1210.1719 (G. Papadopoulos)

New potentials for conformal mechanics    [PDF]

G. Papadopoulos

We show that V=\alpha x^2+\beta x^{-2} arises as a potential of 1-dimensional conformal theories. This class of conformal models includes the DFF model \alpha=0 and the harmonic oscillator \beta=0. The construction is based on a different embedding of the conformal symmetry group into the time re-parameterizations from that of the DFF model and its generalizations. Depending on the range of the couplings $\alpha, \beta$, these models can have a ground state and a well-defined energy spectrum, and exhibit either a $SL(2,\bR)$ or a SO(3) conformal symmetry. The latter group can also be embedded in Diff(S^1). We also present several generalizations of these models which include the Calogero models with harmonic oscillator couplings and non-linear models with suitable metric and potential couplings. In addition, we give the conditions on the couplings for a class of gaugetheories to admit a SL(2,\bR) or SO(3) conformal symmetry. We present examples of such systems with general gauge groups and global symmetries that include the isometries of AdS_2xS^3 and AdS_2x S^3 x S^3 which arise as backgrounds in AdS_2/CFT_1.

View original: http://arxiv.org/abs/1210.1719