An effective approach to D-branes

The purpose of the present thesis is to apply the calculational and conceptual tools of hydrodynamics to the physics of D-branes. These are higher-dimensional quantum objects on which open strings can end. D-branes source closed string states whose low-energy description is provided by extremal p-brane solutions of supergravity. These solutions, and in particular their non-extremal generalizations, obey locally thermodynamic laws. Thus, their dynamics are naturally organized in a derivative expansion, highly constrained by symmetry, much like an ordinary hydrodynamic theory.
In chapter 2 we consider wrapped fivebranes carrying D3-brane charge, embedded in mass-deformed AdS₅ × S⁵ geometries. Such configurations holographically realize the vacua of the N=1* supersymmetric gauge theory, a massive QCD-like theory. By employing a long-wavelength effective description for the fivebrane, we show the existence of regular supergravity solutions with topology R³ × S² × S³, able to describe a generic massive vacuum of the gauge theory at low temperatures, and a deconfined vacuum at high temperatures.
From the perspective of supergravity, D/M-branes are spatially extended conserved objects, and as such the natural notion of symmetry under which they can be charged is that of a higher-form symmetry. In chapter 3, we formulate a Landau paradigm for non-trivial combinations of higher-form symmetries, namely higher-group symmetries. Specializing to Abelian continuous higher-groups involving two higher-form symmetries, we study the different spontaneous symmetry breaking patterns at zero and finite temperature, and develop the associated Goldstone field theories in the presence of higher-group invariance. We show that the low-energy theory on the M5-brane is identified from a symmetry perspective as a 6-group invariant Goldstone field theory.
In chapter 4 we initiate a fluid/gravity duality in ten dimensions, in which the geometrization of anomalous transport through holography becomes complete and manifest. Specifically, we formulate a holographic duality between spinning fluids in ten dimensions and anomalous R-charged fluids in four dimensions. In this context, we provide a geometric interpretation of the R-current anomaly in terms of a gravitational anomaly from the ten-dimensional point of view.