial (at half-integer ν) breaking on eigenstates of the system, and is the automorphism of the osp(2, 2) superconformal symmetry in super-extensions of the model by inducing a transformation between the exact and spontaneously broken phases of N = 2 Poincaré supersymmetry. We exploit the K 4 symmetry and its relation with the conformal symmetry to construct the dual Darboux transformations which generate spectrally shifted pairs of the rationally deformed AFF models. Two distinct pairs of intertwining operators originated from Darboux duality allow us to construct complete sets of the spectrum generating ladder operators that identify specific finite-gap structure of a deformed system and generate three distinct related versions of nonlinearly deformed sl(2, R) algebra as its symmetry. We show that at half-integer ν, the Jordan states associated with confluent Darboux transformations enter the construction, and the spectrum of rationally deformed AFF systems undergoes structural changes.constant g = ν(ν + 1) ≥ −1/4 1 . Its non-relativistic conformal symmetry and supersymmetric extensions [5,6,7,8,9,10] find a variety of interesting applications including the particles dynamics in black hole backgrounds [11,12,13,14,15,16], cosmology [17,18,19], non-relativistic AdS/CFT correspondence [20,21,22,23,24], QCD confinement problem [25,26], and physics of Bose-Einstein condensates [27,28].On the other hand, the time-dependent Schrödinger equation for the AFF conformal mechanics model reveals a discrete Klein four-group symmetry generated by transformation of the parameter ν → −ν − 1, and by the spatial Wick rotation x → ix accompanied by the time reflection t → −t. In the picture of the stationary Schrödinger equation the time reflection transforms into the change of the eigenvalue's sign E → −E. The discrete symmetry K 4 , however, turns out to be completely broken at the level of the quantum states when ν is not a half-integer number : application of the group generators to physical eigenstates produces formal eigenstates which do not satisfy the necessary boundary conditions. In the case of half-integer values of the parameter ν the K 4 discrete symmetry breaks partially, and transformation ν → −ν − 1, as we shall see, turns out to be a true symmetry nontrivially realized on the spectrum of the system. In the physics of anyons, where the AFF model is used to generate the transmutation of statistics, halfinteger values of ν correspond to the two-particle system of identical fermions [29,30,31]. In the context of the problem we consider here, even though the new solutions with arbitrary value of ν generated by transformations of the discrete group are not acceptable from the physical point of view, the analogs of such non-physical states in other q...

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“…We confirm that it can be derived in a natural way from the compactification of R n 1,n 1 at infinity by means of the Cayley transform '.w/ D 1Cw 1 w . Such interplay indicates possibly a remarkably beautiful amalgamation between Dirac-Kähler fermions on the lattice and Einstein's theory on the Anti-de Sitter universe yet still to be investigated in depth such as that proposed in [18,19].…”

Section: Introductionmentioning

confidence: 99%

A conformal group approach to the Dirac–Kähler system on the lattice

Faustino

2017

Math Methods in App Sciences

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Abstract. Starting from the representation of the (n − 1) + n−dimensional Lorentz pseudo-sphere on the projective space PR n,n , we propose a method to derive a class of solutions underlying to a Dirac-Kähler type equation on the lattice. We make use of the Cayley transform ϕ(w) = 1 + w 1 − w to show that the resulting group representation arise from the same mathematical framework as the conformal group representation in terms of the general linear group GL (2, Γ(n − 1, n − 1) ∪ {0}). That allows us to describe such class of solutions as a commutative n−ary product, involving the quasi-monomials ϕ (z j ) − x j h (x j ∈ hZ) with membership in the paravector space R ⊕ Re j e n+j .

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Modular discretization of the AdS2/CFT1 holography

Cited by 24 publications

References 66 publications

Recent Developments in the Holographic Description of Quantum Chaos

Recent Developments in the Holographic Description of Quantum Chaos

Klein four-group and Darboux duality in conformal mechanics

A conformal group approach to the Dirac–Kähler system on the lattice

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