Search

We consider an effective theory of massive scalar fields on a fixed AdS$_{d+1}$ background with a cubic extremal interaction among them. A bulk coupling is called extremal whenever the corresponding conformal dimension of any of the dual CFT$_d$ operators matches the sum of all the others. For cubic bulk couplings, this is $\Delta_i+\Delta_j=\Delta_k$. These bulk interactions are often disregarded in the literature since they do not appear in traditional models of AdS/CFT. Turning them on yields a divergent vertex in the dual CFT, and here we show that these divergences can be regulated. Once renormalized, we demonstrate that this coupling introduces non-trivial mixing between single- and double-trace operators, and we compute the anomalous dimensions of the corrected operators to leading order in perturbation theory., Comment: 20 pages + appendices, improved discussion in Sec. 4.2 and refs added in v2

We show how to incorporate massive spinning fields into the Euclidean path integral of three-dimensional quantum gravity via its Chern-Simons formulation. The coupling of the spinning fields to gravity is captured by a Wilson spool, a collection of Wilson loops winding around closed paths of the geometry, and generalizes the proposal of [1,2]. We present a robust derivation of the Wilson spool by providing a new group-theoretic perspective of the quasinormal mode method for one-loop determinants. We test our proposal on Euclidean BTZ and $S^3$ backgrounds. We also evaluate explicitly the quantum corrections to the path integral on $S^3$, and report on how $G_N$ and the mass are renormalized to leading order in perturbation theory., Comment: 28 pages + appendices, 3 figures

We quantify how constraints on light states affect the asymptotic growth of heavy states in weak Jacobi forms. The constraints we consider are sparseness conditions on the Fourier coefficients of these forms, which are necessary to interpret them as gravitational path integrals. Using crossing kernels, we extract the leading and subleading behavior of these coefficients and show that the leading Cardy-like growth is robust in a wide regime of validity. On the other hand, we find that subleading corrections are sensitive to the constraints placed on the light states, and we quantify their imprint on the asymptotic growth of states. Our approach is tested against the generating function of symmetric product orbifolds, where we provide new insights into the factors contributing to the asymptotic growth of their Fourier coefficients. Finally, we use our methods to revisit the UV/IR connection that relates black hole microstate counting to modular forms. We provide a microscopic interpretation of the logarithmic corrections to the entropy of BPS black holes in N = 2, 4 ungauged supergravity in four and five dimensions, and tie it to consistency conditions in AdS$_3$/CFT$_2$., Comment: 46 pages + appendices, 1 figure; v2: minor edits