Testing and Extending Swampland Conjectures

In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particle’s mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that ‘gravity is the weakest force’. Here, we take a step towards making this expectation more precise by studying ℤN and ℤ2N gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to MPl.

IIB, or not IIB: That is the question

We investigate interactions between branes of various dimensions, both charged and uncharged, in three non-supersymmetric string models. These include the USp(32) and U(32) orientifold projections of the type IIB and type 0B strings, as well as the SO(16)×SO(16) projection of the exceptional heterotic string. The resulting ten-dimensional spectra are free of tachyons, and the combinations of branes that they contain give rise to rich and varied dynamics. We compute static potentials for parallel stacks of branes in three complementary regimes: the probe regime, in which one of the two stacks is parametrically heavier than the other, the string-amplitude regime, in which both stacks are light, and the holographic regime. Whenever comparisons are possible, we find qualitative agreement despite the absence of supersymmetry. For charged branes, our analysis reveals that the Weak Gravity Conjecture is satisfied in a novel way via a renormalization of the effective charge-to-tension ratio.

In this short note we clarify some aspects of the impact that the Weak Gravity Conjecture has on models of (generalized) natural inflation. We address in particular certain technical and conceptual concerns recently raised regarding the stringent constraints and conclusions found in our previous work (arXiv:1503.04783). We also point out the difficulties faced by attempts to evade these constraints. These new considerations improve the understanding of the quantum gravity constraints we found and further support the conclusion that it remains challenging for axions to drive natural inflation.

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale e G_N^{-1/2} with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.

Common features of known quantum gravity theories may hint at the general nature of quantum gravity. The absence of continuous global symmetries is one such feature. This inspired the Weak Gravity Conjecture, which bounds masses of charged particles. We propose the Lattice Weak Gravity Conjecture, which further requires the existence of an infinite tower of particles of all possible charges under both abelian and nonabelian gauge groups and directly implies a cutoff for quantum field theory. It holds in a wide variety of string theory examples and has testable consequences for the real world and for pure mathematics. We sketch some implications of these ideas for models of inflation, for the QCD axion (and LIGO), for conformal field theory, and for algebraic geometry.

In this paper, we analyze inflationary parameters and swampland conjectures in the presence of a scalar field and Chaplygin models. We examine inflationary parameters, such as slow-roll parameters, scalar and tensor power spectra, spectral index, and tensor-to-scalar ratio, in the presence of a scalar field and Chaplygin gas models. We also discuss recently proposed swampland conjectures. We assume that the inflationary expansion is driven by a standard scalar field with a decay ratio Γ that has a generic power-law dependence on the scalar field ϕ and that the temperature of the thermal bath T is given by , where is a dimensionless parameter and a is the inflation decay rate. In a scenario where our model operates within a robust dissipative environment , we analyze both fundamental and perturbative dynamics to extract key inflationary parameters. These include the scalar power spectrum , dissipative ratio R, scalar spectral index , tensor-to-scalar ratio r, running of the scalar spectral index , and generalized ratio of the swampland de-Sitter conjecture for three different potentials.

Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential

Electric flux may be screened by pair nucleation of heavy charges, a process that has a simple description in terms of a worldline instanton. When flux is wrapped around a small compact spatial dimension, worldline instantons still induce flux dissipation, but the leading process does not create real charged pairs. Instead, dissipation can be described in effective field theory as the production of long-wavelength scalar quanta via parametric resonance. The rate is computed semiclassically, and comments are made on the related problem of pair creation at finite temperature, for which differing results appear in the literature. Flux dissipation and the weak gravity conjecture together imply that the proper distance in field space a homogeneous axion field can traverse is bounded.

The chromo-natural inflation (CNI) scenario predicts a potentially detectable chiral gravitational wave signal, generated by a Chern-Simons coupling between a rolling scalar axion field and an SU(2) gauge field with an isotropy-preserving classical background during inflation. However, the generation of this signal requires a very large integer Chern-Simons level, which can be challenging to explain or embed in a UV-complete model. We show that this challenge persists in the phenomenologically viable spectator field CNI (S-CNI) model. Furthermore, we show that a clockwork scenario giving rise to a large integer as a product of small integers can never produce a Chern-Simons level large enough to have successful S-CNI phenomenology. We briefly discuss other constraints on the model, both in effective field theory based on partial-wave unitarity bounds and in quantum gravity based on the Weak Gravity Conjecture, which may be relevant for further explorations of alternative UV completions.

We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.

f (R) theories are the simplest generalisations of General Relativity, Einstein’s theory of gravity. f (R) theories, and modified gravity theories more broadly, have been invoked to explain the accelerated expansion of the universe. A number of “viable” models have been proposed which satisfy cosmological tests and get around present day laboratory and solar system constraints by invoking the chameleon mechanism. It is important to determine whether such alternative models can be distinguished by precision experiments at the laboratory scale. This thesis focuses on recently proposed f (R) models in the context of the upcoming neutron quantum bouncer experiment GRANIT [1], which has the potential to directly observe violations of Einstein gravity. This experiment works by precisely measuring the energy levels of ultra-cold neutrons trapped in the Earth’s gravitational field above a mirror. Neutrons in these states have energies of the order of 10−12 eV (peV) and wavefunctions with spatial extents of ∼ 10 μm. The size of the neutron wavefunctions gives gravitational spectroscopy sensitivity to any change of the Newtonian potential above the mirror surface on a scale of tens of microns. These experiments have a unique opportunity to study gravity and quantum mechanics in an unprecedented regime. GRANIT claims an energy sensitivity of 0.01 peV with an improvement of one or two orders of magnitude expected over the next several years. The theoretical limit to the sensitivity is 10−7 peV. Previous work by Brax and Pignol [2] has shown that scalar-tensor theories, which are closely related to f (R) theories, can give rise to detectable shifts in the energy levels from their Newtonian values. Here the energy levels shifts are examined for three viable f (R) models: the exponential gravity model of Linder [3], the model of Hu and Sawicki [4] and the “new” exponential gravity model of Xu and Chen [5]. It is found that exponential gravity predicts energy level shifts of the order exp ( −10 ) mNc , where mN is the neutron mass. This is unobservable in any experiment lasting less than the age of the universe. The Hu-Sawicki model predicts much larger shifts which depend on the model parameters n and c2, where n, c2 > 0. It is found that the shifts are below the theoretical sensitivity limit for n ≥ 1 2 , with shifts at n = 1 2 of the order of 10 −19 peV. It is unlikely, though not yet ruled out, that n 1 models could be observed at neutron bouncer experiments operating under extreme conditions. The computation of the shifts for n 1 models is hampered by convergence issues. This may be immaterial, however, because Hu-Sawicki models with n 2 Hu-Sawicki model at laboratory scales, hence it is unobservable at a neutron bouncer experiment. The reason for the difference between these results with those of Brax and Pignol is shown to be due to the special form of the scalar potential and matter coupling, which are free in scalar-tensor theory and can be chosen to give a large effect, but are constrained in f (R) gravity. Because of these special features the neutron bouncer experiment can distinguish between f (R) and non-f (R) modified gravity, but not between the f (R) models examined in this thesis. Note the original date of this thesis was 22 November 2012. This version, with several copyrighted figures removed but nothing else modified apart from this notice, was created 21 October 2014.

Constructing an explicit compactification yielding a metastable de Sitter (dS) vacuum in a UV consistent string theory is an incredibly difficult open problem. Motivated by this issue, as well as the conjecture that all non-supersymmetric AdS vacua must decay, we discuss the alternative possibility of realizing an effective four-dimensional dS cosmology on a codimension-one bubble wall separating two AdS5 vacua. The construction further elaborates on the scenario of arXiv:1807.01570, where the aforementioned cosmology arises due to a non-perturbative decay and is embedded in a five-dimensional bulk in a time­ dependent way. In this paper we discuss the relation between this scenario and the weak gravity conjecture and further develop the details of the four-dimensional cosmology. We provide a bulk interpretation for the dS temperature as the Unruh temperature experienced by an accelerated observer riding the bubble. A source of four-dimensional matter arises from a string cloud in the bulk, and we examine the consequences for the particle mass spectrum. Furthermore, we show how effective four-dimensional Einstein gravity on the bubble is obtained from the five-dimensional Gauss equation. We conclude by outlining some implications that this paradigm will have for holography, inflation, the standard model, and black holes.

In axion-Maxwell theory at the minimal axion-photon coupling, we find non-invertible 0- and 1-form global symmetries arising from the naive shift and center symmetries. Since the Gauss law is anomalous, there is no conserved, gauge-invariant, and quantized electric charge. Rather, using half higher gauging, we find a non-invertible Gauss law associated with a non-invertible 1-form global symmetry, which is related to the Page charge. These symmetries act invertibly on the axion field and Wilson line, but non-invertibly on the monopoles and axion strings, leading to selection rules related to the Witten effect. We also derive various crossing relations between the defects. The non-invertible 0- and 1-form global symmetries mix with other invertible symmetries in a way reminiscent of a higher-group symmetry. Using this non-invertible higher symmetry structure, we derive universal inequalities on the energy scales where different infrared symmetries emerge in any renormalization group flow to the axion-Maxwell theory. Finally, we discuss implications for the Weak Gravity Conjecture and the Completeness Hypothesis in quantum gravity.

We study a bosonic four--dimensional effective action corresponding to the heterotic string compactified on a 6--torus (dilaton--axion gravity with one vector field) on a curved space--time manifold possessing a time--like Killing vector field. Previously an existence of the $SO(2,3)\sim Sp(4, R)$ global symmetry ($U$--duality) as well as the symmetric space property of the corresponding $\sigma$--model have been established following Neugebauer and Kramer approach. Here we present an explicit form of the $Sp(4, R)$ generators in terms of coset variables and construct a representation of the coset in terms of the physical target space coordinates. Complex symmetric $2\times 2$ matrix $Z$ (``matrix dilaton --axion'') is introduced for which $U$--duality takes the matrix valued $SL(2, R)$ form. In terms of this matrix the theory is further presented as a K\"ahler $\sigma$--model. This leads to a more concise $2\times 2$ formulation which opens new ways to construct exact classical solutions. New solution (corresponding to constant ${\rm Im} Z$ ) is obtained which describes the system of point massless magnetic monopoles endowed with axion charges equal to minus monopole charges. In such a system mutual magnetic repulsion is exactly balanced by axion attraction so that the resulting space time is locally flat but possesses multiple Taub--NUT singularities.