Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.
Conformal quantum mechanics as the CFT$_1$ dual to AdS$_2$
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abstract
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.
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A thermal representation for conformal ladder integrals
Conformal ladder integrals are represented via thermal free energies of massive scalars, obey a second-order differential equation in even dimensions at any loop order, and admit an all-loop resummation for arbitrary D.