On the Matrix Description of Calabi-Yau Compactifications
Explore the source record for details and available documents.
Kachru, S.↗
SEARCH · Engineering Papers
Results for “COMPACTIFICATION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Self-Dual Nonsupersymmetric Type II String Compactifications
Explore the source record for details and available documents.
Kachru, S.↗
Extended Objects from Warped Compactifications of M Theory
Explore the source record for details and available documents.
Silverstein, E.↗
Lectures on Warped Compactifications and Stringy Brane Constructions
Explore the source record for details and available documents.
Kachru, S.↗
Quantum distillation of Hilbert spaces, semi-classics and anomaly matching
A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the state-sum, without affecting the ground states; we call this effect “quantum distillation”. Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under S 1 compactification. We revisit this point via the ’t Hooft anomaly matching condition when it constrains the vacuum structure of the theory on $\mathbb{R} $ d and upon compactification. We show that there is a precise relation between the persistence of the anomaly upon compactification, the Hilbert space quantum distillation, and the semi-classical analysis of the corresponding symmetry-twisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its non-trivial action in QFT, with the example of the 2D Grassmannian sigma model Gr(N, M). We also discuss the connection of quantum distillation with large-N volume independence and flavor-momentum transmutation.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
String theory and grand unification suggest a submicroelectronvolt QCD axion
Axions, grand unification, and string theory are each compelling extensions of the Standard Model. We show that combining these frameworks imposes strong constraints on the QCD axion mass. Using perturbative unitarity arguments and explicit string compactifications—such as those from the Kreuzer-Skarke (KS) type IIB ensemble—we find that the axion mass is favored to lie within the range 10 −11 eV ≲ 𝑚 𝑎 ≲ 10 −8 eV. This range is directly relevant for near-future axion dark matter searches, including ABRACADABRA/DMRadio and CASPEr. We argue that grand unification and the absence of proton decay suggest a compactification volume that keeps the string scale above the unification scale ( ∼ 10 16 GeV), which in turn limits how heavy the axion can be. The same requirements limit the KS axiverse to have at most ∼ 47 axions. As an additional application of our methodology, we search for axions in the KS axiverse that could explain the recent Dark Energy Spectroscopic Instrument hints of evolving dark energy but find none with high enough decay constant (𝑓 𝑎 ≳ 2.5 ×10 17 GeV); we comment on why such high decay constants and low axion masses are difficult to obtain in string compactifications more broadly.
Axions↗
Cluster Expansion and Resurgence in the Polyakov Model
In the Polyakov model, a nonperturbative mass gap is formed at leading-order semiclassics by instanton effects. By using the notions of critical points at infinity, cluster expansion, and Lefschetz thimbles, we show that a third-order effect in semiclassics gives an imaginary ambiguous contribution to the mass gap, which is supposed to be real and unambiguous. This is troublesome for the original analysis, and it is difficult to resolve this issue directly in quantum field theory (QFT). However, we find a new compactification of the Polyakov model to quantum mechanics, by using a background ’t Hooft flux. The compactification has the merit of remembering the monopole instantons of the full QFT within Born-Oppenheimer approximation, while the periodic compactification does not. In the quantum mechanical limit, we prove the resurgent cancellation of the ambiguity in three-instanton sector against ambiguity in the Borel resummation of the perturbation theory around one instanton. Assuming that this result holds in QFT, we provide a large-order asymptotics of perturbation theory around perturbative vacuum and instanton.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Flux flattening in axion monodromy inflation
String theory models of axion monodromy inflation exhibit scalar potentials which are quadratic for small values of the inflaton field and evolve to a more complicated function for large field values. Oftentimes the large field behaviour is gentler than quadratic, lowering the tensor-to-scalar ratio. This effect, known as flattening, has been observed in the string theory context through the properties of the DBI+CS D-brane action. We revisit such flattening effects in type IIB flux compactifications with mobile D7-branes, with the inflaton identified with the D7-brane position. We observe that here, with a generic choice of background fluxes, flattening effects are larger than previously observed, allowing to fit these models within current experimental bounds. In particular, we compute the cosmological observables in scenarios compatible with closed-string moduli stabilisation, finding tensor-to-scalar ratios as low as r ~ 0.04. These are models of single field inflation in which the inflaton is much lighter than the other scalars through a mild tuning of the compactification data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Generalising G 2 geometry: involutivity, moment maps and moduli
We analyse the geometry of generic Minkowski N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E 7(7) × $\mathbb{R}$ + generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E 7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G 2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G 2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
PQ axiverse
We show that the strong CP problem is solved in a large class of compactifications of string theory. The Peccei-Quinn mechanism solves the strong CP problem if the CP-breaking effects of the ultraviolet completion of gravity and of QCD are small compared to the CP-preserving axion potential generated by low-energy QCD instantons. We characterize both classes of effects. To understand quantum gravitational effects, we consider an ensemble of flux compactifications of type IIB string theory on orientifolds of Calabi-Yau hypersurfaces in the geometric regime, taking a simple model of QCD on D7-branes. We show that the D-brane instanton contribution to the neutron electric dipole moment falls exponentially in N 4 , with N the number of axions. In particular, this contribution is negligible in all models in our ensemble with N > 17. We interpret this result as a consequence of large N effects in the geometry that create hierarchies in instanton actions and also suppress the ultraviolet cutoff. We also compute the CP breaking due to high-energy instantons in QCD. In the absence of vectorlike pairs, we find contributions to the neutron electric dipole moment that are not excluded, but that could be accessible to future experiments if the scale of supersymmetry breaking is sufficiently low. The existence of vectorlike pairs can lead to a larger dipole moment. Finally, we show that a significant fraction of models are allowed by standard cosmological and astrophysical constraints.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Weak gravity conjecture, multiple point principle and the standard model landscape
The requirement for an ultraviolet completable theory to be well-behaved upon compactification has been suggested as a guiding principle for distinguishing the landscape from the swampland. Motivated by the weak gravity conjecture and the multiple point principle, we investigate the vacuum structure of the standard model compactified on S 1 and T 2 . The measured value of the Higgs mass implies, in addition to the electroweak vacuum, the existence of a new vacuum where the Higgs field value is around the Planck scale. We explore two- and three-dimensional critical points of the moduli potential arising from compactifications of the electroweak vacuum as well as this high scale vacuum, in the presence of Majorana/Dirac neutrinos and/or axions. We point out potential sources of instability for these lower dimensional critical points in the standard model landscape. We also point out that a high scale AdS 4 vacuum of the Standard Model, if exists, would be at odd with the conjecture that all non-supersymmetric AdS vacua are unstable. We argue that, if we require a degeneracy between three- and four-dimensional vacua as suggested by the multiple point principle, the neutrinos are predicted to be Dirac, with the mass of the lightest neutrino ≈O(1–10) meV, which may be tested by future CMB, large scale structure and 21cm line observations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The F-theory geometry with most flux vacua
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold M max gives rise to O(10 272,000 ) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O(10 –3000 ). The fourfold M max arises from a generic elliptic fibration over a specific toric threefold base B max , and gives a geometrically non-Higgsable gauge group of E 8 9 × F 4 8 × (G 2 × SU(2)) 16 , of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in M max , or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E 8 factor. Furthermore, the results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on M max .
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
On the possibility of large axion moduli spaces
We study the diameters of axion moduli spaces, focusing primarily on type IIB compactifications on Calabi-Yau three-folds. In this case, we derive a stringent bound on the diameter in the large volume region of parameter space for Calabi-Yaus with simplicial Kähler cone. This bound can be violated by Calabi-Yaus with non-simplicial Kähler cones, but additional contributions are introduced to the effective action which can restrict the field range accessible to the axions. We perform a statistical analysis of simulated moduli spaces, finding in all cases that these additional contributions restrict the diameter so that these moduli spaces are no more likely to yield successful inflation than those with simplicial Kähler cone or with far fewer axions. Further heuristic arguments for axions in other corners of the duality web suggest that the difficulty observed in http://dx.doi.org/10.1088/1475-7516/2003/06/001 of finding an axion decay constant parametrically larger than M{sub p} applies not only to individual axions, but to the diagonals of axion moduli space as well. This observation is shown to follow from the weak gravity conjecture of http://dx.doi.org/10.1088/1126-6708/2007/06/060, so it likely applies not only to axions in string theory, but also to axions in any consistent theory of quantum gravity.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Atlas of solar hidden photon emission
Hidden photons, gauge bosons of a U(1) symmetry of a hidden sector, can constitute the dark matter of the universe and a smoking gun for large volume compactifications of string theory. In the sub-eV mass range, a possible discovery experiment consists on searching the copious flux of these particles emitted from the Sun in a helioscope setup à la Sikivie. In this paper, we compute in great detail the flux of HPs from the Sun, a necessary ingredient for interpreting such experiments. We provide a detailed exposition of transverse photon-HP oscillations in inhomogenous media, with special focus on resonance oscillations, which play a leading role in many cases. The region of the Sun emitting HPs resonantly is a thin spherical shell for which we justify an averaged-emission formula and which implies a distinctive morphology of the angular distribution of HPs on Earth in many cases. Low mass HPs with energies in the visible and IR have resonances very close to the photosphere where the solar plasma is not fully ionised and requires building a detailed model of solar refraction and absorption. We present results for a broad range of HP masses (from 0–1 keV) and energies (from the IR to the X-ray range), the most complete atlas of solar HP emission to date.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Calculations of inflaton decays and reheating: with applications to no-scale inflation models
We discuss inflaton decays and reheating in no-scale Starobinsky-like models of inflation, calculating the effective equation-of-state parameter, w, during the epoch of inflaton decay, the reheating temperature, T{sub reh}, and the number of inflationary e-folds, N{sub ∗}, comparing analytical approximations with numerical calculations. We then illustrate these results with applications to models based on no-scale supergravity and motivated by generic string compactifications, including scenarios where the inflaton is identified as an untwisted-sector matter field with direct Yukawa couplings to MSSM fields, and where the inflaton decays via gravitational-strength interactions. Finally, we use our results to discuss the constraints on these models imposed by present measurements of the scalar spectral index n{sub s} and the tensor-to-scalar perturbation ratio r, converting them into constraints on N{sub ∗}, the inflaton decay rate and other parameters of specific no-scale inflationary models.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Constraints on axion inflation from the weak gravity conjecture
We derive constraints facing models of axion inflation based on decay constant alignment from a string-theoretic and quantum gravitational perspective. In particular, we investigate the prospects for alignment and ‘anti-alignment’ of C{sub 4} axion decay constants in type IIB string theory, deriving a strict no-go result in the latter case. We discuss the relationship of axion decay constants to the weak gravity conjecture and demonstrate agreement between our string-theoretic constraints and those coming from the ‘generalized’ weak gravity conjecture. Finally, we consider a particular model of decay constant alignment in which the potential of C{sub 4} axions in type IIB compactifications on a Calabi-Yau three-fold is dominated by contributions from D7-branes, pointing out that this model evades some of the challenges derived earlier in our paper but is highly constrained by other geometric considerations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Starobinsky-type inflation from α{sup ′}-corrections
Working in the Large Volume Scenario (LVS) of IIB Calabi-Yau flux compactifications, we construct inflationary models from recently computed higher derivative (α{sup ′}){sup 3}-corrections. Inflation is driven by a Kähler modulus whose potential arises from the aforementioned corrections, while we use the inclusion of string loop effects just to ensure the existence of a graceful exit when necessary. The effective inflaton potential takes a Starobinsky-type form V=V{sub 0}(1−e{sup −νϕ}){sup 2}, where we obtain one set-up with ν=−1/√3 and one with ν=2/√3 corresponding to inflation occurring for increasing or decreasing ϕ respectively. The inflationary observables are thus in perfect agreement with PLANCK, while the two scenarios remain observationally distinguishable via slightly varying predictions for the tensor-to-scalar ratio r. Both set-ups yield r≃(2…7) ×10{sup −3}. They hence realise inflation with moderately large fields (Δϕ∼6 M{sub Pl}) without saturating the Lyth bound. Control over higher corrections relies in part on tuning underlying microscopic parameters, and in part on intrinsic suppressions. The intrinsic part of control arises as a leftover from an approximate effective shift symmetry at parametrically large volume.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
New model of axion monodromy inflation and its cosmological implications
We propose a new realization of axion monodromy inflation in which axion monodromy arises from torsional cycles in a type IIB compactification. A class of monomial potentials is obtained with specific values for the power index. Moreover, the inflaton mass changes profile due to the couplings between various fields after compactification. Consequently, the potential obtains a step-like profile at some critical scale. We study the cosmological implications of one concrete realization of this model. At the background level, it realizes a sufficiently long inflationary stage, which allows for the violation of the slow-roll conditions for a short period of time when the inflaton is close to the critical scale. Accordingly, the Hubble horizon is perturbed and affects the dynamics of primordial cosmological perturbations. In particular, we analyze the angular power spectrum of B-mode polarization and find a boost on very large scales. We also find that the amplitude of scalar perturbations is suppressed near the critical scale. Thus our model provides an interpretation for the low-ℓ suppression of temperature anisotropies in the CMB power spectrum. We examine these effects and confront the model to observations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗