New potentials for conformal mechanics

G. Papadopoulos

doi:10.1088/0264-9381/30/7/075018

New potentials for conformal mechanics

G. Papadopoulos^*

^*Corresponding author for this work

Stanford University

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

We find under some mild assumptions that the most general potential of one-dimensional conformal systems with time-independent couplings is expressed as V = V0 + V1, where V0 is a homogeneous function with respect to a homothetic motion in configuration space and V 1 is determined from an equation with source a homothetic potential. Such systems admit at most an conformal symmetry which, depending on the couplings, is embedded in in three different ways. In one case, is also embedded in Diff(S1). Examples of such models include those with potential V = αx2 + βx-2 for arbitrary couplings α and β, the Calogero models with harmonic oscillator couplings and nonlinear models with suitable metrics and potentials. In addition, we give the conditions on the couplings for a class of gauge theories to admit a conformal symmetry. We present examples of such systems with general gauge groups and global symmetries that include the isometries of AdS2 × S 3 and AdS2 × S3 × S3 which arise as backgrounds in AdS2/CFT1.

Original language	English
Article number	075018
Number of pages	13
Journal	Classical and Quantum Gravity
Volume	30
Issue number	7
DOIs	https://doi.org/10.1088/0264-9381/30/7/075018
Publication status	Published - 7 Apr 2013

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abstract = "We find under some mild assumptions that the most general potential of one-dimensional conformal systems with time-independent couplings is expressed as V = V0 + V1, where V0 is a homogeneous function with respect to a homothetic motion in configuration space and V 1 is determined from an equation with source a homothetic potential. Such systems admit at most an conformal symmetry which, depending on the couplings, is embedded in in three different ways. In one case, is also embedded in Diff(S1). Examples of such models include those with potential V = αx2 + βx-2 for arbitrary couplings α and β, the Calogero models with harmonic oscillator couplings and nonlinear models with suitable metrics and potentials. In addition, we give the conditions on the couplings for a class of gauge theories to admit a conformal symmetry. We present examples of such systems with general gauge groups and global symmetries that include the isometries of AdS2 × S 3 and AdS2 × S3 × S3 which arise as backgrounds in AdS2/CFT1. ",

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N2 - We find under some mild assumptions that the most general potential of one-dimensional conformal systems with time-independent couplings is expressed as V = V0 + V1, where V0 is a homogeneous function with respect to a homothetic motion in configuration space and V 1 is determined from an equation with source a homothetic potential. Such systems admit at most an conformal symmetry which, depending on the couplings, is embedded in in three different ways. In one case, is also embedded in Diff(S1). Examples of such models include those with potential V = αx2 + βx-2 for arbitrary couplings α and β, the Calogero models with harmonic oscillator couplings and nonlinear models with suitable metrics and potentials. In addition, we give the conditions on the couplings for a class of gauge theories to admit a conformal symmetry. We present examples of such systems with general gauge groups and global symmetries that include the isometries of AdS2 × S 3 and AdS2 × S3 × S3 which arise as backgrounds in AdS2/CFT1.

AB - We find under some mild assumptions that the most general potential of one-dimensional conformal systems with time-independent couplings is expressed as V = V0 + V1, where V0 is a homogeneous function with respect to a homothetic motion in configuration space and V 1 is determined from an equation with source a homothetic potential. Such systems admit at most an conformal symmetry which, depending on the couplings, is embedded in in three different ways. In one case, is also embedded in Diff(S1). Examples of such models include those with potential V = αx2 + βx-2 for arbitrary couplings α and β, the Calogero models with harmonic oscillator couplings and nonlinear models with suitable metrics and potentials. In addition, we give the conditions on the couplings for a class of gauge theories to admit a conformal symmetry. We present examples of such systems with general gauge groups and global symmetries that include the isometries of AdS2 × S 3 and AdS2 × S3 × S3 which arise as backgrounds in AdS2/CFT1.

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New potentials for conformal mechanics

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