Extensions of the gauge/gravity duality and application to strongly coupled systems
Final Report Abstract
Nature provides many strongly-coupled systems which appear to be inaccessible to all established methods and understanding. The basic idea of this project was to use the gauge/gravity correspondence to exactly solve toy models of such systems. Hereby we gained a qualitative understanding of and quantitative guidance for the systems under consideration. In some cases these results enabled us to find a direct description or effective field theory for these systems. We derived the first top-down realization of a holographic superconductor from string theory. It was studied in depth and established as a useful model for condensation processes at strong coupling. The rich phenomenology of this model bears implications for particle physics as well as condensed matter: In condensed matter physics the high temperature superconductors involve strongly correlated electron systems, in which traditional methods fail, but our holographic system may be understood as a good qualitative model. Hence our novel geometric understanding of our toy model pairing mechanism leading to condensation may help understand the condensation process in high temperature superconductors. The latter also have a so-called non-Fermi liquid phase which is not yet well-understood. Indeed our model has this peculiar phase as well, as a computation of its critical exponents revealed. Our model realizes a p-wave superconductor similar to the material strontium ruthenate, which is studied intensely because of its possible relevance for building a quantum computer. In the context of particle physics our holographic model has strong implications for the phase diagram of strongly-interacting matter, i.e. the quantum chromodynamics phase diagram. We found a new phase which can be interpreted as a ρ-meson superfluid appearing at large densities of a particular charge (isospin). This new phenomenon may be found e.g. in neutron stars. In a different collaboration we challenged the century-old theory of hydrodynamics. Our results can affect hydrodynamic models used in all disciplines including biology, medical science, engineering, cosmology, etc. We discovered new field theoretic methods as well as new transport effects, which had been previously overlooked in this context. The new transport effects are related to parity-violation and may be seen in adequate condensed matter experiments along with the known Hall viscosity and anomalous Hall conductivity. Traditionally, the most general transport coefficients are restricted by a local version of the famous second law of thermodynamics: entropy has to increase or remain unchanged in physical processes. We proposed an equivalent method using only two-point functions and a particular generating functional. In particular, we successfully tested our new method in the most general derivation of parity-violating (2+l)-dimensional hydrodynamics. Our new method can be considered an independent check, and is also applicable in cases where the definition of an entropy current is obstructed. Along the same line of research a new way of constructing generating functionals was developed. These allow to easily restrict a particular subset of all transport coefficients, and n-point correlators. A geometric understanding was gained for: (l+l)-dimensional p-wave superconductors, operator mixing, and (partly previously unknown) sum rules, now proven for a large class of theories.
Publications
- "Parity-Violating Hydrodynamics in 2+1 Dimensions", JHEP
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom
- "Fermionic Operator Mixing in Holographic p-wave Superfluids," JHEP 1005, 053 (2010)
M. Ammon, J. Erdmenger, M. Kaminski and A. O'Bannon
- "Holographic Operator Mixing and Quasinormal Modes on the Brane," JHEP 1002, 021 (2010)
M. Kaminski, K. Landsteiner, J. Mas, J. P. Shock and J. Tarrio
- "Sum Rules from an Extra Dimension," JHEP 1101, 148 (2011)
D. R. Gulotta, C. P. Herzog and M. Kaminski
