@phdthesis{CamargoMolina2015,
  author    = {Camargo Molina, Jos{\´e} Eliel},
  title     = {Vacuum stability of models with many scalars},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-112755},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {One of the most popular extensions of the SM is Supersymmetry (SUSY). It is a symmetry relating fermions and bosons and also the only feasible extension to the symmetries of spacetime. With SUSY it is then possible to explain some of the open questions left by the SM while at the same time opening the possibility of gauge unification at a high scale. SUSY theories require the addition of new particles, in particular an extra Higgs doublet and at least as many new scalars as fermions in the SM. Much in the same way that the Higgs boson breaks SU (2)L symmetry, these new scalars can break any symmetry for which they carry a charge through spontaneous symmetry breaking. Let us assume there is a local minimum of the potential that reproduces the correct phenomenol- ogy for a parameter point of a given model. By exploring whether there are other deeper minima with VEVs that break symmetries we want to conserve, like SU (3)C or U (1)EM , it is possible to exclude regions of parameter space where that happens. The local minimum with the correct phenomenology might still be metastable, so it is also necessary to calculate the probability of tunneling between minima. In this work we propose and apply a framework to constrain the parameter space of models with many scalars through the minimization of the one-loop eff e potential and the calculation of tunneling times at zero and non zero temperature.After a brief discussion about the shortcomings of the SM and an introduction of the basics of SUSY, we introduce the theory and numerical methods needed for a successful vacuum stability analysis. We then present Vevacious, a public code where we have implemented our proposed framework. Afterwards we go on to analyze three interesting examples. For the constrained MSSM (CMSSM) we explore the existence of charge- and color- breaking (CCB) minima and see how it constraints the phenomenological relevant region of its parameter space at T = 0. We show that the regions reproducing the correct Higgs mass and the correct relic density for dark matter all overlap with regions suffering from deeper CCB minima. Inspired by the results for the CMSSM, we then consider the natural MSSM and check the region of parameter space consistent with the correct Higgs mass against CCB minima at T /= 0. We find that regions of parameter space with CCB minima overlap significantly with that reproducing the correct Higgs mass. When thermal eff are considered the majority of such points are then found to have a desired symmetry breaking minimum with very low survival probability. In both these studies we find that analytical conditions presented in the literature fail in dis- criminating regions of parameter space with CCB minima. We also present a way of adapting our framework so that it runs quickly enough for use with parameter fit studies. Lastly we show a different example of using vacuum stability in a phenomenological study. For the BLSSM we investigate the violation of R-parity through sneutrino VEVs and where in parameter space does this happen. We find that previous analyses in literature fail to identify regions with R-parity conservation by comparing their results to our full numerical analysis.},
  subject      = {Supersymmetry},
  language  = {en}
}
@phdthesis{Du2019,
  author    = {Du, Yiqiang},
  title     = {Gauge/Gravity Duality with Backreacting Background},
  doi       = {10.25972/OPUS-18786},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-187869},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {The topic of this thesis is generalizations of the Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence, often referred to as holography, and their application to models relevant for condensed matter physics. A particular virtue of AdS/CFT is to map strongly coupled quantum field theories, for which calculations are inherently difficult, to more tractable classical gravity theories. I use this approach to study the crossover between Bose-Einstein condensation (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superconductivity mechanism. I also study the phase transitions between the AdS black hole and AdS soliton spacetime in the presence of disorder. Moreover, I consider a holographic model of a spin impurity interacting with a strongly correlated electron gas, similar to the Kondo model. In AdS/CFT, the BEC/BCS crossover is modeled by a soliton configuration in the dual geometry and we study the BEC and BCS limits. The backreaction of the matter field on the background geometry is considered, which provides a new approach to study the BEC/BCS crossover. The behaviors of some physical quantities such as depletion of charge density under different strength of backreaction are presented and discussed. Moreover, the backreaction enables us to obtain the effective energy density of the soliton configurations, which together with the surface tension of the solitons leads to an argument for the occurrence of so called snake instability for dark solitons, i.e. for the solitons to form a vortex-like structures. Disordering strongly coupled and correlated quantum states of matter may lead to new insights into the physics of many body localized (MBL) strongly correlated states, which may occur in the presence of strong disorder. We are interested in potential insulator-metal transitions induced by disorder, and how disorder affects the Hawking-Page phase transition in AdS gravity in general. We introduce a metric ansatz and numerically construct the corresponding disordered AdS soliton and AdS black hole solutions, and discuss the calculation of the free energy in these states. In the Kondo effect, the rise in resistivity in metals with scarce magnetic impurities at low temperatures can be explained by the RG flow of the antiferromagnetic coupling between the impurity and conduction electrons in CFT. The generalizations to SU(N) in the large N limit make the treatment amenable to the holographic approach. We add a Maxwell term to a previously existing holographic model to study the conductivity of the itinerant electrons. Our goal is to find the log(T) behavior in the DC resistivity. In the probe limit, we introduce junction conditions to connect fields crossing the defect. We then consider backreactions, which give us a new metric ansatz and new junction conditions for the gauge fields.},
  language  = {en}
}
@phdthesis{Abt2019,
  author    = {Abt, Raimond},
  title     = {Implementing Aspects of Quantum Information into the AdS/CFT Correspondence},
  doi       = {10.25972/OPUS-18801},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-188012},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {In recent years many discoveries have been made that reveal a close relation between quantum information and geometry in the context of the AdS/CFT correspondence. In this duality between a conformal quantum field theory (CFT) and a theory of gravity on Anti-de Sitter spaces (AdS) quantum information quantities in CFT are associated with geometric objects in AdS. Subject of this thesis is the examination of this intriguing property of AdS/CFT. We study two central elements of quantum information: subregion complexity -- which is a measure for the effort required to construct a given reduced state -- and the modular Hamiltonian -- which is given by the logarithm of a considered reduced state. While a clear definition for subregion complexity in terms of unitary gates exists for discrete systems, a rigorous formulation for quantum field theories is not known. In AdS/CFT, subregion complexity is proposed to be related to certain codimension one regions on the AdS side. The main focus of this thesis lies on the examination of such candidates for gravitational duals of subregion complexity. We introduce the concept of \textit{topological complexity}, which considers subregion complexity to be given by the integral over the Ricci scalar of codimension one regions in AdS. The Gauss-Bonnet theorem provides very general expressions for the topological complexity of CFT\(_2\) states dual to global AdS\(_3\), BTZ black holes and conical defects. In particular, our calculations show that the topology of the considered codimension one bulk region plays an essential role for topological complexity. Moreover, we study holographic subregion complexity (HSRC), which associates the volume of a particular codimension one bulk region with subregion complexity. We derive an explicit field theory expression for the HSRC of vacuum states. The formulation of HSRC in terms of field theory quantities may allow to investigate whether this bulk object indeed provides a concept of subregion complexity on the CFT side. In particular, if this turns out to be the case, our expression for HSRC may be seen as a field theory definition of subregion complexity. We extend our expression to states dual to BTZ black holes and conical defects. A further focus of this thesis is the modular Hamiltonian of a family of states \(\rho_\lambda\) depending on a continuous parameter \(\lambda\). Here \(\lambda\) may be associated with the energy density or the temperature, for instance. The importance of the modular Hamiltonian for quantum information is due to its contribution to relative entropy -- one of the very few objects in quantum information with a rigorous definition for quantum field theories. The first order contribution in \(\tilde{\lambda}=\lambda-\lambda_0\) of the modular Hamiltonian to the relative entropy between \(\rho_\lambda\) and a reference state \(\rho_{\lambda_0}\) is provided by the first law of entanglement. We study under which circumstances higher order contributions in \(\tilde{\lambda}\) are to be expected. We show that for states reduced to two entangling regions \(A\), \(B\) the modular Hamiltonian of at least one of these regions is expected to provide higher order contributions in \(\tilde{\lambda}\) to the relative entropy if \(A\) and \(B\) saturate the Araki-Lieb inequality. The statement of the Araki-Lieb inequality is that the difference between the entanglement entropies of \(A\) and \(B\) is always smaller or equal to the entanglement entropy of the union of \(A\) and \(B\). Regions for which this inequality is saturated are referred to as entanglement plateaux. In AdS/CFT the relation between geometry and quantum information provides many examples for entanglement plateaux. We apply our result to several of them, including large intervals for states dual to BTZ black holes and annuli for states dual to black brane geometries.},
  subject      = {AdS-CFT-Korrespondenz},
  language  = {en}
}