Cordonier Tello, Fabrizio Bastián (2019): Modified gravitational backgrounds: Horndeski's theory and nongeometrical backgrounds in string theory. Dissertation, LMU München: Faculty of Physics 

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Abstract
This thesis addresses a twopart study of modified backgrounds in theories that generalize gravity. In the first part of this work we explore Horndeski's theory within Cartan's first order formalism, and study gravitational waves considering torsion to be nonvanishing. In part two we move on to string theory and study Tduality transformations for a particular nonlinear sigma model containing open strings. This prompts the study of the backgrounds arising from such transformations. In part one we analyze Horndeski's Lagrangian in Cartan's firstorder formalism. This formalism allows torsion to be nonzero, whereas in standard general relativity it is a vanishing quantity. Horndeski's Lagrangian is the most general Lagrangian in four dimensions featuring all possible interactions between a scalar field $\phi$ and gravity whose equations of motion are partial differential equations up to second order. This feature of such equations of motion prevents the existence of ghosts. Since this Lagrangian contains wellknown modified theories of gravity as particular cases, we focus on the role of torsion and its impact at the linear perturbation regime. In order to make our analysis manageable, we cast Horndeski's Lagrangian in differential form language and we take the spin connection $\omega^{ab}$ and the vierbein $e^a$ to be independent of each other, following Cartan's formalism. We take the full Horndeski Lagrangian and compute the equations of motion for the scalar field, the spin connection and the vierbein. We argue that in order to recover the torsionless case and make contact with standard General Relativity, we have to impose a constraint via Lagrange multipliers. As a preparation for the analysis of the linear perturbation regime, we define several differential operators capable to discern spacetime torsion. These operators are capable to act covariantly on $p$forms carrying Lorentz indices. In particular, we provide with a generalization of the Weitzenböck identity that includes torsion. Later on, we consider linear perturbations around a generic background for the vielbein, spin connection and scalar field and study Horndeski's Lagrangian under such perturbations. What we find is that nonminimal couplings and second derivatives of the scalar field are generic sources of torsion. This makes a contrast to what was known from the EinsteinCartanSciamaKibble framework, where torsion can be sourced only from fermions. In fact, we find that background torsion couples with the propagating metric degrees of freedom. This provides with a potential way to falsify torsion via gravitational waves. In part two we work inside the framework of string theory and we set to study Tduality transformations via Buscher's procedure for the open string. Such transformations lead to the study of interesting geometries which play an important role in string theory, as in moduli stabilization or in the construction of inflationary potentials. Such spaces are called nongeometric backgrounds. In this second part, we work out technical details which have been missing in the literature. These details regard the presence of Dbranes and the effect of Tduality transformations on them. We study a nonlinear sigma model for the open string with fields defined on the worldsheet of such open string $\Sigma$ and on its boundary $\partial\Sigma$. We take into account nontrivial topologies for this worldsheet and we present the appropriate boundary conditions for the open string. According to Buscher's procedure, we assume certain conditions for the background configuration and define additional fields on $\Sigma$ and $\partial\Sigma$ taking into account the presence of Dbranes. We follow Buscher's procedure and perform Tduality transformations by gauging a worldsheet symmetry and intregratingout worldsheet gauge fields. We reach in this way the dual configuration for the open and closed string sector. In particular, we find that the dual KalbRamond field $B$ features a residual part which will play a major role when we discuss the dual configuration for the open string. To illustrate our formalism, we consider the standard configuration of the threetorus with $H$flux and perform one, two and three collective Tduality transformations for different Dbrane configurations. We read off the dual backgrounds for the closed and open string sector. We find the standard nongeometric backgrounds found in the literature, noting that such backgrounds can receive contributions coming from the dual open string sector. Regarding the dual open string sector, we study the boundary conditions of the open strings in the dual configuration and we find that they comply with the usual results in CFT. We study the global welldefinedness of these Dbranes on such dual backgrounds and we illustrate the application of the FreedWitten anomaly cancelation condition for some of the examples presented.
Item Type:  Theses (Dissertation, LMU Munich) 

Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  24. September 2019 
1. Referee:  Lüst, Dieter 
MD5 Checksum of the PDFfile:  ad7500f32599c6e272d7d6a68e30e742 
Signature of the printed copy:  0001/UMC 26882 
ID Code:  25490 
Deposited On:  07. Feb 2020 13:55 
Last Modified:  07. Feb 2020 13:55 