Special geometry and the swampland

Abstract In the context of 4d effective gravity theories with 8 supersymmetries, we propose to unify, strenghten, and refine the several swampland conjectures into a single statement: the structural criterion, modelled on the structure theorem in Hodge theory. In its most abstract form the new swampland criterion applies to all 4d $$ \mathcal{N} $$ N = 2 effective theories (having a quantum-consistent UV completion) whether supersymmetry is local or rigid: indeed it may be regarded as the more general version of Seiberg-Witten geometry which holds both in the rigid and local cases.As a first application of the new swampland criterion we show that a quantum-consistent $$ \mathcal{N} $$ N = 2 supergravity with a cubic pre-potential is necessarily a truncation of a higher-$$ \mathcal{N} $$ N sugra. More precisely: its moduli space is a Shimura variety of ‘magic’ type. In all other cases a quantum-consistent special Kähler geometry is either an arithmetic quotient of the complex hyperbolic space SU(1, m)/U(m) or has no local Killing vector.Applied to Calabi-Yau 3-folds this result implies (assuming mirror symmetry) the validity of the Oguiso-Sakurai conjecture in Algebraic Geometry: all Calabi-Yau 3-folds X without rational curves have Picard number ρ = 2, 3; in facts they are finite quotients of Abelian varieties. More generally: the Kähler moduli of X do not receive quantum corrections if and only if X has infinite fundamental group. In all other cases the Kähler moduli have instanton corrections in (essentially) all possible degrees.

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Swampland geometry and the gauge couplings

Journal of High Energy Physics ◽

10.1007/jhep09(2021)136 ◽

2021 ◽

Vol 2021 (9) ◽

Author(s):

Sergio Cecotti

Keyword(s):

Complex Structure ◽

Gauge Coupling ◽

Geometric Description ◽

Energy Limit ◽

Kahler Geometry ◽

Theories Of Gravity ◽

Gauge Couplings ◽

Underlying Manifold ◽

The Right ◽

Effective Theories

Abstract The purpose of this paper is two-fold. First we review in detail the geometric aspects of the swampland program for supersymmetric 4d effective theories using a new and unifying language we dub “domestic geometry”, the generalization of special Kähler geometry which does not require the underlying manifold to be Kähler or have a complex structure. All 4d SUGRAs are described by domestic geometry. As special Kähler geometries, domestic geometries carry formal brane amplitudes: when the domestic geometry describes the supersymmetric low-energy limit of a consistent quantum theory of gravity, its formal brane amplitudes have the right properties to be actual branes. The main datum of the domestic geometry of a 4d SUGRA is its gauge coupling, seen as a map from a manifold which satisfies the geometric Ooguri-Vafa conjectures to the Siegel variety; to understand the properties of the quantum-consistent gauge couplings we discuss several novel aspects of such “Ooguri-Vafa” manifolds, including their Liouville properties.Our second goal is to present some novel speculation on the extension of the swampland program to non-supersymmetric effective theories of gravity. The idea is that the domestic geometric description of the quantum-consistent effective theories extends, possibly with some qualifications, also to the non-supersymmetric case.

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MIRROR SYMMETRY FOR TOPOLOGICAL SIGMA MODELS WITH GENERALIZED KÄHLER GEOMETRY

International Journal of Modern Physics A ◽

10.1142/s0217751x06029351 ◽

2006 ◽

Vol 21 (11) ◽

pp. 2377-2389 ◽

Cited By ~ 16

Author(s):

STEFANO CHIANTESE ◽

FLORIAN GMEINER ◽

CLAUS JESCHEK

Keyword(s):

Field Strength ◽

Sigma Models ◽

Special Class ◽

Mirror Symmetry ◽

Kahler Geometry ◽

Generalized Kähler Geometry ◽

Mirror Map ◽

Topological Models

We consider topological sigma models with generalized Kähler target spaces. The mirror map is constructed explicitly for a special class of target spaces and the topological A and B model are shown to be mirror pairs in the sense that the observables, the instantons and the anomalies are mapped to each other. We also apply the construction to open topological models and show that A branes are mapped to B branes. Furthermore, we demonstrate a relation between the field strength on the brane and a two-vector on the mirror manifold.

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High Resolution Electron Microscopy of internal interfaces in layered materials

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100174734 ◽

1990 ◽

Vol 48 (4) ◽

pp. 320-321

Author(s):

Yoichi Ishida ◽

Hideki Ichinose ◽

Yutaka Takahashi ◽

Jin-yeh Wang

Keyword(s):

Grain Boundaries ◽

Mirror Symmetry ◽

Functional Materials ◽

High Resolution Electron Microscopy ◽

Layered Materials ◽

Plane Boundary ◽

Chemical Information ◽

Layer Plane ◽

High Tc ◽

Cubic Metals

Layered materials draw attention in recent years in response to the world-wide drive to discover new functional materials. High-Tc superconducting oxide is one example. Internal interfaces in such layered materials differ significantly from those of cubic metals. They are often parallel to the layer of the neighboring crystals in sintered samples(layer plane boundary), while periodically ordered interfaces with the two neighboring crystals in mirror symmetry to each other are relatively rare. Consequently, the atomistic features of the interface differ significantly from those of cubic metals. In this paper grain boundaries in sintered high-Tc superconducting oxides, joined interfaces between engineering ceramics with metals, and polytype interfaces in vapor-deposited bicrystal are examined to collect atomic information of the interfaces in layered materials. The analysis proved that they are not neccessarily more complicated than that of simple grain boundaries in cubic metals. The interfaces are majorly layer plane type which is parallel to the compound layer. Secondly, chemical information is often available, which helps the interpretation of the interface atomic structure.

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The limits of strain and lattice parameter measurements by CBED

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154561 ◽

1989 ◽

Vol 47 ◽

pp. 518-519

Author(s):

Hamish L. Fraser

Keyword(s):

Electron Beam ◽

Mirror Symmetry ◽

Local Symmetry ◽

Lattice Parameter ◽

Growth Direction ◽

Surface Relaxation ◽

Strained Layer ◽

Axis Parallel ◽

Local Lattice ◽

Strained Layer Superlattice

The topic of strain and lattice parameter measurements using CBED is discussed by reference to several examples. In this paper, only one of these examples is referenced because of the limitation of length. In this technique, scattering in the higher order Laue zones is used to determine local lattice parameters. Work (e.g. 1) has concentrated on a model strained-layer superlattice, namely Si/Gex-Si1-x. In bulk samples, the strain is expected to be tetragonal in nature with the unique axis parallel to [100], the growth direction. When CBED patterns are recorded from the alloy epi-layers, the symmetries exhibited by the patterns are not tetragonal, but are in fact distorted from this to lower symmetries. The spatial variation of the distortion close to a strained-layer interface has been assessed. This is most readily noted by consideration of Fig. 1(a-c), which show enlargements of CBED patterns for various locations and compositions of Ge. Thus, Fig. 1(a) was obtained with the electron beam positioned in the center of a 5Ge epilayer and the distortion is consistent with an orthorhombic distortion. When the beam is situated at about 150 nm from the interface, the same part of the CBED pattern is shown in Fig. 1(b); clearly, the symmetry exhibited by the mirror planes in Fig. 1 is broken. Finally, when the electron beam is positioned in the center of a 10Ge epilayer, the CBED pattern yields the result shown in Fig. 1(c). In this case, the break in the mirror symmetry is independent of distance form the heterointerface, as might be expected from the increase in the mismatch between 5 and 10%Ge, i.e. 0.2 to 0.4%, respectively. From computer simulation, Fig.2, the apparent monocline distortion corresponding to the 5Ge epilayer is quantified as a100 = 0.5443 nm, a010 = 0.5429 nm and a001 = 0.5440 nm (all ± 0.0001 nm), and α = β = 90°, γ = 89.96 ± 0.02°. These local symmetry changes are most likely due to surface relaxation phenomena.

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Structural Transformation of a Germanium Σ=13 (510) [001] Tilt Grain Boundary under the Electron Beam

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179014 ◽

1990 ◽

Vol 48 (1) ◽

pp. 52-53 ◽

Cited By ~ 1

Author(s):

Jean-Luc Rouvière ◽

Alain Bourret

Keyword(s):

Electron Microscopy ◽

High Resolution ◽

Grain Boundary ◽

Structural Transformation ◽

Mirror Symmetry ◽

High Resolution Electron Microscopy ◽

Structural Transformations ◽

Covalent Bonds ◽

Resolution Electron ◽

Tilt Grain Boundary

The possible structural transformations during the sample preparations and the sample observations are important issues in electron microscopy. Several publications of High Resolution Electron Microscopy (HREM) have reported that structural transformations and evaporation of the thin parts of a specimen could happen in the microscope. Diffusion and preferential etchings could also occur during the sample preparation.Here we report a structural transformation of a germanium Σ=13 (510) [001] tilt grain boundary that occurred in a medium-voltage electron microscopy (JEOL 400KV).Among the different (001) tilt grain boundaries whose atomic structures were entirely determined by High Resolution Electron Microscopy (Σ = 5(310), Σ = 13 (320), Σ = 13 (510), Σ = 65 (1130), Σ = 25 (710) and Σ = 41 (910), the Σ = 13 (510) interface is the most interesting. It exhibits two kinds of structures. One of them, the M-structure, has tetracoordinated covalent bonds and is periodic (fig. 1). The other, the U-structure, is also tetracoordinated but is not strictly periodic (fig. 2). It is composed of a periodically repeated constant part that separates variable cores where some atoms can have several stable positions. The M-structure has a mirror glide symmetry. At Scherzer defocus, its HREM images have characteristic groups of three big white dots that are distributed on alternatively facing right and left arcs (fig. 1). The (001) projection of the U-structure has an apparent mirror symmetry, the portions of good coincidence zones (“perfect crystal structure”) regularly separate the variable cores regions (fig. 2).

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Correlational Methods for Analysis of Dance Movements

Dance Research ◽

10.3366/drs.2011.0021 ◽

2011 ◽

Vol 29 (supplement) ◽

pp. 283-304 ◽

Cited By ~ 8

Author(s):

Timothy R. Brick ◽

Steven M. Boker

Keyword(s):

Motion Capture ◽

Mirror Symmetry ◽

Cross Correlation ◽

The Other ◽

Free Form ◽

Motion Capture Data ◽

Complex Interactions ◽

Dance Movements ◽

Time Lagged ◽

Insight Into

Among the qualities that distinguish dance from other types of human behavior and interaction are the creation and breaking of synchrony and symmetry. The combination of symmetry and synchrony can provide complex interactions. For example, two dancers might make very different movements, slowing each time the other sped up: a mirror symmetry of velocity. Examining patterns of synchrony and symmetry can provide insight into both the artistic nature of the dance, and the nature of the perceptions and responses of the dancers. However, such complex symmetries are often difficult to quantify. This paper presents three methods – Generalized Local Linear Approximation, Time-lagged Autocorrelation, and Windowed Cross-correlation – for the exploration of symmetry and synchrony in motion-capture data as is it applied to dance and illustrate these with examples from a study of free-form dance. Combined, these techniques provide powerful tools for the examination of the structure of symmetry and synchrony in dance.

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Existence

10.23943/princeton/9780691166902.003.0016 ◽

2017 ◽

Author(s):

Bernhard M¨uhlherr ◽

Holger P. Petersson ◽

Richard M. Weiss

Keyword(s):

Division Algebra ◽

Quadratic Forms ◽

Structure Theorem ◽

Quadratic Extension ◽

Quadratic Space ◽

Division Algebras ◽

Separable Extension ◽

Valued Fields ◽

Quaternion Division Algebra

This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadratic extension, a tamely ramified division algebra, a ramified separable quadratic extension, and a unique unramified quaternion division algebra. The chapter also describes ramified quaternion division algebras D₁, D₂, and D₃ over K containing a common subfield E such that E/K is a ramified separable extension.

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On Lattice-Ordered Rees Matrix Γ-Semigroups

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/v10157-012-0033-8 ◽

2013 ◽

Vol 59 (1) ◽

pp. 209-218 ◽

Cited By ~ 2

Author(s):

Kostaq Hila ◽

Edmond Pisha

Keyword(s):

Structure Theorem ◽

Lattice Of Congruences

Abstract The purpose of this paper is to introduce and give some properties of l-Rees matrix Γ-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix Γ-semigroups, the structure theorem of l-congruences lattice of l - Γ-semigroup M = μº(G : I; L; Γe) is given, from which it follows that this l-congruences lattice is distributive.

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