# Rotational KMS states and type I conformal nets

August 31, 2016

We consider KMS states on a local conformal net on the unit circle with
respect to rotations. We prove that, if the conformal net is of type I, namely
if it admits only type I DHR representations, then the extremal KMS states are
the Gibbs states in an irreducible representation. Completely rational nets,
the U(1)-current net, the Virasoro nets and their finite tensor products are
shown to be of type I. In the completely rational case, we also give a direct
proof that all factorial KMS states are Gibbs states.

Keywords:

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