Microscopic quantum interactions between elementary particles control transport in macroscopic states of matter, such as in fluids and plasmas. In numerous states of interest, these microscopic interactions are strong, including in water, among electrons in graphene and in quark-gluon plasma — a state of nuclear matter that filled the early Universe and that is currently being recreated in particle colliders. While macroscopic theories describing the dynamics of such states, in particular, hydrodynamics (of fluids) and magnetohydrodynamics (of magnetized plasmas) have been partially understood, a full description of transport also requires a certain microscopic knowledge of its underlying quantum physics. After more than a century of striking advance in quantum theories, our theoretical understanding of these microscopic processes remains mostly limited to states with weak interactions. Recently, however, string theory also enabled explorations of strongly interacting states through the mathematical statement of holographic duality, which translates otherwise intractable problems into simpler analyses of black holes and gravitational waves.

In my talk, I will first discuss new aspects of the macroscopic theory of hydrodynamics, focusing on the properties of the infinite series of higher-order corrections to the infamous Navier-Stokes equations. By using a novel concept of generalized global symmetries, which can encode the fact that the number of magnetic flux lines in Nature is conserved, I will then describe the construction of a new, comprehensive theory of magnetohydrodynamics. This reformulation has led to a number of general theoretical and experimental predictions for transport in magnetized plasmas. I will then move on to discuss the microscopic physics responsible for transport in strongly interacting states. Beginning with an introduction of holographic duality, this section will summarize holographic insights into the problem of the “unreasonable effectiveness of hydrodynamics” for the description of quark-gluon plasma. Then, I will discuss how the descriptions of microscopic physics and transport transition between strongly and weakly interacting pictures. Finally, by utilizing the mathematical structure behind our new theory of magnetohydrodynamics, a holographic dual of magnetized plasmas will be presented along with the first analyses of strongly interacting magnetized transport.