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Register a new userLectures on the Swampland Program in String Compactifications
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The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. Different proposals have been formulated in the form of Swampland conjectures. In these lecture notes, we provide a pedagogical introduction to the most important Swampland conjectures, their connections and their realization in string theory compactifications. The notes are based on the series of lectures given by Irene Valenzuela at the online QFT and Geometry summer school in July 2020.
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The First and Second Swampland Conjectures (FSC & SSC) are substantially modified in non-critical string cosmology, in which cosmic time is identified with the time-like Liouville mode of the supercritical string. In this scenario the Friedmann equation receives additional contributions due to the non-criticality of the string. These are potentially important when one seeks to apply the Bousso bound for the entropy of states that may become light as the dilaton takes on trans-Planckian values, as in a de Sitter phase, and restore consistency with the FSC and in at least some cases also the SSC. The weak gravity conjecture (WGC) for scalar potentials is saturated in the supercritical string scenarios discussed in this work, but only if one uses the dilaton as appears in the string effective action, with a kinetic term that is not canonically normalised. In the case of a non-critical Starobinsky potential, the WGC is satisfied by both the canonically-normalised dilaton and the dilaton used in the string effective action.
We make a number of conjectures about the geometry of continuous moduli parameterizing the string landscape. In particular we conjecture 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. We also conjecture that points at infinity in a moduli space correspond to points where an infinite tower of massless states appear, and that near these regions the moduli space is negatively curved. We also propose that there is no non-trivial 1-cycle of minimum length in the moduli space. This leads in particular to the prediction of the existence of a radially massive partner to the axion. These conjectures put strong constraints on inflaton potentials that can appear in a consistent quantum theory of gravity. Our conjectures are supported by a number of highly non-trivial examples from string theory. Moreover it is shown that these conditions can be violated if gravity is decoupled.
These lectures give an introduction to the interrelated topics of Calabi-Yau compactification of the type II string, black hole attractors, the all-orders entropy formula, the dual (0,4) CFT, topological strings and the OSV conjecture. Based on notes by MG of lectures by AS at the 2006 Cargese summer school.
These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of the problem requires `ultraviolet completion because of the sensitivity of inflation to quantum gravity effects, including back reaction and non-adiabatic production of heavy degrees of freedom. Cosmological observations imply accelerated expansion of the late universe, and provide increasingly precise constraints and discovery potential on the amplitude and shape of primordial tensor and scalar perturbations, and some of their correlation functions. Most backgrounds of string theory have positive potential energy, with a rich but still highly constrained landscape of solutions. The theory contains novel mechanisms for inflation, some subject to significant observational tests. Although the detailed ultraviolet completion is not accessible experimentally, some of these mechanisms directly stimulate a more systematic analysis of the space of low energy theories and signatures relevant for analysis of data, which is sensitive to physics orders of magnitude above the energy scale of inflation as a result of long time evolution (dangerous irrelevance) and the substantial amount of data. Portions of these lectures appeared previously in Les Houches 2013, Post-Planck Cosmology .
The Swampland de Sitter conjecture in combination with upper limits on the tensor-to-scalar ratio $r$ derived from observations of the cosmic microwave background endangers the paradigm of slow-roll single field inflation. This conjecture constrains the first and the second derivatives of the inflationary potential in terms of two ${cal O} (1)$ constants $c$ and $c$. In view of these restrictions we reexamine single-field inflationary potentials with $S$-duality symmetry, which ameliorate the unlikeliness problem of the initial condition. We compute $r$ at next-to-leading order in slow-roll parameters for the most general form of $S$-dual potentials and confront model predictions to constraints imposed by the de Sitter conjecture. We find that $c sim {cal O} (10^{-1})$ and $c sim {cal O} (10^{-2})$ can accommodate the 95% CL upper limit on $r$. By imposing at least 50 $e$-folds of inflation with the effective field theory description only valid over a field displacement ${cal O} (1)$ when measured as a distance in the target space geometry, we further restrict $c sim {cal O} (10^{-2})$, while the constraint on $c$ remains unchanged. We comment on how to accommodate the required small values of $c$ and $c$.
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