Conformal quantum mechanics and holography in noncommutative space-time
arXiv:1704.03666 · doi:10.1016/j.physletb.2017.07.045
Abstract
We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the -deformed space-time as a prototype. Upto the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.
8 pages, typos corrected. To appear in PLB
References in corpus (28)
- Comments on the Sachdev-Ye-Kitaev model
- The quantum structure of spacetime at the Planck scale and quantum fields
- Electron-Electron Interactions in Graphene: Current Status and Perspectives
- Kappa-Minkowski space-time and the star product realizations
- New realizations of Lie algebra kappa-deformed Euclidean space
- Near-Horizon Conformal Structure of Black Holes
- Twisted Statistics in kappa-Minkowski Spacetime
- Conformal quantum mechanics as the CFT dual to AdS
- Quantum Anomaly in Molecular Physics
- Anomaly in conformal quantum mechanics: From molecular physics to black holes
- Further Evidence for the Conformal Structure of a Schwarzschild Black Hole in an Algebraic Approach
- Quantum Gravity in 2+1 Dimensions
- Constraints on the quantum gravity scale from kappa - Minkowski spacetime
- Inequivalent Quantizations of the Rational Calogero Model
- Noncommutative BTZ Black Hole and Discrete Time
- Novel Quantum States of the Rational Calogero Models Without the Confining Interaction
- Symmetries of quantum space-time in 3 dimensions
- Electron Capture and Scaling Anomaly in Polar Molecules
- Effects of Noncommutativity on the Black Hole Entropy
- On the Real Spectra of Calogero Model with Complex Coupling
- Bound States in Graphene
- Quantum Fields with Noncommutative Target Spaces
- Bound States in Gapped Graphene with Impurities : Effective Low-Energy Description of Short-Range Interactions
- Quantum statistics and noncommutative black holes
- -Minkowski star product in any dimension from symplectic realization
- AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation
- A Dirac type xp-Model and the Riemann Zeros
- Inequivalent quantization of the rational Calogero model with a Coulomb type interaction