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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Physical Yukawa couplings in heterotic string compactifications

One of the challenges of heterotic compactification on a CalabiYau threefold is to determine the physical (27) 3 Yukawa couplings of the resulting four-dimensional $\mathcal{N}$ = 1 theory. In general, the calculation necessitates knowledge of the Ricci-flat metric. However, in the standard embedding, which references the tangent bundle, we can compute normalized Yukawa couplings from the Weil-Petersson metric on the moduli space of complex structure deformations of the Calabi-Yau manifold. In various examples (the Fermat quintic, the intersection of two cubics in $\mathbb{P}$ 5 , and the TianYau manifold), we calculate the normalized Yukawa couplings for (2,1)-forms using the Weil-Petersson metric obtained from the Kodaira-Spencer map. In cases where $h^{1,1}$ = 1 , this is compared to a complementary calculation based on performing period integrals. A third expression for the normalized Yukawa couplings is obtained from a machine learned approximate Ricci-flat metric making use of explicit harmonic representatives. Finally, the excellent agreement between the different approaches opens the door to precision string phenomenology.

Butbaia, Giorgi↗
DOE OSTI2016

Bubbles of nothing and supersymmetric compactifications

We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such “topologically unobstructed” cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to M{sub 3}×S{sub 1} presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Effects on the CMB from compactification before inflation

Many theories beyond the Standard Model include extra dimensions, though these have yet to be directly observed. In this work we consider the possibility of a compactification mechanism which both allows extra dimensions and is compatible with current observations. This compactification is predicted to leave a signature on the CMB by altering the amplitude of the low l multipoles, dependent on the amount of inflation. Recently discovered CMB anomalies at low multipoles may be evidence for this. In our model we assume the spacetime is the product of a four-dimensional spacetime and flat extra dimensions. Before the compactification, both the four-dimensional spacetime and the extra dimensions can either be expanding or contracting independently. Taking into account physical constraints, we explore the observational consequences and the plausibility of these different models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

BPS equations and non-trivial compactifications

We consider the problem of finding exact, eleven-dimensional, BPS supergravity solutions in which the compactification involves a non-trivial Calabi-Yau manifold, Y, as opposed to simply a T 6 . Since there are no explicitly-known metrics on non-trivial, compact Calabi-Yau manifolds, we use a non-compact “local model” and take the compactification manifold to be Y = M GH × T 2 , where MGH is a hyper-Kähler, Gibbons-Hawking ALE space. We focus on backgrounds with three electric charges in five dimensions and find exact families of solutions to the BPS equations that have the same four supersymmetries as the three-charge black hole. Our exact solution to the BPS system requires that the Calabi-Yau manifold be fibered over the space-time using compensators on Y. The role of the compensators is to ensure smoothness of the eleven-dimensional metric when the moduli of Y depend on the space-time. The Maxwell field Ansatz also implicitly involves the compensators through the frames of the fibration. In conclusion, we examine the equations of motion and discuss the brane distributions on generic internal manifolds that do not have enough symmetry to allow smearing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Time reversal and CP invariance in Calabi-Yau compactifications

We revisit the question of time reversal and CP invariance in Calabi-Yau compactifications. We show that time reversal invariance is respected by quantum corrections to the prepotential. In particular, field independent θ angles whose presence is dictated by requiring integrality of relevant monodromy transformations can take precisely the quantized values compatible with time reversal invariance. Furthermore, monodromy symmetry enlarges the region on moduli space on which time reversal is not spontaneously broken. We define the action of the CP transformation for multi-parameter models and argue that on the slice of moduli space where it is defined, CP> is trivially a symmetry of the theory. For supersymmetric vacua that lie in this slice, we derive a condition on the third cohomology of the compactification manifold which determines whether CPpreserving fluxes exist that stabilize the moduli to such points. In the case of one-parameter models, the condition is always satisfied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Ubiquity of non-geometry in heterotic compactifications

Here, we study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest nontrivial elliptic fibration the effect is quite dramatic: the I 1 degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the T 2 . This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety due to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

Yukawa couplings in superstring compactification

A topological formula is given for the entire tree-level contribution to the low-energy effective action of a Calabi-Yau superstring compactification. The constraints on proton lifetime in the Calabi-Yau compactification are discussed in detail.

Strominger, A.↗
DOE OSTI2018

The global gauge group structure of F-theory compactification with U(1)s

We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell-Weil generators. This results in constraints on the u(1) charges of non-abelian matter consistent with observations made throughout the literature. Specifically, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU( 3 ) × SU( 2 ) × U( 1 )]/Ζ 6 . Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an su(2)⊕u(1) gauge theory can either unhiggs into an SU( 2 ) × SU( 2 ) or an SU( 3 ) × SU( 2 ) theory. We also study implications of the charge constraints as a criterion for the F-theory ‘swampland’.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

The role of singletons in S7 compactifications

We derive the isometry irrep content of squashed seven-sphere compactifications of eleven-dimensional supergravity, i.e., the left-squashed (LS7) with N = 1 and right-squashed (RS7) with N = 0 supersymmetry, in a manner completely independent of the round sphere. Then we compare this result with the spectrum obtained by Higgsing the round sphere spectrum. This way we discover features of the spectra which makes it possible to argue that the only way the round spectrum can be related by a Higgs mechanism to the one of LS7 is if the singletons are included in the round sphere spectrum. For this to work also in the RS7 case it seems that the gravitino of the LS7 spectrum must be replaced by a fermionic singleton present in the RS7 spectrum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

AdS 5 compactifications with punctures in massive IIA supergravity

We find AdS 5 solutions holographically dual to compactifications of six- dimensional N = (1, 0) supersymmetric field theories on Riemann surfaces with punctures. We simplify a previous analysis of supersymmetric AdS 5 IIA solutions, and with a suitable Ansatz we find explicit solutions organized in three classes, where an O8-D8 stack, D6-and D4-branes are simultaneously present, localized and partially localized. The D4-branes are smeared over the Riemann surface and this is interpreted as the presence of a uniform distribution of punctures. For the first class we identify the corresponding six-dimensional theory as an E-string theory coupled to a quiver gauge theory. The second class of solutions lacks D6-branes and its central charge scales as n 5/2 , suggesting a five-dimensional origin for the dual field theory. The last class has elements of the previous two.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Foliated backgrounds for M-theory compactifications (I)

Using the theory of foliations, we give a geometric and topological description of compact eight-manifolds which arise as internal spaces in N = 1 flux compactifications of M-theory down to AdS{sub 3}. We prove that specifying such a supersymmetric background is equivalent with giving a codimension one foliation defined by a closed one-form and which carries a leafwise G{sub 2} structure, whose geometry we characterize explicitly. It can be shown that the leaves of this foliation acquire singularities on the chiral locus, which is a set with empty interior when the equations of motion for the supregravity four-form field strength are imposed, but here we concentrate only on the case of an everywhere non-chiral spinor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

N-flation with hierarchically light axions in string compactifications

We propose a possible embedding of axionic N-flation in type IIB string compactifications where most of the Kähler moduli are stabilised by perturbative effects, and so are hierarchically heavier than the corresponding N>> 1 axions whose collective dynamics drives inflation. This is achieved in the framework of the LARGE Volume Scenario for moduli stabilisation. Our set-up can be used to realise a model of either large field inflation or quintessence, just by varying the volume of the internal space which controls the scale of the axionic potential. Both cases predict a very high scale of supersymmetry breaking. A fully explicit stringy embedding of N-flation would require control over dangerous back-reaction effects due to a large number of species. A viable reheating of the Standard Model degrees of freedom can be achieved after the end of inflation due to the perturbative decay of the N light axions which drive inflation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Correlation between dark matter and dark radiation in string compactifications

Reheating in string compactifications is generically driven by the decay of the lightest modulus which produces Standard Model particles, dark matter and light hidden sector degrees of freedom that behave as dark radiation. This common origin allows us to find an interesting correlation between dark matter and dark radiation. By combining present upper bounds on the effective number of neutrino species N{sub eff} with lower bounds on the reheating temperature as a function of the dark matter mass m{sub DM} from Fermi data, we obtain strong constraints on the (N{sub eff}, m{sub DM})-plane. Most of the allowed region in this plane corresponds to non-thermal scenarios with Higgsino-like dark matter. Thermal dark matter can be allowed only if N{sub eff} tends to its Standard Model value. We show that the above situation is realised in models with perturbative moduli stabilisation where the production of dark radiation is unavoidable since bulk closed string axions remain light and do not get eaten up by anomalous U(1)s.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Can compactifications solve the cosmological constant problem?

Recently, there have been claims in the literature that the cosmological constant problem can be dynamically solved by specific compactifications of gravity from higher-dimensional toy models. These models have the novel feature that in the four-dimensional theory, the cosmological constant Λ is much smaller than the Planck density and in fact accumulates at Λ=0. Here we show that while these are very interesting models, they do not properly address the real cosmological constant problem. As we explain, the real problem is not simply to obtain Λ that is small in Planck units in a toy model, but to explain why Λ is much smaller than other mass scales (and combinations of scales) in the theory. Instead, in these toy models, all other particle mass scales have been either removed or sent to zero, thus ignoring the real problem. To this end, we provide a general argument that the included moduli masses are generically of order Hubble, so sending them to zero trivially sends the cosmological constant to zero. We also show that the fundamental Planck mass is being sent to zero, and so the central problem is trivially avoided by removing high energy physics altogether. On the other hand, by including various large mass scales from particle physics with a high fundamental Planck mass, one is faced with a real problem, whose only known solution involves accidental cancellations in a landscape.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Three-Forms, Supersymmetry and String Compactifications

We review a duality procedure that relates standard matter-coupled N=1 supergravity to dual formulations in which auxiliary fields are replaced by field-strengths of gauge three-forms. As examples, we consider the dualization of the rigid Polonyi model and of effective field theories associated with Type IIA string compactifications with fluxes in supergravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Compactifications of deformed conifolds, branes and the geometry of qubits $\mathfrak S

We present three families of exact, cohomogeneity-one Einstein metrics in (2n + 2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces CP n+1 , written in a Stenzel form, whose principal orbits are the Stiefel manifolds V 2 ($\mathbb R^{2+3}$) = SO(n+2)/SO(n) divided by Z 2 . The second family are also Einstein-Kahler metrics, now on the Grassmannian manifolds G 2 (R n+3 ) = SO(n+3)/((SO(n+1)×SO(2)), whose principal orbits are the Stiefel manifolds V 2 ($\mathbb R^{2+3}$) (with no Z 2 factoring in this case). Furthermore, the third family are Einstein metrics on the product manifolds S n+1 × S n+1 , and are Kahler only for n = 1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. Also, we elaborate on the geometric approach to quantum mechanics based on the Kahler geometry of Fubini-Study metrics on $\mathbb CP^{n+1}$, and we apply the formalism to study the quantum entanglement of qubits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Three-family particle physics models from global F-theory compactifications

We construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and the Trinification Model. These models result from compactification on toric hypersurface fibrations X with the choice of base $\mathbb P^{3}$. We observe that the F-theory conditions on the G 4 -flux restrict the number of families to be at least three. We comment on the phenomenology of the models, and for Pati-Salam and Trinification models discuss the Higgsing to the Standard Model. A central point of this work is the construction of globally consistent G 4 -flux. For this purpose we compute the vertical cohomology H V (2,2) (X) in each case and solve the conditions imposed by matching the M- and F-theoretical 3D Chern-Simons terms. Finally, we explicitly check that the expressions found for the G 4 -flux allow for a cancelation of D3-brane tadpoles. We also use the integrality of 3D Chern-Simons terms to ensure that our G 4 -flux solutions are adequately quantized.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Higher derivative terms, toroidal compactification, and Weyl anomalies in six-dimensional (2, 0) theories

We systematically analyze the effective action on the moduli space of (2,0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally supersymmetric Yang-Mills theories in five and four dimensions. We present a streamlined approach to non-renormalization theorems that constrain this effective action. The first several orders in its derivative expansion are determined by a one-loop calculation in five-dimensional Yang-Mills theory. This fixes the leading higher-derivative operators that describe the renormalization group flow into theories residing at singular points on the moduli space of the compactified (2,0) theories. This understanding allows us to compute the a-type Weyl anomaly for all (2,0) superconformal theories. We show that it decreases along every renormalization group flow that preserves (2,0) supersymmetry, thereby establishing the a-theorem for this class of theories. Along the way, we encounter various field-theoretic arguments for the ADE classification of (2,0) theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗