ETD

• asymptotics
• conformal field theory
• density of states
• effective field theory
• teorie di campo conformi
• teorie efficaci
• thermal effective action

This thesis studies the asymptotic spectrum of three-dimensional conformal field theories with a global U(1) symmetry. Using a thermal effective action on S1 x S2, with sources for rotation and charge, we derive the coarse-grained density of states at large scaling dimension, spin, and charge. Conformal characters are used to distinguish fixed angular momentum component along a fixed direction from fixed total spin and to remove descendants, yielding an explicit asymptotic density of primary operators. At leading order, the result depends on the thermal free-energy coefficient and the charge susceptibility; charge produces a Gaussian suppression whose form is determined by an inverse Laplace–Fourier transform. We establish the regime in which the high-temperature, small-holonomy, and saddle-point approximations are controlled. A formal continuation towards the spectral edge reproduces the expected large-charge scaling Delta ~ q^3/2 and a small-spin correction J^2/q^3/2, but cannot determine their coefficients reliably because the relevant holonomy is of order one. The framework is tested in free scalar and fermion theories and against Kerr–Newman–AdS thermodynamics through the AdS/CFT correspondence.