Conformal quantum mechanics as the CFT1 dual to AdS2

Chamon, Claudio; Jackiw, R.; Pi, So‐Young; Santos, Luiz

doi:10.1016/j.physletb.2011.06.023

Cited by 109 publications

(135 citation statements)

References 10 publications

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“…The spectrum of the Hamiltonian (9) was found by de Alfaro, Fubini and Furlan [34]. It is worth to mention that the conformal quantum mechanics appears in different contexts, from black-holes to atomic physics [35,36,37] and has been proposed as the CF T 1 dual to AdS 2 [38,39]. We will show that this Hamiltonian appears in diffusion phenomena too.…”

Section: Conformal Quantum Mechanicssupporting

confidence: 53%

A relation between massive scalar field inAdS_d+1and diffusion in channels

Romero

Gaona

2014

J. Phys.: Conf. Ser.

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Abstract. It is shown that, when the diffusion coefficient is a constant and is taken a particular family of channels, the Fick-Jacobs equation is invariant under conformal symmetry. In addition, using the diffusion coefficient and the geometric parameters of the channels, a representation for the conformal algebra is obtained. Furthermore, it is found that for these systems the Fick-Jacobs equation is equivalent to the Schrödinger equation for the 1-dimensional conformal quantum mechanics. Moreover, using this equivalence, it is found a relation between a massive scalar field equation in AdS d+1 background and Fick-Jacobs equation, where the geometric parameter of the channels and the geometric parameters of AdS d+1 are identified.

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Section: Conformal Quantum Mechanicssupporting

confidence: 53%

A relation between massive scalar field inAdS_d+1and diffusion in channels

Romero

Gaona

2014

J. Phys.: Conf. Ser.

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“…For example, although the vector fields (86) obey a standard Diff S 1 algebra, the corresponding surface deformation algebra (83) contains three-derivative terms, so the separation of "central" and "boundary" terms in (84) depends on details of the choice of B[ξ] (see, for instance, [77]). The integral over time, on the other hand, is more mysterious, although a similar time averaging has recently been suggested for the AdS 2 /CFT 1 correspondence in a rather different context [78].…”

Section: Two-dimensional Dilaton Gravitymentioning

confidence: 71%

Effective Conformal Descriptions of Black Hole Entropy

Carlip

2011

Entropy

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It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though, is the universality of these thermodynamic properties: their exceptionally simple and general form, and the fact that they can be derived from many very different descriptions of the underlying microscopic degrees of freedom. I review the proposal that this universality arises from an approximate conformal symmetry, which permits an effective "conformal dual" description that is largely independent of the microscopic details.

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“…For superconformal actions with oscillator potentials see [15,16,1]. (Super)conformal mechanics is currently a very active area of research; among the motivations for this interest one can mention the AdS 2 /CF T 1 correspondence [17,18], or the possibility to apply it to test particles moving in the proximity of the horizon of certain black holes, see [12]. N = 4 superconformal models based on the exceptional (see [19]) Lie superalgebra D(2, 1; α) were investigated in [20]- [26].…”

Section: Introductionmentioning

confidence: 99%

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(
Cunha¹,
Holanda²,
Toppan³
2017
Phys. Rev. D
16
2
10
0
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In this paper we quantize superconformal σ-models defined by worldline supermultiplets. Two types of superconformal mechanics, with and without a DFF term, are considered. Without a DFF term (Calogero potential only) the supersymmetry is unbroken. The models with a DFF term correspond to deformed (if the Calogero potential is present) or undeformed oscillators. For these (un)deformed oscillators the classical invariant superconformal algebra acts as a spectrum-generating algebra of the quantum theory.Besides the osp(1|2) examples, we explicitly quantize the superconformally-invariant worldine σ-models defined by the N = 4 (1, 4, 3) supermultiplet (with D(2, 1; α) invariance, for α = 0, −1) and by the N = 2 (2, 2, 0) supermultiplet (with two-dimensional target and sl(2|1) invariance). The parameter α is the scaling dimension of the (1, 4, 3) supermultiplet and, in the DFF case, has a direct interpretation as a vacuum energy. In the DFF case, for the sl(2|1) models, the scaling dimension λ is quantized (either λ = 1 2 + Z or λ = Z). The ordinary two-dimensional oscillator is recovered, after imposing a superselection restriction, from the λ = − 1 2 model. In particular a single bosonic vacuum is selected. The spectrum of the unrestricted two-dimensional theory is decomposed into an infinite set of lowest weight representations of sl(2|1). Extra fermionic raising operators, not belonging to the original sl(2|1) superalgebra, allow (for λ = 1 2 + Z) to construct the whole spectrum from the two degenerate (one bosonic and one fermionic) vacua.

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Conformal quantum mechanics as the CFT1 dual to AdS2

Cited by 109 publications

References 10 publications

A relation between massive scalar field inAdS_d+1and diffusion in channels

A relation between massive scalar field inAdS_d+1and diffusion in channels

Effective Conformal Descriptions of Black Hole Entropy

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(
Cunha¹,
Holanda²,
Toppan³
2017
Phys. Rev. D
16
2
10
0
View full text Add to dashboard Cite

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Conformal quantum mechanics as the CFT1 dual to AdS2

Cited by 109 publications

References 10 publications

A relation between massive scalar field inAdSd+1and diffusion in channels

A relation between massive scalar field inAdSd+1and diffusion in channels

Effective Conformal Descriptions of Black Hole Entropy

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(Cunha1, Holanda2, Toppan3 2017Phys. Rev. D162100View full textAdd to dashboardCite

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A relation between massive scalar field inAdS_d+1and diffusion in channels

A relation between massive scalar field inAdS_d+1and diffusion in channels

From worldline to quantum superconformal mechanics with and without oscillatorial terms: D(2,1;α) and sl(
Cunha¹,
Holanda²,
Toppan³
2017
Phys. Rev. D
16
2
10
0
View full text Add to dashboard Cite