Worldsheet instantons and coupling selection rules in heterotic orbifolds

We review recent results on string coupling selection rules for heterotic orbifolds, derived using conformal field theory. Such rules are the first step towards understanding the viability of the recently obtained compactifications with potentially realistic particle spectra. They arise from the properties of the worldsheet instantons that mediate the couplings, and include stringy effects that would seem 'miraculous' to an effective field theory observer.Comment: 4 pages, talk presented at SQS'13, JINR, Dubna, Russia, 29 July - 03 August, 201

Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications

We study to what extent Wilson lines in heterotic Calabi-Yau compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson lines are basic ingredients for Standard Model constructions but their induced H-flux may affect the consistency of the leading order background geometry and of the two-dimensional worldsheet theory. Moreover H-flux in heterotic compactifications would play an important role for moduli stabilization and could strongly constrain the supersymmetry breaking scale. We show how to compute H-flux and the corresponding superpotential, given an explicit complete intersection Calabi-Yau compactification and choice of Wilson lines. We do so by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding how the Wilson lines project onto these submanifolds, and computing their Chern-Simons invariants. We illustrate our procedure with the quintic hypersurface as well as the split-bicubic, which can provide a potentially realistic three generation model.Comment: 41 pages, 7 figures. v2: Minor corrections, published versio

Dark Energy with a Little Help from its Friends

We analyse theories that do not have a de Sitter vacuum and cannot lead to slow-roll quintessence, but which nevertheless support a transient era of accelerated cosmological expansion due to interactions between a scalar $\phi$ and either a hidden sector thermal bath, which evolves as Dark Radiation, or an extremely-light component of Dark Matter. We show that simple models can explain the present-day Dark Energy of the Universe consistently with current observations. This is possible both when $\phi$'s potential has a hilltop form and when it has a steep exponential run-away, as might naturally arise from string theory. We also discuss a related theory of multi-field quintessence, in which $\phi$ is coupled to a sector that sources a subdominant component of Dark Energy, which overcomes many of the challenges of slow-roll quintessence.Comment: 30 pages + appendices (two columns), 9 figure

Gravity at the Tip of the Throat

We study the gravitational signatures that arise from compactifying Type IIB supergravity on a compact space containing a Klebanov-Strassler warped throat. After reviewing the dimensional reduction of the 10d graviton and explicitly obtaining the equations of motion for the 4d tensor $h_{\mu\nu}$, vector $h_{\mu n}$ and scalar $h_{mn}$ modes, we find the masses and wavefunctions of the Kaluza-Klein tower of spin-2 states. We explore how the masses and wavefunctions depend on the balance between the strength of the warping and the size of the bulk, and how these relate to the range and strength of the interactions which correct the Newtonian gravitational potential. By computing the modified Newtonian potential for sources on a brane somewhere along the throat, and applying consistency constraints on the Klebanov-Strassler parameters, we obtain predictions for the phenomenological parameter space. In the case of a fully warped throat, and depending on where the brane is along the throat, these predictions are narrow in range and consistent with current observational and experimental constraints. We also begin an exploration of gravitational wave signatures of KK gravitons in warped throats, finding that strong warping can bring the corresponding frequencies down to the windows of current and proposed experiments.Comment: 49 pages, 13 figures, 5 table

De Sitter vacua -- when are `subleading corrections' really subleading?

We consider various string-loop, warping and curvature corrections that are expected to appear in type IIB moduli stabilisation scenarios. It has recently been argued, in the context of strongly-warped LVS de Sitter vacua, that it is impossible to achieve parametric suppression in all of these corrections simultaneously \cite{Junghans:2022exo}. We investigate corrections in the context of the recently discovered weakly-warped LVS de Sitter vacua, which represent a distinct branch of solutions in type IIB flux compactifications, supported by small conifold flux numbers $MK \lesssim 32$. Warping corrections become less problematic in this regime, and some corrections even help to reach the weakly-warped regime of parameter space. Other corrections continue to be dangerous and would require numerical coefficients to be computed -- and found to be small -- in order not to destroy the consistency of the weakly-warped LVS de Sitter solution.Comment: 35 pages, 5 figures and 3 table

A guide to frames, 2π2\pi's, scales and corrections in string compactifications

This note is intended to serve as a reference for conventions used in the literature on string compactifications, and how to move between them, collected in a single and easy-to-find place, using type IIB as an illustrative example. We hope it may be useful to beginners in the field and busy experts. E.g. string constructions proposed to address the moduli stabilisation problem are generically in regions of parameter space at the boundaries of control, so that consistent use of $2\pi$'s and frame conventions can be pivotal when computing their potentially dangerous corrections.Comment: 17 page

Runaway quintessence, out of the swampland

We propose a simple, well-motivated and robust alternative to a metastable de Sitter vacuum in string theory, consistent with current observations of dark energy and naturally satisfying conjectured swampland constraints. Inflation ends in a supersymmetric Minkowski minimum, with a flat direction that is protected by non-renormalisation theorems. At some scale non-perturbative effects kick in, inducing a runaway scalar potential. The tail of this runaway potential cannot sustain a late-time dominating, slow-roll quintessence. However, the potential always contains a dS maximum. If the modulus starts close to the hilltop, it remains frozen there by Hubble friction for much of the cosmological history, at first sourcing a tiny classical vacuum energy and then constituting a rolling quintessence, with observable consequences. So long as the modulus is localised away from the Standard Model in the extra dimensions, there are no observable fifth forces nor is there time-variation of fundamental constants, and the modulus mass is protected from radiative corrections. We revisit concrete string models based on heterotic orbifold compactifications, and show that their de Sitter extrema satisfy the recently refined dS Swampland Conjecture.Comment: 12 pages, 5 figures. v2: minor modifications, references and comments adde

Modular invariance, misalignment and finiteness in non-supersymmetric strings

In this article we show that finite perturbative corrections in non-supersymmetric strings can be understood via an interplay between modular invariance and misaligned supersymmetry. While modular invariance is known to be crucial in closed-string models, its presence and role for open strings is more subtle. Nevertheless, we argue that it leads to cancellations in physical quantities such as the one-loop cosmological constant and prevents them from diverging. In particular, we show that if the sector-averaged number of states does not grow exponentially, as predicted by misaligned supersymmetry, all exponential divergences in the one-loop cosmological constant cancel out as well. To account for the absence of power-law divergences, instead, we need to resort to the modular structure of the partition function. We finally comment on the presence of misaligned supersymmetry in the known 10-dimensional tachyon-free non-supersymmetric string theories.Comment: 36 pages + appendices, 4 figure

A new de Sitter solution with a weakly warped deformed conifold

We revisit moduli stabilisation for type IIB flux compactifications that include a warped throat region corresponding to a warped deformed conifold, with an anti-D3-brane sitting at its tip. The warping induces a coupling between the conifold's deformation modulus and the bulk volume modulus in the K\"ahler potential. Previous works have studied the scalar potential assuming a strong warping such that this coupling term dominates, and found that the anti-D3-brane uplift may destabilise the conifold modulus and/or volume modulus, unless flux numbers within the throat are large, which makes tadpole cancellation a challenge. We explore the regime of parameter space corresponding to a weakly-but-still warped throat, such that the coupling between the conifold and volume moduli is subdominant. We thus discover a new metastable de Sitter solution within the four-dimensional effective field theory. We discuss the position of this de Sitter vacuum in the string theory landscape and swampland.Comment: 36 pages, 7 figures and 4 tables; references added and minor typos fixe

A new mechanism to enhance primordial tensor fluctuations in single field inflation

We discuss a new mechanism to enhance the spectrum of primordial tensor fluctuations in single field inflationary scenarios. The enhancement relies on a transitory non-attractor inflationary phase, which amplifies the would-be decaying tensor mode, and gives rise to a growth of tensor fluctuations at superhorizon scales. We show that the enhancement produced during this phase can be neatly treated via a tensor duality between an attractor and non-attractor phase, which we introduce. We illustrate the mechanism and duality in a kinetically driven scenario of inflation, with non-minimal couplings between the scalar and the metric.Comment: 23 pages, 3 figures, Typos fixed, Appendix B is revised, published versio