Symmetry Resolution at High Energy

The density of states of a unitary conformal field theory is known to have a universal behavior at high energy. In two dimensions, this behavior is described by the Cardy formula. If the theory has symmetry, it is interesting to understand the symmetry resolution, namely the decomposition of its Hilbert space into irreducible representations of the symmetry. In this talk, I will present universal formulas for the symmetry resolution with respect to both internal global symmetry and spacetime symmetry. I will also discuss the entanglement entropy, the entanglement spectra, and the high energy properties of the three-point functions. The formulas are derived by using thermal effective field theory and are applicable to any unitary conformal field theory in arbitrary spacetime dimensions. 



Caltech & Kavli IPMU