Explorations in Precision Holography and Higher-derivative Supergravity

This thesis explores topics related to the study of quantum gravity, with a focus on precision holography and higher-derivative supergravity. First, we study subleading corrections to the free energy of a particular 3D N=3 Chern-Simons-matter theory found by Gaiotto and Tomasiello, which is given by a matrix model after supersymmetric localization. This theory is dual to massive IIA supergravity on AdS4, and consequently, the structure of subleading corrections to the field theory naturally elucidates the higher-derivative corrections to the gravity dual. We extract the first order of corrections to the free energy using resolvent methods, and our results imply that particular terms in the supergravity action should vanish on-shell. Next, we consider the unreasonable effectiveness of five-dimensional minimal gauged supergravity. There are three independent supersymmetric four-derivative terms that one can add to the action; nevertheless, after going on-shell (or, equivalently, after a field redefinition that pushes the off-shell discrepancies to six-derivative order), there is a unique supersymmetric invariant. Third, we consider the effect of higher-derivative corrections in holographic renormalization group flows across dimensions. In particular, we construct a local holographic c-function out of metric functions and show its monotonicity via the Null Energy Condition. We also construct a c-function from the entanglement entropy for flows with a CFT2 IR fixed point, and we show that such flows are monotonic. Finally, we consider consistent truncations of four-derivative heterotic supergravity. In particular, we show that reducing both on a torus $T^n$ or on $S^3$ and truncating the vector multiplets is indeed a consistent truncation at the four-derivative level. Moreover, we find examples of two-derivative consistent truncations which fail to extend to four-derivative ones.