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Abstract |
Abstract: We show irreversibility of the renormalization group flow in non-
unitary but PT-
invariant quantum field theory in two space-time dimensions. In addition to
unbroken PT-symmetry and a positive energy spectrum, we assume standard
properties of quantum field theory including a local energy-momentum tensor
and relativistic invariance. This generalizes Zamolodchikov's c-theorem to PT-
symmetric hamiltonians. Our proof follows closely Zamolodchikov's arguments.
We show that a function c_eff (s) of the renormalization group parameter s
exists which is non-negative and monotonically decreasing along
renormalization group flows. Its value at a critical point is the "effective
central
charge" entering the specific free energy. At least in rational models, this
equals
c_eff =c-24 Delta, where c is the central charge and Delta is the lowest
primary field dimension in the conformal field theory which describes the
critical point. |
