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This thesis investigates applications of the gauge/gravity duality to strongly coupled quantum field theories. After a review of the duality and of correlators and transport in quantum systems, we present our results on second-order non-conformal hydrodynamics. We derive new Kubo formulae for five second-order transport coefficients in non-conformal relativistic fluids. We then apply these Kubo formulae to a class of non-conformal holographic fluids at infinite coupling. We find strong evidence that the Haack-Yarom identity, known to relate second-order coefficients in conformal holographic fluids at infinite coupling, continues to hold in holographic fluids without conformal symmetry: Within our class of models, we prove that it still holds when leading non-conformal corrections are taken into account, and we show numerically that it is also obeyed beyond leading order. This provides further evidence that the identity may be a universal feature of strongly coupled fluids. Next, we present our results on magnetic spin impurities in strongly correlated systems. We build a holographic two-impurity Kondo model, identifying the inter-impurity interaction as double-trace deformation. Our numerical results for the phase diagram suggest a quantum phase transition between a trivial phase with uncorrelated spins and no Kondo screening, and a non-trivial phase with anti-ferromagnetic correlations and simultaneous Kondo screening. Computing the spectrum in the single-impurity case, we observe Fano resonances, which at low temperatures we identify with the Kondo resonance.

The N= 4 Super Yang-Mills theory in four dimensions admits deformations and the exactly marginal deformations of its SU(3) R-symmetry sub-sector are known as Leigh-Strassler. Leigh-Strassler deformations break the N= 4 supersymmetry down to N= 1 while preserving conformal symmetry. With exactly marginal deformations only the F-terms are deformed thus Leigh-Strassler deformations only affect the superpotential in the Lagrangian. In this thesis we study the symmetry of the marginally deformed N= 4 SYM and demonstrate that its algebraic structure can be understood in terms of quasi-Hopf algebras. Quasi-Hopf algebras have a notion of twisting due to Drinfeld which makes them a natural mathematical language with which to treat deformations. Furthermore the deformation of the N= 4 SYM superpotential is automated by the definition of a suitable star product. / Thesis (PhD)--University of Pretoria, 2020. / NiTheP / Physics / PhD / Unrestricted

<p>This thesis investigates aspects of field theories and soliton solutions with nontrivial topology. In particular we explore the following effective models: a limited sector of the scalar Electroweak theory called extended Abelian Higgs model, and a classical mechanics model derived from the low energy SU(2) Yang-Mills theory.</p><p>The extended Abelian Higgs model applied on two-component plasma of charged particles is studied numerically. We find evidence that the model admits straight twisted line vortices. The result is described by an energy function that acquires a minimum value for a non-trivial twist. In addition to the twisted line vortices the result also suggests that stable torus shaped solitons are solutions of the theory. </p><p>Furthermore we construct a classical mechanics model exhibiting some of the key properties of the low-energy Yang-Mills theory. The dynamics of the model is studied numerically. We find that its classical equations of motion support stable periodic orbits. In a three dimensional projection these trajectories are self-linked in a topologically non-trivial manner suggesting the existence of knotted configurations in low energy SU(2) Yang-Mills theory. </p><p>We calculate the one-loop effective action for the Abelian Higgs model with extended Higgs sector. The resulting first order quantum corrected model shows close resemblance to a modified model where texture stabilizing term has been added to the system. In the limit where the gauge field can be entirely expressed by the scalar fields, the both models become identical suggesting that the theories are closely connected. This implies that quantum corrections have stabilising effect on the soliton solutions. </p><p>These studies have contributed to a better understanding of the dynamics of non-linear low energy systems, and brought us a step closer to exploring full scale physically realistic models.</p>

This thesis investigates aspects of field theories and soliton solutions with nontrivial topology. In particular we explore the following effective models: a limited sector of the scalar Electroweak theory called extended Abelian Higgs model, and a classical mechanics model derived from the low energy SU(2) Yang-Mills theory. The extended Abelian Higgs model applied on two-component plasma of charged particles is studied numerically. We find evidence that the model admits straight twisted line vortices. The result is described by an energy function that acquires a minimum value for a non-trivial twist. In addition to the twisted line vortices the result also suggests that stable torus shaped solitons are solutions of the theory. Furthermore we construct a classical mechanics model exhibiting some of the key properties of the low-energy Yang-Mills theory. The dynamics of the model is studied numerically. We find that its classical equations of motion support stable periodic orbits. In a three dimensional projection these trajectories are self-linked in a topologically non-trivial manner suggesting the existence of knotted configurations in low energy SU(2) Yang-Mills theory. We calculate the one-loop effective action for the Abelian Higgs model with extended Higgs sector. The resulting first order quantum corrected model shows close resemblance to a modified model where texture stabilizing term has been added to the system. In the limit where the gauge field can be entirely expressed by the scalar fields, the both models become identical suggesting that the theories are closely connected. This implies that quantum corrections have stabilising effect on the soliton solutions. These studies have contributed to a better understanding of the dynamics of non-linear low energy systems, and brought us a step closer to exploring full scale physically realistic models.