We study the landscape of axion theories in compactifications of type IIB string theory on orientifolds of Calabi-Yau threefolds. In a sample of approximately 400,000 geometries we find that in the regime of perturbative control there are only a handful of distinct axion minima per geometry, despite there being infinitely many instanton contributions to the potential with unbounded charges. The ensemble we consider has numbers of axion fields ranging from 1 to 491, but the median number of distinct minima is 1, the mean number is 1.9 and the largest is 54. These small numbers of minima occur because the leading axion charge matrix is quite sparse, while the subleading corrections are increasingly exponentially suppressed as the charges increase. On their own, such potentials are nowhere near rich enough to be of interest anthropically. This is in stark contrast to potentials for which the charge matrix is less sparse or the hierarchies between the instanton contributions are less steep, where one can find $$ \mathcal{O}\left({10}^{500}\right) $$ minima for $$ \mathcal{O}(500) $$ axions. To generate a sufficiently large landscape from string compactifications our results indicate that one would need to rely on varying flux or topology, or to develop tools that allow one to go beyond the regime we can control with current techniques.

United States

Naomi Gendler

Italy

Switzerland

Oliver Janssen

Matthew Kleban

Joan Madrid

Germany

Viraf Mehta

Axion minima in string theory

<p>During slow-roll inflation, nonperturbative transitions can produce bubbles of metastable vacuum. These bubbles expand exponentially during inflation to superhorizon size, and later collapse into black holes when the expansion of the Universe is decelerating. Estimating the rate for these transitions during a time-dependent slow-roll phase requires the development of new techniques. Our results show that in a broad class of models, the inflationary fine-tuning that gives rise to small density fluctuations causes these bubbles to appear only during a time interval that is short compared to the inflationary Hubble time. As a result, despite the fact that the final mass of the black hole is exponentially sensitive to the moment bubbles form during inflation, the resulting primordial black hole mass spectrum can be nearly monochromatic. If the transition occurs near the middle of inflation, the mass can fall in the “asteroid” range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>17</mn></msup><mi>–</mi><msup><mn>10</mn><mn>22</mn></msup><mtext> </mtext><mtext> </mtext><mi mathvariant="normal">g</mi></math> in which all known observations are compatible with black holes comprising 100% of dark matter.</p>

Cameron Norton

Monochromatic mass spectrum of primordial black holes

The Brownian loop soup (BLS) is a conformally invariant statistical ensemble of random loops in two dimensions characterized by an intensity λ &gt; 0. Recently, we constructed families of operators in the BLS and showed that they transform as conformal primary operators. In this paper we provide an explicit expression for the BLS stress-energy tensor and compute its operator product expansion with other operators. Our results are consistent with the conformal Ward identities and our previous result that the central charge is c = 2λ. In the case of domains with boundary we identify a boundary operator that has properties consistent with the boundary stress-energy tensor. We show that this operator generates local deformations of the boundary and that it is related to a boundary operator that induces a Brownian excursion starting or ending at its insertion point.

United Arab Emirates

Netherlands

Federico Camia

Valentino Foit

Alberto Gandolfi

The Brownian loop soup stress-energy tensor

Electric fields can spontaneously decay via the Schwinger effect, the nucleation of a charged particle-anti particle pair separated by a critical distance d. What happens if the available distance is smaller than d? Previous work on this question has produced contradictory results. Here, we study the quantum evolution of electric fields when the field points in a compact direction with circumference L &lt; d using the massive Schwinger model, quantum electrodynamics in one space dimension with massive charged fermions. We uncover a new and previously unknown set of instantons that result in novel physics that disagrees with all previous estimates. In parameter regimes where the field value can be well-defined in the quantum theory, generic initial fields E are in fact stable and do not decay, while initial values that are quantized in half-integer units of the charge E = (k/2)g with k ∈ ℤ oscillate in time from +(k/2)g to −(k/2)g, with exponentially small probability of ever taking any other value. We verify our results with four distinct techniques: numerically by measuring the decay directly in Lorentzian time on the lattice, numerically using the spectrum of the Hamiltonian, numerically and semi-analytically using the bosonized description of the Schwinger model, and analytically via our instanton estimate.

Xu-Yao Hu

Cedric Yu

Electric field decay without pair production: lattice, bosonization and novel worldline instantons

We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system known as the Brownian Loop Soup. These correlation functions depend on multiple continuous parameters: the insertion points of the operators, the intensity of the soup, and the charges of the operators. In the case of the four-point function there is non-trivial dependence on five continuous parameters: the cross-ratio, the intensity, and three real charges. The four-point function is crossing symmetric. We analyze its conformal block expansion and discover a previously unknown set of new conformal primary operators.

Exact correlation functions in the Brownian Loop Soup

We study the dynamics of the massive Schwinger model on a lattice using exact diagonalization. When periodic boundary conditions are imposed, analytic arguments indicate that a nonzero electric flux in the initial state can “unwind” and decrease to a minimum value equal to minus its initial value, due to the effects of a pair of charges that repeatedly traverse the spatial circle. Our numerical results support the existence of this flux unwinding phenomenon, both for initial states containing a charged pair inserted by hand, and when the charges are produced by Schwinger pair production. We also study boundary conditions where charges are confined to an interval and flux unwinding cannot occur, and the massless limit, where our results agree with the predictions of the bosonized description of the Schwinger model.

China

Chris Nagele

J. Eduardo Cejudo

Japan

Tim Byrnes

Flux unwinding in the lattice Schwinger model

We describe a systematic framework for periodic potentials of arbitrary dimension, such as those governing multiple axions. A novel type of alignment renders even complex theories analytically tractable. Theories with <math><mo>∼</mo><mn>100</mn></math> axions and random parameters have an exponential number of metastable vacua. Decay from a metastable minimum can occur via a thin-wall instanton and allows for a sufficient period of slow-roll inflation that ends in a vacuum containing axion dark matter and a cosmological constant, both consistent with current observations. Hence, this model can reproduce many macroscopic features of our Universe without tuned parameters.

Thomas C. Bachlechner

Kate Eckerle

Multiple-axion framework

We describe a novel technique that renders theories of N axions tractable, and more generally can be used to efficiently analyze a large class of periodic potentials of arbitrary dimension. Such potentials are complex energy landscapes with a number of local minima that scales as  <math><msqrt><mrow><mi>N</mi><mo>!</mo></mrow></msqrt></math> $$ \sqrt{N!} $$, and so for large N appear to be analytically and numerically intractable. Our method is based on uncovering a set of approximate symmetries that exist in addition to the N periods. These approximate symmetries, which are exponentially close to exact, allow us to locate the minima very efficiently and accurately and to analyze other characteristics of the potential. We apply our framework to evaluate the diameters of flat regions suitable for slow-roll inflation, which unifies, corrects and extends several forms of “axion alignment” previously observed in the literature. We find that in a broad class of random theories, the potential is smooth over diameters enhanced by N 3/2 compared to the typical scale of the potential. A Mathematica implementation of our framework is available online.

Thomas Bachlechner

Systematics of aligned axions

In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that arbitrarily inhomogeneous and anisotropic cosmologies with ``flat'' (including toroidal) and ``open'' (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some region at a rate bounded from below by a positive number, despite the presence of arbitrarily large density fluctuations and/or the formation of black holes. Because the set of 3-manifold topologies is countable, a single integer determines the ultimate fate of the universe, and, in a specific sense, most 3-manifolds are ``flat'' or ``open''. Our result has important implications for inflation: if there is a positive cosmological constant (or suitable inflationary potential) and initial conditions for the inflaton, cosmologies with ``flat'' or ``open'' topology must expand forever in some region at least as fast as de Sitter space, and are therefore very likely to begin inflationary expansion eventually, regardless of the scale of the inflationary energy or the spectrum and amplitude of initial inhomogeneities and gravitational waves. Our result is also significant for numerical general relativity, which often makes use of periodic (toroidal) boundary conditions.

Leonardo Senatore

Inhomogeneous anisotropic cosmology

Using numerical solutions of the full Einstein field equations coupled to a scalar inflaton field in 3+1 dimensions, we study the conditions under which a universe that is initially expanding, highly inhomogeneous and dominated by gradient energy can transition to an inflationary period. If the initial scalar field variations are contained within a sufficiently flat region of the inflaton potential, and the universe is spatially flat or open on average, inflation will occur following the dilution of the gradient and kinetic energy due to expansion. This is the case even when the scale of the inhomogeneities is comparable to the initial Hubble length, and overdense regions collapse and form black holes, because underdense regions continue expanding, allowing inflation to eventually begin. This establishes that inflation can arise from highly inhomogeneous initial conditions and solve the horizon and flatness problems, at least as long as the variations in the scalar field do not include values that exceed the inflationary plateau.