Master's thesis defence by Jakob Lorenzen – Niels Bohr Institute - University of Copenhagen

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Master's thesis defence by Jakob Lorenzen

Jakob Lorenzen

Title: Hyperscaling Violation in N=2 gauged supergravity

Abstract:

In recent years there has been much interest in the application of holography to condensed matter physics. In particular, gravity duals with non-relativistic scaling symmetries have been constructed for this purpose. These are known as Lifshitz and Schrödinger spacetimes. Recently, metrics with hyperscaling violation have also become important. These are not invariant under the non-relativistic scaling, but instead scale covariantly.

In this thesis, the equations of motion of four-dimensional N=2 gauged supergravity are derived in order to find Lifshitz solutions with non-zero hyperscaling violation. Both vector multiplets and gauged hypermultiplets are included in this general analysis. Focussing then on the $F=-iX^0X^1$ model, which contains a single vector multiplet coupled to gravity, explicit solutions are found. Further, it is showed that one of these solutions solves supersymmetric first-order flow equations. This indicates that the solution is supersymmetric.

Along the way, relevant topics are introduced, such as special Kähler manifolds, quaternionic Kähler manifolds, gauging of N=2 supergravity, and also some aspects of non-relativistic holography, as well as first-order flow equations.

MSc supervisor: Niels Obers

MSc co-supervisor: Jelle Hartong