Abstract
Two-dimensional conformal field theories with just Virasoro symmetry are endowed with integrable structure. We review how to construct the integrable charges in a two-dimensional conformal field theory and how to relate them to the charges of quantum Sinh-Gordon theory when c>25. We then explicitly calculate the single charge characters in the large c limit for all charges and thereby reveal how their degeneracies grow within one module. This, in particular, allows us to approximate the characters in the limit of small chemical potential, which source the respective charges. The latter give us insights into possible transformation properties of the characters. We also comment on the full generalized Gibbs ensemble and approximations to pure states.
Highlights
At the heart of th solvability of two-dimensional (2D) conformal field theories (CFTs) lies the infinite dimensional Virasoro algebra
The full generalized Gibbs ensemble is obtained by taking the sum over all generalized Gibbs ensembles (GGE) characters that appear in the CFT
With this note we have shed some light on the implications that follow from the integrable structure of 2D CFT
Summary
At the heart of th solvability of two-dimensional (2D) conformal field theories (CFTs) lies the infinite dimensional Virasoro algebra. The question arising here is whether generic pure states in integrable systems might be approximated by GGE states, rather than thermal states, when waiting long enough This implies that generic energy eigenstates would always look like states in equilibrium with respect to all the conserved charges of the system. In both cases it shows qualitatively the same behavior This matches the well-known results of thermal states and might indicate that there is some transformation that relates high and low chemical potentials. In the appendixes we give specific formulas to compute the classical and quantum KdV charges, give some explicit checks on the large c eigenvalues of the second KdV charge, and compute the global character of the second charge which appears as a factor of the GGE characters in a primary module
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