Complexity vs. Vorticity

In the study of “holographic complexity”, upper bounds on the rate of growth of the (specific) complexity of field theories with holographic duals have attracted much attention. Underlying these upper bounds there are inequalities relating the parameters of the dual black hole. We derive such an inequality in the case of the five-dimensional AdS-Kerr black hole, dual to a four-dimensional field theory with a non-zero angular momentum density. We propose to test these underlying inequalities “experimentally”, by using the conjectured analogy of the field theory with phenomenological models of the Quark-Gluon Plasma. The test consists of comparing data for the parameters of the QGP with the upper bound on the relevant combination of black hole parameters. The bound in the non-rotating case passes the test: in this sense, it is confirmed “experimentally”. In the rotating case, the inequality makes predictions regarding the entropy density of the vortical plasma, recently observed by the STAR collaboration.