Massive-Scalar Effective Actions on Anti-de Sitter Spacetime

Closed forms are derived for the effective actions for free, massive spinless fields in anti-de Sitter spacetimes in arbitrary dimensions. The results have simple expressions in terms of elementary functions (for odd dimensions) or multiple Gamma functions (for even dimensions). We use these to argue against the quantum validity of a recently-proposed duality relating such theories with differing masses and cosmological constants.Comment: 23 pages, plain TeX, one figur

Who You Gonna Call? Runaway Ghosts, Higher Derivatives and Time-Dependence in EFTs

We briefly review the formulation of effective field theories (EFTs) in time-dependent situations, with particular attention paid to their domain of validity. Our main interest is the extent to which solutions of the EFT capture the dynamics of the full theory. For a simple model we show by explicit calculation that the low-energy action obtained from a sensible UV completion need not take the restrictive form required to obtain only second-order field equations, and we clarify why runaway solutions are nevertheless typically not a problem for the EFT. Although our results will not be surprising to many, to our knowledge they are only mentioned tangentially in the EFT literature, which (with a few exceptions) largely addresses time-independent situations.Comment: 12 page

Self-Tuning at Large (Distances): 4D Description of Runaway Dilaton Capture

We complete here a three-part study (see also arXiv:1506.08095 and 1508.00856) of how codimension-two objects back-react gravitationally with their environment, with particular interest in situations where the transverse `bulk' is stabilized by the interplay between gravity and flux-quantization in a dilaton-Maxwell-Einstein system such as commonly appears in higher-dimensional supergravity and is used in the Supersymmetric Large Extra Dimensions (SLED) program. Such systems enjoy a classical flat direction that can be lifted by interactions with the branes, giving a mass to the would-be modulus that is smaller than the KK scale. We construct the effective low-energy 4D description appropriate below the KK scale once the transverse extra dimensions are integrated out, and show that it reproduces the predictions of the full UV theory for how the vacuum energy and modulus mass depend on the properties of the branes and stabilizing fluxes. In particular we show how this 4D theory learns the news of flux quantization through the existence of a space-filling four-form potential that descends from the higher-dimensional Maxwell field. We find a scalar potential consistent with general constraints, like the runaway dictated by Weinberg's theorem. We show how scale-breaking brane interactions can give this potential minima for which the extra-dimensional size, $\ell$, is exponentially large relative to underlying physics scales, $r_B$, with $\ell^2 = r_B^2 e^{- \varphi}$ where $-\varphi \gg 1$ can be arranged with a small hierarchy between fundamental parameters. We identify circumstances where the potential at the minimum can (but need not) be parametrically suppressed relative to the tensions of the branes, provide a preliminary discussion of the robustness of these results to quantum corrections, and discuss the relation between what we find and earlier papers in the SLED program.Comment: 37 pages + appendice

Inflating in a Trough: Single-Field Effective Theory from Multiple-Field Curved Valleys

We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective low-energy approximation involving only the light field, $\ell$. (Typically only one of these -- the mass of the heavy field transverse to the trough -- is used in the literature when justifying the truncation of heavy fields.) We explicitly compute the resulting effective field theory, which has the form of a $P(\ell,X)$ model, with $X = - 1/2(\partial \ell)^2$, as a function of these scales. This gives the leading ways each scale contributes to any low-energy dynamics, including (but not restricted to) those relevant for cosmology. We check our results with the special case of a homogeneous roll near the valley floor, placing into a broader context recent cosmological calculations that show how the truncation approximation can fail. By casting our results covariantly in field space, we provide a geometrical criterion for model-builders to decide whether or not the single-field and/or the truncation approximation is justified, identify its leading deviations, and to efficiently extract cosmological predictions.Comment: 28 pages + 3 appendices, references added and typos corrected, matches published versio

String Inflation After Planck 2013

We briefly summarize the impact of the recent Planck measurements for string inflationary models, and outline what might be expected to be learned in the near future from the expected improvement in sensitivity to the primordial tensor-to-scalar ratio. We comment on whether these models provide sufficient added value to compensate for their complexity, and ask how they fare in the face of the new constraints on non-gaussianity and dark radiation. We argue that as a group the predictions made before Planck agree well with what has been seen, and draw conclusions from this about what is likely to mean as sensitivity to primordial gravitational waves improves.Comment: LaTeX, 21 pages plus references; slight modification of the discussion of inflection point inflation, references added and typos correcte

The Gravity of Dark Vortices: Effective Field Theory for Branes and Strings Carrying Localized Flux

A Nielsen-Olesen vortex usually sits in an environment that expels the flux that is confined to the vortex, so flux is not present both inside and outside. We construct vortices for which this is not true, where the flux carried by the vortex also permeates the `bulk' far from the vortex. The idea is to mix the vortex's internal gauge flux with an external flux using off-diagonal kinetic mixing. Such `dark' vortices could play a phenomenological role in models with both cosmic strings and a dark gauge sector. When coupled to gravity they also provide explicit ultra-violet completions for codimension-two brane-localized flux, which arises in extra-dimensional models when the same flux that stabilizes extra-dimensional size is also localized on space-filling branes situated around the extra dimensions. We derive simple formulae for observables such as defect angle, tension, localized flux and on-vortex curvature when coupled to gravity, and show how all of these are insensitive to much of the microscopic details of the solutions, and are instead largely dictated by low-energy quantities. We derive the required effective description in terms of a world-sheet brane action, and derive the matching conditions for its couplings. We consider the case where the dimensions transverse to the bulk compactify, and determine how the on- and off-vortex curvatures and other bulk features depend on the vortex properties. We find that the brane-localized flux does not gravitate, but just renormalizes the tension in a magnetic-field independent way. The existence of an explicit UV completion puts the effective description of these models on a more precise footing, verifying that brane-localized flux can be consistent with sensible UV physics and resolving some apparent paradoxes that can arise with a naive (but commonly used) delta-function treatment of the brane's localization within the bulk.Comment: 36 pages + appendices, 7 figure

EFT for Vortices with Dilaton-dependent Localized Flux

We study how codimension-two objects like vortices back-react gravitationally with their environment in theories (such as 4D or higher-dimensional supergravity) where the bulk is described by a dilaton-Maxwell-Einstein system. We do so both in the full theory, for which the vortex is an explicit classical `fat brane' solution, and in the effective theory of `point branes' appropriate when the vortices are much smaller than the scales of interest for their back-reaction (such as the transverse Kaluza-Klein scale). We extend the standard Nambu-Goto description to include the physics of flux-localization wherein the ambient flux of the external Maxwell field becomes partially localized to the vortex, generalizing the results of a companion paper to include dilaton-dependence for the tension and localized flux. In the effective theory, such flux-localization is described by the next-to-leading effective interaction, and the boundary conditions to which it gives rise are known to play an important role in how (and whether) the vortex causes supersymmetry to break in the bulk. We track how both tension and localized flux determine the curvature of the space-filling dimensions. Our calculations provide the tools required for computing how scale-breaking vortex interactions can stabilize the extra-dimensional size by lifting the dilaton's flat direction. For small vortices we derive a simple relation between the near-vortex boundary conditions of bulk fields as a function of the tension and localized flux in the vortex action that provides the most efficient means for calculating how physical vortices mutually interact without requiring a complete construction of their internal structure. In passing we show why a common procedure for doing so using a $\delta$-function can lead to incorrect results. Our procedures generalize straightforwardly to general co-dimension objects.Comment: 45 pages + appendix, 6 figure

Inflating with Large Effective Fields

We re-examine large scalar fields within effective field theory, in particular focussing on the issues raised by their use in inflationary models (as suggested by BICEP2 to obtain primordial tensor modes). We argue that when the large-field and low-energy regimes coincide the scalar dynamics is most effectively described in terms of an asymptotic large-field expansion whose form can be dictated by approximate symmetries, which also help control the size of quantum corrections. We discuss several possible symmetries that can achieve this, including pseudo-Goldstone inflatons characterized by a coset $G/H$ (based on abelian and non-abelian, compact and non-compact symmetries), as well as symmetries that are intrinsically higher dimensional. Besides the usual trigonometric potentials of Natural Inflation we also find in this way simple {\em large-field} power laws (like $V \propto \phi^2$) and exponential potentials, $V(\phi) = \sum_{k} V_k \; e^{-k \phi/M}$. Both of these can describe the data well and give slow-roll inflation for large fields without the need for a precise balancing of terms in the potential. The exponential potentials achieve large $r$ through the limit $|\eta| \ll \epsilon$ and so predict $r \simeq \frac83(1-n_s)$; consequently $n_s \simeq 0.96$ gives $r \simeq 0.11$ but not much larger (and so could be ruled out as measurements on $r$ and $n_s$ improve). We examine the naturalness issues for these models and give simple examples where symmetries protect these forms, using both pseudo-Goldstone inflatons (with non-abelian non-compact shift symmetries following familiar techniques from chiral perturbation theory) and extra-dimensional models.Comment: 21 pages + appendices, 3 figure