Conformal quantum mechanics as the CFT$_1$ dual to AdS$_2$
  A 0+1-dimensional candidate theory for the CFT$_1$ dual to AdS$_2$ is discussed. The quantum mechanical system does not have a ground state that is invariant under the three generators of the conformal group. Nevertheless, we show that there are operators in the theory that are not primary, but whose "non-primary character" conspires with the "non-invariance of the vacuum" to give precisely the correlation functions in a conformally invariant theory. 
C. Chamon, R. Jackiw, S.-Y. Pi, L. Santos
hep-th