W. Li: Holography and Regge Phases with U(1) Charge

We use holography to study the large spin J limit of the spectrum of low energy state. We study in detail the holographic description of such states at Q > 2, by considering the contribution to the energies of Q scalar particles coming from single photon and graviton exchange in the bulk of AdS; in some cases, scalar exchange and bulk contact terms are also included. For a range of finite values of Q and J, we numerically diagonalize the Hamiltonian for such states and examine the resulting spectrum and wavefunctions as a function of the dimension ∆ of the charge-one operator and the central charges, finding multiple regions in parameter space with qualitatively different behavior. We discuss the extension of these results to the regime of parametrically large charge Q, as well as to what extent such results are expected to hold universally, beyond the limit of holographic CFTs. We compare our holographic computations to results from the conformal bootstrap for the 3d O(2) model at Q = 3 and Q = 4 and find excellent agreement.