Abstract
Starting from the lattice A3 realization of the Ising model defined on a strip with integrable boundary conditions, theexact spectrum (including excited states) of all the local integrals of motion is derivedin the continuum limit by means of thermodynamic Bethe ansatz techniques.It is also possible to follow the massive flow of this spectrum between the UVc = 1/2 conformal fixed point and the massive IR theory. The UV expression of the eigenstates ofsuch integrals of motion in terms of Virasoro modes is found to have only rationalcoefficients and their fermionic representation turns out to be simply related to thequantum numbers describing the spectrum.
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