Conformal mechanics inspired by extremal black holes in d = 4

Galajinsky, Anton; Nersessian, Armen

doi:10.1007/jhep11(2011)135

Cited by 25 publications

(28 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [18] the construction was done using action-angle variables. Thus, as a by-product of the present studies we present explicit expressions for these variables.…”

Section: Introductionmentioning

confidence: 99%

Action-Angle Variables for the Particle Near Extreme Kerr Throat

2012

Self Cite

View full text Add to dashboard Cite

We construct the action-angle variables for the spherical part of conformal mechanics describing the motion of a particle near extreme Kerr throat. We indicate the existence of the critical point |pϕ| = mcR Sch (with m being the mass of the particle, c denoting the speed of light, R Sch = 2γM/c 2 being the Schwarzschild radius of a black hole with mass M , and γ denoting the gravitational constant), where these variables are expressed in terms of elementary functions. Away from this point the action-angle variables are defined by elliptic integrals. The proposed formulation allows one to easily reconstruct the whole dynamics of the particle both in initial coordinates, as well as in the so-called conformal basis, where the Hamiltonian takes the form of conventional non-relativistic conformal mechanics. The related issues, such as semiclassical quantization and supersymmetrization are also discussed.

show abstract

“…In [18] the construction was done using action-angle variables. Thus, as a by-product of the present studies we present explicit expressions for these variables.…”

Section: Introductionmentioning

confidence: 99%

Action-Angle Variables for the Particle Near Extreme Kerr Throat

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…Their explicit form depends on the details of a black hole under consideration [9]- [13]. A comparison with (20) gives…”

Section: Spherical Mechanicsmentioning

confidence: 99%

“…In order to split them, we perform a canonical transformation (r, p r , ϕ a , p a ) → (R, p R , ϕ a , p a ), which is defined by (18) and by the following transformation of the remaining variables (for related earlier studies see [5,9,13])…”

Section: Spherical Mechanicsmentioning

confidence: 99%

“…In contrast with the canonical transformation suggested in [13], the one above does not appeal to a formulation in terms of action-angle variables.…”

Section: Spherical Mechanicsmentioning

confidence: 99%

“…Because Killing vectors are linked to first integrals of the geodesic equations, a massive relativistic particle propagating on such a background inherits the conformal invariance and belongs to the class of conformal mechanics models. A salient feature of this system is that, by applying a suitable canonical transformation, the radial canonical pair can be separated from angular variables and the model can be put in the conventional conformal mechanics form [5,9,13]. At the off-shell Lagrangian level the radial motion of the particle was related to d = 1 conformal mechanics in an earlier paper [7].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension

Galajinsky

Nersessian

Saghatelian

2013

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We provide a systematic account of integrability of the spherical mechanics associated with the near horizon extremal Myers-Perry black hole in arbitrary dimension for the special case that all rotation parameters are equal. The integrability is established both in the original coordinates and in action-angle variables. It is demonstrated that the spherical mechanics associated with the black hole in d = 2n + 1 is maximally superintegrable, while its counterpart related to the black hole in d = 2n lacks for only one integral of motion to be maximally superintegrable.

show abstract

N =4 superconformal mechanics from the su(2) perspective

Galajinsky

2015

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

The issue of constructing an N = 4 superconformal mechanics in one dimension is reconsidered with a special emphasis put on the realizations of the su(2)-subalgebra in the full su(1, 1|2)-superalgebra. New dynamical realizations of su(1, 1|2) are constructed which describe an interaction of the (0, 4, 4)-supermultiplet with either the (1, 4, 3)-, or (3, 4, 1)-, or (4, 4, 0)-supermultiplet. A relation of the N = 4 superconformal mechanics with massive superparticles propagating near the black hole horizons is discussed. Background geometry associated with the model based on the (4, 4, 0)supermultiplet is identified with the near horizon limit of the d = 5, N = 2 supergravity interacting with one vector multiplet.

show abstract

Conformal mechanics inspired by extremal black holes in d = 4

Cited by 25 publications

References 32 publications

Action-Angle Variables for the Particle Near Extreme Kerr Throat

Action-Angle Variables for the Particle Near Extreme Kerr Throat

Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension

N =4 superconformal mechanics from the su(2) perspective

Contact Info

Product

Resources

About