New potentials for conformal mechanics

G. Papadopoulos

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

paper

New potentials for conformal mechanics

arXiv:1210.1719 · doi:10.1088/0264-9381/30/7/075018

Abstract

We find under some mild assumptions that the most general potential of 1-dimensional conformal systems with time independent couplings is expressed as $V = V_{0} + V_{1}$ , where $V_{0}$ 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 $SL(2,\bR)$ conformal symmetry which, depending on the couplings, is embedded in Diff(R) $in t h r ee d i f f er e n tw a y s . I n o n ec a se,$ SL(2,\bR) $i s a l soe mb e dd e d in D i f f (S^{1}) . E x am pl eso f s u c hm o d e l s in c l u d e t h ose w i t h p o t e n t ia l$ V=αx^2+βx^{-2} $f or a r bi t r a r y co u pl in g s$ α $an d$ β $, t h e C a l o g er o m o d e l s w i t hha r m o ni cosc i l l a t or co u pl in g s an d n o n - l in e a r m o d e l s w i t h s u i t ab l e m e t r i cs an d p o t e n t ia l s . I na dd i t i o n, w e g i v e t h eco n d i t i o n so n t h eco u pl in g s f or a c l a sso f g a ug e t h eor i es t o a d mi t a$ SL(2,\bR) $co n f or ma l sy mm e t r y . W e p r ese n t e x am pl eso f s u c h sy s t e m s w i t h g e n er a l g a ug e g r o u p s an d g l o ba l sy mm e t r i es t ha t in c l u d e t h e i so m e t r i eso f$ AdS_2 x S^3 $an d$ AdS_2 x S^3 x S^3 $w hi c ha r i se a s ba c k g r o u n d s in$ AdS_2/CFT_1$.

15 pages, significant changes, references added

New potentials for conformal mechanics

Abstract

References in corpus (8)

Cited by in corpus (15)