Connecting flux vacua through scalar field excursions

Abstract: We study the notion of a metric over the space of AdS solution in string theory, leading to an associated distance between them. Such a distance is the idea underlying the AdS distance conjecture. We utilise the previously developed prescription for extracting such a metric: taking an off-shell quadratic variation of the string theory effective action and then evaluating it over the space of on-shell solutions. It was shown that this prescription leads to a well-defined positive metric over M-theory Freund-Rubin vacua. In this work, we use the same prescription to calculate the metric over type IIA DGKT vacua. These are much more involved, they have multiple flux parameters and exhibit scale separation. While it remains an open question whether these vacua exist as fully localised solutions of string theory, they are well-defined within the four-dimensional effective theory, which is all that is required for the calculation. We find that they also have a positive metric over them. Interestingly, this metric turns out to be independent of the many flux parameters in the solution, similarly to what happens for metrics over scalar field spaces. This non-trivial flux cancellation, as well as results from explicit vacua, lead us to propose a Swampland condition: that the metric over the space of vacua in quantum gravity, as defined by the above prescription, is always positive.

TL;DR: This review synthesizes scale separation in string theory, focusing on parametric scale separation in flux compactifications, and discusses its implications, limitations, and Swampland arguments, providing a comprehensive overview of the subject's current state.

TL;DR: Researchers explore the connection between confinement scale in gauge theories and cosmological constant in quantum gravity, finding a relationship between the two through distance in metric space configurations in string compactifications and swampland program constraints.

TL;DR: In this paper, the authors make a number of conjectures about the geometry of continuous moduli parameterizing the string landscape, including that such moduli are always given by expectation value of scalar fields and that moduli spaces with finite non-zero diameter belong to the swampland.

TL;DR: In this paper, it was shown that the near-flat limit of pure AdS belongs to the Swampland, as it is necessarily accompanied by an infinite tower of light states.

TL;DR: In this paper, the effects of adding RR, NS and metric fluxes on a T^6/(\Omega (-1)^{F_L} I_3) Type IIA orientifold were studied.

TL;DR: In this article, the effective N = 1, D = 4 supergravity for the seven main moduli of type IIA orientifolds with D6 branes, compactified on T 6 /(Z2 × Z2) in the presence of general fluxes, was derived.