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At least 127 records · Page 7

New solutions with accelerated expansion in string theory

We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple accelerating solutions. Our solutions respect an approximate scaling symmetry and realize discrete sequences of values for the equation of state, including one with an accumulation point at w = –1 and another accumulating near w = –1/3 from below. In another class of models, a density of defects generates scaling solutions with accelerated expansion. Here, we briefly discuss potential applications to dark energy phenomenology, and to holography for cosmology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

Here, we use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be ~ 10 48 . Moreover, the distribution of bases peaks around h 1,1 ~ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We also find that the number of non-Higgsable gauge group factors grows roughly linearly in h 1,1 of the threefold base. Typical bases have ~ 6 isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3) x SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) x SU(2) is the third most common connected two-factor product group, following SU(2) x SU(2) and G2 x SU(2), which arise more frequently.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermally Conductive Backsheets (TCB) for Reduced Operating Temperatures

The performance of photovoltaic (PV) modules is primarily influenced by the plane of array (POA) irradiance and their operating temperature. The lower the module operating temperature, the higher is its performance. Increasing a module’s operating temperature reduces its power output due to an increase in the semiconductor’s intrinsic carrier density, leading to a reduction in the open-circuit voltage and, subsequently, reducing the maximum power point voltage. Reducing the operating temperature lowers the levelized cost of energy (LCOE) via increased energy production (i.e., more kilowatt hour over the life of the asset) and increased service lifetime (years in the field). The module operating temperature is dictated by the weather parameters and the thermal properties of module construction materials. The primary weather parameters influencing the PV module temperature are: the ambient temperature (directly related), irradiance (directly related), and wind speed (inversely related). The primary thermal properties of module construction materials influencing the PV module temperature are: the optical transmissivity and thermal conductivity of superstrate, the thermal conductivity of substrate, the thermal conductivity of encapsulant and the efficiency of the encapsulated solar cells. The primary goal of this study is to reduce the operating temperature of PV modules using thermally conductive backsheet (TCB) substrates developed by the industry. The temperature of PV modules installed in a large multi-MW plant can also be influenced by their physical locations in the plants due to the influence of wind direction. A thermal mapping of PV plants has also been investigated and presented in this study. The most commonly used PV backsheet material has been polyvinyl fluoride (DuPont trade name “Tedlar”)-based backsheet, which typically has three layers: Tedlar–polyethylene terephthalate (PET)–Tedlar (TPT). The primary goal of this project is to reduce the module operating temperature below the benchmark TPT backsheet temperature using newly developed TCBs by the industry. The overall approach of this project involves six focus areas: i) select and procure one TPT and thirteen promising TCBs available in the industry; ii) construct a large number of 1-cell and 9-cell modules using benchmark TPT and selected TCBs [all other construction materials are fixed and they are: glass superstrate, EVA encapsulant, mono-Si cell and junction box]; iii) to identify best performing TCBs, monitor the long-term field operating temperatures of the constructed modules which are installed in three climatic conditions (hot-low wind [Mesa, AZ], hot-high wind [Maricopa County, AZ] and temperate [Cumberland County, NC]; iv) to identify the most durable TCB, perform extended accelerated reliability testing of modules constructed with best three TCBs and benchmark TPT; v) to predict module temperature, develop physical and empirical thermal models with and without thermal properties of all construction materials in the modules, respectively; and vi) to determine the influence of wind speed and direction on the module operating temperature in a plant, and perform thermal mapping of PV modules in two large PV plants [Maricopa County, AZ and Cumberland County, NC]. The key achievements of this project are listed below: Backsheet selection: 14 backsheets were procured after an extensive literature and industry search. Finally, based on the thermal and other selection criteria, 1 TPT and 4 thermally conductive backsheets were selected for this project. Fabrication of mini modules: 50 one-cell modules were fabricated in year 1 for thermal performance evaluation. The module design was changed to nine-cell module at start of year 2 to mimic commercial design. 20 nine-cell modules were fabricated in year 2 for thermal performance evaluation. 28 four-cell modules were fabricated in year 3 for accelerated stress-testing. Thermal conductivity of backsheets: Year 1 TCBs showed at least 8% higher thermal conductivities than TPT. Year 2 and 3 TCBs showed at least 20% higher thermal conductivities than TPT. Installation of mini PV modules at three sites: 6 one-cell modules and 8 nine-cell modules were installed at AZ-1 site [Mesa, AZ]. 12 one-cell modules and 6 nine-cell modules were installed at each of two powerplants (AZ-2 [Maricopa County, AZ] and NC sites). Nominal operating cell temperatures (NOCT) of mini PV modules: NOCT of TCBs were observed to be lower than TPT with differences as high as 2°C. Comparison of thermal performance: The median operating temperature of one-cell modules was found to be reduced by 2°C by using TCB_A modules compared to TPT modules on several days in a month for few months in a year. The median temperature improvement of 4oC was achieved at several instances on a few days, but not all days, in a year using multiple TCBs compared to TPT. The final project milestone of achieving median temperature improvement of 5oC was achieved at several instances on a few days, but not all days, in a year using TCB_A compared to TPT. Empirical thermal model (without the need of construction material properties): Empirical thermal model for one-cell module was developed based on the input data of irradiance, wind speed and ambient temperatures. The primary input data differentiator for temperature differences between TPT and TCBs appears to be the irradiance level (solar gain). Accelerated durability testing: 20 four-cell modules using 4 backsheets (1 TPT and 3 TCBs) were exposed to Damp Heat 1000 hours (8 modules), UV/Thermal cycling (50 cycles)/Humidity freeze (10 cycles) test sequence (8 modules) and UV Weathering for qualification (8 modules). All the modules with four selected backsheets passed the stress tests per the retest guidelines of IEC 61215 standard for the backsheet change. Simplified comparative LCOE analysis: Using backsheet-specific power degradation levels in the accelerated tests (for TCB_A and TPT only), efficiency, service lifetime and assuming same cost for all backsheets, the LCOE of modules using TCB_A is determined to be lower than TPT. Due to lower operating temperature of TCB_A-based modules compared to TPT-based modules, the operating efficiency and service life of TCB_A-based modules are calculated to be higher than TPT-based modules. Temperature mapping of PV power plants: A distinct temperature difference (as high as 4°C) has been observed between the modules located in various parts of a single PV plant.

14 SOLAR ENERGY↗

Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z n . Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z n . By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairs for symmetric examples with Z 2 and Z 3 , in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.

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↗

Weak Scale Supersymmetry Emergent from the String Landscape

Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different 4−d laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological constant, it may also predict the form of weak scale supersymmetry which is expected to emerge. Rather general arguments suggest a power-law draw to large soft terms, but these are subject to an anthropic selection of a not-too-large value for the weak scale. The combined selection allows one to compute relative probabilities for the emergence of supersymmetric models from the landscape. Models with weak scale naturalness appear most likely to emerge since they have the largest parameter space on the landscape. For finetuned models such as high-scale SUSY or split SUSY, the required weak scale finetuning shrinks their parameter space to tiny volumes, making them much less likely to appear compared to natural models. Probability distributions for sparticle and Higgs masses from natural models show a preference for Higgs mass mh∼125 GeV, with sparticles typically beyond the present LHC limits, in accord with data. From these considerations, we briefly describe how natural SUSY is expected to be revealed at future LHC upgrades. This article is a contribution to the Special Edition of the journal Entropy, honoring Paul Frampton on his 80th birthday.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

BPS Wilson loop in $\mathcal{N}$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

We consider the expectation value \( \left\langle \mathcal{W}\right\rangle \) of the circular BPS Wilson loop in \( \mathcal{N} \) = 2 superconformal SU( N ) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to \( \mathcal{N} \) = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS 5 × S 5 superstring theory. On the string theory side \( \left\langle \mathcal{W}\right\rangle \) is represented by the path integral expanded near the same AdS 2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the \( \mathcal{N} \) = 4 SYM case and in the \( \mathcal{N} \) = 2 SU( N ) × SU( N ) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/ N 2 correction in \( \left\langle \mathcal{W}\right\rangle \) should have the universal λ 3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for \( \left\langle \mathcal{W}\right\rangle \) . We complement the analytic derivation of the λ 3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

1/N Expansion↗

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ 12

Here, we consider the spectrum of BPS states of the heterotic sigma model with (0, 8) supersymmetry and T 8 target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds’ automorphic form Φ 12 , a modular form which exhibits automorphy for O(2, 26; Ζ). Here, we comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A note on T-folds and $T^3$ fibrations

We study stringy modifications of T 3 -fibered manifolds, where the fiber undergoes a monodromy in the T-duality group. We determine the fibration data defining such T-folds from a geometric model, by using a map between the duality group and the group of large diffeomorphisms of a four-torus. We describe the monodromies induced around duality defects where such fibrations degenerate and we argue that local solutions receive corrections from the winding sector, dual to the symmetry-breaking modes that correct semi-flat metrics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On axionic field ranges, loopholes and the weak gravity conjecture

Here, we clarify some aspects of the impact that the Weak Gravity Conjecture has on models of (generalized) natural inflation. In particular we address certain technical and conceptual concerns recently raised regarding the stringent constraints and conclusions found in our previous work. We also point out the difficulties faced by attempts to evade these constraints. Furthermore, these new considerations improve the understanding of the quantum gravity constraints we found and further support the conclusion that it remains challenging for axions to drive natural inflation.

79 ASTRONOMY AND ASTROPHYSICS↗

Non-vanishing heterotic superpotentials on elliptic fibrations

We present models of heterotic compactification on Calabi-Yau threefolds and compute the non-perturbative superpotential for vector bundle moduli. The key feature of these models is that the threefolds, which are elliptically fibered over del Pezzo surfaces, have homology classes with a unique holomorphic, isolated genus-zero curve. Using the spectral cover construction, we present vector bundles for which we can explicitly calculate the Pfaffians associated with string instantons on these curves. These are shown to be non-zero, thus leading to a non-vanishing superpotential in the 4D effective action. We discuss, in detail, why such compactifications avoid the Beasley-Witten residue theorem.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nanoimprinted Diffraction Gratings for Light Trapping in Crystal-Silicon Film Photovoltaics

Crystal-silicon (c-Si) film photovoltaics hold the promise of combining the advantages of state-of-the-art wafer-silicon technology with the scalability and the inherently much lower cost of thin-film solar technologies. In the thickness range of 2-20 μm very effective light trapping is essential to absorb sufficient red and near-infrared (NIR) light and reach targeted efficiencies of 16% 18%, as defined by the U.S. National Solar Technology Roadmap. One proposed method is diffractive light trapping, which, at least in certain wavelength ranges, can theoretically outperform light trapping through random scattering at a rough surface or interface. The goals of this project were (1) to develop a nanoimprinting process for a high-refractive-index dielectric material, (2) to fabricate diffraction gratings as back-reflectors using this material, and (3) to demonstrate for a 2c-Si film an improvement in AM1.5 photon absorption of at least 80% relative to single-pass absorption. We achieved goals (1) and (2). We developed a soft-imprint method for sol-based titanium dioxide precursor films (index range 2.3-2.4) and integrated imprinted films in thin-film silicon devices. We did not fully reach goal (3): depending on the model used for interpretation of the optical experimental data, AM1.5 photon absorption was improved by only 53% (coherent electromagnetic model) to 66% (non-coherent ray-tracing model). When compared to a metallized flat reference film (double-pass absorption), the improvement due to the grating is only 6%, if the (more conservative) electromagnetic model is used. Other important achievements from this project were: • We perfected an imprinting method for another ceramic material, aluminum oxide phosphate, which is index-matched with glass. • We tested diffractive light trapping at different incidence angles and found positive evidence for light trapping for angles up to 50°, although the light-trapping efficiency decreased with increasing incidence angle. • The extent of the trapped wavelength range scales with the refractive index of the dielectric material. The full benefit of a high refractive index, however, is only achieved if the dielectric layer underneath the grating layer (the residual layer) is sufficiently thick (several 100 nm). For a very thin residual layer, the light wave is predominantly localized in the underlying material during diffraction, and this material's refractive index then determines the trapping range. The (welcomed) consequence is that if this material is the silicon absorber layer, e.g. in a thin-film superstrate configuration, a very large trapping range can be achieved even if a low-index dielectric is used. We tested this directly through light-trapping experiments in glass plates using two different imprinted dielectric materials, titanium dioxide (index range 2.3-2.4) and aluminum oxide phosphate (index 1.5), with thick and thin residual layers. • We tested both copper and aluminum as low-cost reflector alternatives to silver on the grating back sides. In the relevant wavelength range above 650 nm, copper not only has the same high reflectance as silver, but the diffraction efficiency is also on par with silver. • A total of five scientific publications resulting from this work have either been published or are in preparation for submission (see Detailed Technical Report, below). Two conference presentations were given. In conclusion, we successfully developed nanoimprinting techniques for two ceramic precursor materials and tested diffractive light trapping in c-Si and nc-Si:H thin-film devices. The measured amount of light trapping did not fully reach our target value. The lessons learned from this project, however, both concerning experimental techniques and theoretical/modeling methods, have been extensive. Light trapping remains a central issue in thin c-Si technology, and we recommend to the US Department of Energy to increase research in this important area.

14 SOLAR ENERGY↗

cymyc: $\underline{C}$alabi-$\underline{Y}$au $\underline{M}$etrics, $\underline{Y}$ukawas, and $\underline{C}$urvature

We introduce cymyc, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. cymyc includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.

differential and algebraic geometry↗

Unitarity of bespoke amplitudes

We use partial wave unitarity to constrain various bespoke four-point amplitudes. We start by constructing bespoke generalizations of the type-I superstring amplitude, which we show satisfy dual resonance and have suitable high-energy limits. By analyzing the behavior of partial wave coefficients for highly massive states, we strictly rule out all bespoke amplitudes with asymptotically nonlinear Regge trajectories and place constraints on the first few nontrivial parameters in asymptotically linear cases. Finally, we argue that while a large class of unitary bespoke amplitudes fails to satisfy Regge sum rules, there exists a smaller subclass with a vanishing mass gap that is superpolynomially bounded.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stable vacua with realistic phenomenology and cosmology in heterotic M-theory satisfying Swampland conjectures

We recently described a protocol for computing the potential energy in heterotic M-theory for the dilaton, complex structure and Kähler moduli. This included the leading order non-perturbative contributions to the complex structure, gaugino condensation and worldsheet instantons assuming a hidden sector that contains an anomalous U(1) structure group embedded in E8. In this paper, we elucidate, in detail, the mathematical and computational methods required to utilize this protocol. These methods are then applied to a realistic heterotic M-theory model, the B – L MSSM, whose observable sector is consistent with all particle physics requirements. Within this context, it is shown that the dilaton and universal moduli can be completely stabilized at values compatible with every phenomenological and mathematical constraint — as well as with ΛCDM cosmology. We also show that the heterotic M-theory vacua are consistent with all well-supported Swampland conjectures based on considerations of string theory and quantum gravity, and we discuss the implications of dark energy theorems for compactified theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Right-handed neutrinos and U(1) X symmetry-breaking

In [1] we proposed a model for Heterotic F-theory duality with Wilson line symmetry-breaking and a 4 + 1 split of the F-theory spectral divisor. One goal of this note is to call attention to the existence of right-handed neutrinos in our F-theory model. As pointed out in section 4 of [2] such existence may be evidence for the U(1) X -symmetry that remains after the Higgsing of E 8 via E 8 $\Rightarrow$ SU(5) gauge ⊕ [SU(4) ⊕ U(1) X ] Higgs occasioned by the 4 + 1 split of the spectral divisor. In addition, as a result of the $\mathbb{Z}$ 2 -action that supports the Wilson line we argue that the U(1) X -symmetry is, in fact, broken to $\mathbb{Z}$ 2 -matter parity. Finally we identify co-dimension 3 singularities which determine Yukawa couplings for the MSSM matter fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On the asymptotic states and the quantum S matrix of the η-deformed AdS 5 × S 5 superstring

We investigate the worldsheet S matrix of string theory in η-deformed AdS 5 × S 5 . By computing the six-point tree-level S matrix we explicitly show that there is no particle production at this level, as required by the classical integrability of the theory. At one and two loops we show that integrability requires that the classical two-particle states be redefined in a non-local and η-dependent way. This is a significant departure from the undeformed theory which is probably related to the quantum group symmetry of the worldsheet theory. We use generalized unitarity to carry out the loop calculations and identify a set of integrals that allow us to give a two-loop Feynman integral representation of the logarithmic terms of the two-loop S matrix. We finally also discuss aspects of the calculation of the two-loop rational terms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗