arXiv subjects

Liam McAllister

Publications and source records attributed to Liam McAllister.

At least 55 records · Page 3Linked to original sources

arXiv2014

Drifting Oscillations in Axion Monodromy

We study the pattern of oscillations in the primordial power spectrum in axion monodromy inflation, accounting for drifts in the oscillation period that can be important for comparing to cosmological data. In these models the potential energy has a monomial form over a super-Planckian field range, with superimposed modulations whose size is model-dependent. The amplitude and frequency of the modulations are set by the expectation values of moduli fields. We show that during the course of inflation, the diminishing energy density can induce slow adjustments of the moduli, changing the modulations. We provide templates capturing the effects of drifting moduli, as well as drifts arising in effective field theory models based on softly broken discrete shift symmetries, and we estimate the precision required to detect a drifting period. A non-drifting template suffices over a wide range of parameters, but for the highest frequencies of interest, or for sufficiently strong drift, it is necessary to include parameters characterizing the change in frequency over the e-folds visible in the CMB. We use these templates to perform a preliminary search for drifting oscillations in a part of the parameter space in the Planck nominal mission data.

hep-th↗

arXiv2014

Planckian Axions in String Theory

We argue that super-Planckian diameters of axion fundamental domains can naturally arise in Calabi-Yau compactifications of string theory. In a theory with $N$ axions $θ^i$, the fundamental domain is a polytope defined by the periodicities of the axions, via constraints of the form $-π \sqrt{N}$. This result is robust in the presence of $P>N$ constraints, while for $P=N$ the diameter is further enhanced by eigenvector delocalization to $N^{3/2}f_N$. We directly verify our results in explicit Calabi-Yau compactifications of type IIB string theory. In the classic example with $h^{1,1}=51$ where parametrically controlled moduli stabilization was demonstrated by Denef et al. in [1], the largest metric eigenvalue obeys $f_N \approx 0.013 M_{pl}$. The random matrix analysis then predicts, and we exhibit, axion diameters $>M_{pl}$ for the precise vacuum parameters found in [1]. Our results provide a framework for achieving large-field axion inflation in well-understood flux vacua.

hep-th↗

arXiv2014

Charting an Inflationary Landscape with Random Matrix Theory

We construct a class of random potentials for N >> 1 scalar fields using non-equilibrium random matrix theory, and then characterize multifield inflation in this setting. By stipulating that the Hessian matrices in adjacent coordinate patches are related by Dyson Brownian motion, we define the potential in the vicinity of a trajectory. This method remains computationally efficient at large N, permitting us to study much larger systems than has been possible with other constructions. We illustrate the utility of our approach with a numerical study of inflation in systems with up to 100 coupled scalar fields. A significant finding is that eigenvalue repulsion sharply reduces the duration of inflation near a critical point of the potential: even if the curvature of the potential is fine-tuned to be small at the critical point, small cross-couplings in the Hessian cause the curvature to grow in the neighborhood of the critical point.

hep-th↗

arXiv2014

Aligned Natural Inflation in String Theory

We propose a scenario for realizing super-Planckian axion decay constants in Calabi-Yau orientifolds of type IIB string theory, leading to large-field inflation. Our construction is a simple embedding in string theory of the mechanism of Kim, Nilles, and Peloso, in which a large effective decay constant arises from alignment of two smaller decay constants. The key ingredient is gaugino condensation on magnetized or multiply-wound D7-branes. We argue that, under very mild assumptions about the topology of the Calabi-Yau, there are controllable points in moduli space with large effective decay constants.

hep-th↗

arXiv2014

The Powers of Monodromy

Flux couplings to string theory axions yield super-Planckian field ranges along which the axion potential energy grows. At the same time, other aspects of the physics remain essentially unchanged along these large displacements, respecting a discrete shift symmetry with a sub-Planckian period. After a general overview of this monodromy effect and its application to large-field inflation, we present new classes of specific models of monodromy inflation, with monomial potentials $μ^{4-p}ϕ^p$. A key simplification in these models is that the inflaton potential energy plays a leading role in moduli stabilization during inflation. The resulting inflaton-dependent shifts in the moduli fields lead to an effective flattening of the inflaton potential, i.e. a reduction of the exponent from a fiducial value $p_0$ to $p<p_0$. We focus on examples arising in compactifications of type IIB string theory on products of tori or Riemann surfaces, where the inflaton descends from the NS-NS two-form potential $B_2$, with monodromy induced by a coupling to the R-R field strength $F_1$. In this setting we exhibit models with $p=2/3,4/3,2,$ and $3$, corresponding to predictions for the tensor-to-scalar ratio of $r\approx 0.04, 0.09, 0.13,$ and $0.2$, respectively. Using mirror symmetry, we also motivate a second class of examples with the role of the axions played by the real parts of complex structure moduli, with fluxes inducing monodromy.

hep-th↗

arXiv2014

Heavy Tails in Calabi-Yau Moduli Spaces

We study the statistics of the metric on Kähler moduli space in compactifications of string theory on Calabi-Yau hypersurfaces in toric varieties. We find striking hierarchies in the eigenvalues of the metric and of the Riemann curvature contribution to the Hessian matrix: both spectra display heavy tails. The curvature contribution to the Hessian is non-positive, suggesting a reduced probability of metastability compared to cases in which the derivatives of the Kähler potential are uncorrelated. To facilitate our analysis, we have developed a novel triangulation algorithm that allows efficient study of hypersurfaces with $h^{1,1}$ as large as 25, which is difficult using algorithms internal to packages such as Sage. Our results serve as input for statistical studies of the vacuum structure in flux compactifications, and of the distribution of axion decay constants in string theory.

hep-th↗

arXiv2014

A New Angle on Chaotic Inflation

N-flation is a radiatively stable scenario for chaotic inflation in which the displacements of $N \gg 1$ axions with decay constants $f_1 \le \ldots \le f_N < M_P$ lead to a super-Planckian effective displacement equal to the Pythagorean sum $f_{Py}$ of the $f_i$. We show that mixing in the axion kinetic term generically leads to the phenomenon of kinetic alignment, allowing for effective displacements as large as $\sqrt{N} f_{N} \ge f_{Py}$, even if $f_1, \ldots, f_{N-1}$ are arbitrarily small. At the level of kinematics, the necessary alignment occurs with very high probability, because of eigenvector delocalization. We present conditions under which inflation can take place along an aligned direction. Our construction sharply reduces the challenge of realizing N-flation in string theory.

hep-th↗

arXiv2014

Inflation and String Theory

We review cosmological inflation and its realization in quantum field theory and in string theory. This material is a portion of a book, also entitled "Inflation and String Theory", to be published by Cambridge University Press.

hep-th↗

arXiv2013

On Moduli Spaces in $\bf{AdS_4}$ Supergravity

We study the structure of the supersymmetric moduli spaces of ${\cal N}=1$ and ${\cal N}=2$ supergravity theories in $AdS_4$ backgrounds. In the ${\cal N}=1$ case, the moduli space cannot be a complex submanifold of the Kähler field space, but is instead real with respect to the inherited complex structure. In ${\cal N}=2$ supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a Kähler submanifold of the quaternionic-Kähler field space. These findings are in agreement with AdS/CFT considerations.

hep-th↗

arXiv2013

On Chiral Mesons in AdS/CFT

We analyze the spectra of non-chiral and chiral bifundamental mesons arising on intersecting D7-branes in $AdS_{5}\times S^{5}$. In the absence of magnetic flux on the curve of intersection, the spectrum is non-chiral, and the dual gauge theory is conformal in the quenched/probe approximation. For this case we calculate the dimensions of the bifundamental mesonic operators. We then consider magnetization of the D7-branes, which deforms the dual theory by an irrelevant operator and renders the mesons chiral. The magnetic flux spoils the conformality of the dual theory, and induces a D3-brane charge that becomes large in the ultraviolet, where the non-normalizable bifundamental modes are rapidly divergent. An ultraviolet completion is therefore necessary to calculate the correlation functions in the chiral case. On the other hand, the normalizable modes are very well localized in the infrared, leading to new possibilities for local model-building on intersecting D7-branes in warped geometries.

hep-th↗

arXiv2013

D-brane Bremsstrahlung

We study the dynamics of ultrarelativistic D-branes. The dominant phenomenon is bremsstrahlung: mild acceleration induced by closed string interactions triggers extremely rapid energy loss through radiation of massless closed strings. After characterizing bremsstrahlung from a general k-dimensional extended object in a D-dimensional spacetime, we incorporate effects specific to D-branes, including velocity-dependent forces and open string pair creation. We then show that dissipation due to bremsstrahlung can substantially alter the dynamics in DBI inflation.

hep-th↗

arXiv2013

Planck-Suppressed Operators

We show that the recent Planck limits on primordial non-Gaussianity impose strong constraints on light hidden sector fields coupled to the inflaton via operators suppressed by a high mass scale Λ. We study a simple effective field theory in which a hidden sector field is coupled to a shift-symmetric inflaton via arbitrary operators up to dimension five. Self-interactions in the hidden sector lead to non-Gaussianity in the curvature perturbations. To be consistent with the Planck limit on local non-Gaussianity, the coupling to any hidden sector with light fields and natural cubic couplings must be suppressed by a very high scale Λ> 10^5 H. Even if the hidden sector has Gaussian correlations, nonlinearities in the mixing with the inflaton still lead to non-Gaussian curvature perturbations. In this case, the non-Gaussianity is of the equilateral or orthogonal type, and the Planck data requires Λ> 10^2 H.

hep-th↗

arXiv2012

A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll

We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects, in which three or more fields influence the perturbations, are often important. However, in a large fraction of models consistent with constraints on the tilt the signatures of multifield evolution occur on unobservably large scales. Our scenario is a concrete microphysical realization of quasi-single-field inflation, with scalar masses of order $H$, but the cubic and quartic couplings are typically too small to produce detectable non-Gaussianity. We argue that our results are characteristic of a broader class of models arising from multifield potentials that are natural in the Wilsonian sense.

astro-ph.CO↗

arXiv2012

Supersymmetric Vacua in Random Supergravity

We determine the spectrum of scalar masses in a supersymmetric vacuum of a general N=1 supergravity theory, with the Kahler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P = exp(-2N^2|W|^2/m_{susy}^2), with W denoting the superpotential and m_{susy} the supersymmetric mass scale; for more general distributions of the entries, our result is accurate when N >> 1. We conclude that for |W| \gtrsim m_{susy}/N, tachyonic instabilities are ubiquitous in configurations obtained by uplifting supersymmetric vacua.

hep-th↗

arXiv2012

The Wasteland of Random Supergravities

We show that in a general \cal{N} = 1 supergravity with N \gg 1 scalar fields, an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking the superpotential and Kahler potential to be random functions, we construct a random matrix model for the Hessian matrix, which is well-approximated by the sum of a Wigner matrix and two Wishart matrices. We compute the eigenvalue spectrum analytically from the free convolution of the constituent spectra and find that in typical configurations, a significant fraction of the eigenvalues are negative. Building on the Tracy-Widom law governing fluctuations of extreme eigenvalues, we determine the probability P of a large fluctuation in which all the eigenvalues become positive. Strong eigenvalue repulsion makes this extremely unlikely: we find P \propto exp(-c N^p), with c, p being constants. For generic critical points we find p \approx 1.5, while for approximately-supersymmetric critical points, p \approx 1.3. Our results have significant implications for the counting of de Sitter vacua in string theory, but the number of vacua remains vast.

hep-th↗

arXiv2011

Challenges for String Cosmology

We critically assess the twin prospects of describing the observed universe in string theory, and using cosmological experiments to probe string theory. For the purposes of this short review, we focus on the limitations imposed by our incomplete understanding of string theory. After presenting an array of significant obstacles, we indicate a few areas that may admit theoretical progress in the near future.

hep-th↗

arXiv2011

A Toolkit for Perturbing Flux Compactifications

We develop a perturbative expansion scheme for solving general boundary value problems in a broad class of type IIB flux compactifications. The background solution is any conformally Calabi-Yau compactification with imaginary self-dual (ISD) fluxes. Upon expanding in small deviations from the ISD solution, the equations of motion simplify dramatically: we find a simple basis in which the n-th order equations take a triangular form. This structure implies that the system can be solved iteratively whenever the individual, uncoupled equations can be solved. We go on to demonstrate the solution of the system for a general warped Calabi-Yau cone: we present an algorithm that yields an explicit Green's function solution for all the supergravity fields, to any desired order, in terms of the harmonic functions on the base of the cone. Our results provide a systematic procedure for obtaining the corrections to a warped throat geometry induced by attachment to a compact bulk. We also present a simple method for determining the sizes of physical effects mediated through warped geometries.

hep-th↗

arXiv2011

Dynamic SU(2) Structure from Seven-branes

We obtain a family of supersymmetric solutions of type IIB supergravity with dynamic SU(2) structure, which describe the local geometry near a stack of four D7-branes and one O7-plane wrapping a rigid four-cycle. The deformation to a generalized complex geometry is interpreted as a consequence of nonperturbative effects in the seven-brane gauge theory. We formulate the problem for seven-branes wrapping the base of an appropriate del Pezzo cone, and in the near-stack limit in which the four-cycle is flat, we obtain an exact solution in closed form. Our solutions serve to characterize the local geometry of nonperturbatively-stabilized flux compactifications.

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