We derive the precise form of the lowenergy fourdimensional EFT for type IIB string theory compactified on the complex cone over KählerEinstein del Pezzo surfaces, including N spacetimefilling D3branes and assuming Minkowski externally. We explicitly derive the theory for the K\"ahler modulus in the simplest case of a complex cone over the complex projective plane, with a stack of four D7branes and one O7plane wrapped around the base of the cone. An effective scalar potential appears in the theory, due to gaugino condensation taking place at low energies over the D7branes stack, exhibiting a runaway direction and an unstable de Sitter vacuum. We find an explicit cosmologicallike solution for the K\"ahler modulus, showing that the warped volume of the internal complex projective plane inflates with time in a runaway fashion. We conclude that type IIB string theory compactified on the complex cone over the complex projective plane, with four D7branes and one O7plane wrapped around the complex projective plane, is unstable. We explicitly derive the tendimensional equations of motion for maximally symmetric timedependent metric perturbations by means of an ad hoc procedure, and we exhibit both stationary and timedependent solutions, whose boundary conditions are imposed in part by the gaugino condensate stressenergy tensor. We partially fix the free parameters of the timedependent solution using the results from the fourdimensional lowenergy EFT. This thesis contains also an introduction to string compactifications, to the KKLT scenario and to the literature about tendimensional effects of gaugino condensation.
We derive the precise form of the lowenergy fourdimensional EFT for type IIB string theory compactified on the complex cone over KählerEinstein del Pezzo surfaces, including N spacetimefilling D3branes and assuming Minkowski externally. We explicitly derive the theory for the K\"ahler modulus in the simplest case of a complex cone over the complex projective plane, with a stack of four D7branes and one O7plane wrapped around the base of the cone. An effective scalar potential appears in the theory, due to gaugino condensation taking place at low energies over the D7branes stack, exhibiting a runaway direction and an unstable de Sitter vacuum. We find an explicit cosmologicallike solution for the K\"ahler modulus, showing that the warped volume of the internal complex projective plane inflates with time in a runaway fashion. We conclude that type IIB string theory compactified on the complex cone over the complex projective plane, with four D7branes and one O7plane wrapped around the complex projective plane, is unstable. We explicitly derive the tendimensional equations of motion for maximally symmetric timedependent metric perturbations by means of an ad hoc procedure, and we exhibit both stationary and timedependent solutions, whose boundary conditions are imposed in part by the gaugino condensate stressenergy tensor. We partially fix the free parameters of the timedependent solution using the results from the fourdimensional lowenergy EFT. This thesis contains also an introduction to string compactifications, to the KKLT scenario and to the literature about tendimensional effects of gaugino condensation.
On Gaugino Condensation in String Theory
ANGELINI, LUIGI
2022/2023
Abstract
We derive the precise form of the lowenergy fourdimensional EFT for type IIB string theory compactified on the complex cone over KählerEinstein del Pezzo surfaces, including N spacetimefilling D3branes and assuming Minkowski externally. We explicitly derive the theory for the K\"ahler modulus in the simplest case of a complex cone over the complex projective plane, with a stack of four D7branes and one O7plane wrapped around the base of the cone. An effective scalar potential appears in the theory, due to gaugino condensation taking place at low energies over the D7branes stack, exhibiting a runaway direction and an unstable de Sitter vacuum. We find an explicit cosmologicallike solution for the K\"ahler modulus, showing that the warped volume of the internal complex projective plane inflates with time in a runaway fashion. We conclude that type IIB string theory compactified on the complex cone over the complex projective plane, with four D7branes and one O7plane wrapped around the complex projective plane, is unstable. We explicitly derive the tendimensional equations of motion for maximally symmetric timedependent metric perturbations by means of an ad hoc procedure, and we exhibit both stationary and timedependent solutions, whose boundary conditions are imposed in part by the gaugino condensate stressenergy tensor. We partially fix the free parameters of the timedependent solution using the results from the fourdimensional lowenergy EFT. This thesis contains also an introduction to string compactifications, to the KKLT scenario and to the literature about tendimensional effects of gaugino condensation.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/48921