Talks

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs). In large N CFTs with a large gap to single-trace higher spin operators, we show that the coupling of two stress tensors to other single-trace operators ("TTO") is suppressed by powers of the higher spin gap, dual to the mass scale of higher spin particles in AdS. The absence of light higher spin particles is thus a necessary condition for the existence of a consistent truncation to general relativity in AdS. We are led to propose that, in general, the inverse gap scale is the CFT "dual" of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on TTO-type couplings valid in any CFT.

If a black hole horizon has its microscopic structure as is conjectured by the candidates of quantum gravity, the dispersion relation of gravitational waves (GWs) near the horizon may be drastically modified since its wavelength can be comparable to the size of the microscopic structure because of its infinite gravitational blue-shift near the horizon.  We investigate ringdown-GWs from a perturbed black hole with such a modified dispersion relation and found that the change of modified dispersion relation near the horizon would lead to the partial reflection of infalling GWs at the horizon and echo-signals may appear in the late-time of ringdown-GWs. This implies that the echoes can be a supporting evidence of the existence of microscopic degrees of freedom on black hole horizons.