Exact (1 + 3 + 6)-Dimensional Cosmological-Type Solutions in Gravitational Model with Yang–Mills Field, Gauss–Bonnet Term and Λ Term by V. D. Ivashchuk, K. K. Ernazarov, A. A. Kobtsev

“…We study so-called cosmological-type solutions defined on the product manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>=</mo><mi mathvariant="double-struck">R</mi><mo>×</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mn>3</mn></msup><mo>×</mo><mi>K</mi></mrow></semantics></math></inline-formula>, where <i>K</i> is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>6</mn><mi>d</mi></mrow></semantics></math></inline-formula> a Calabi–Yau manifold. By setting the gauge field 1-form to coincide with the 1-form spin connection on <i>K</i>, we obtain exact cosmological solutions with exponential dependence of scale factors (upon <i>t</i>-variable) governed by two non-coinciding Hubble-like parameters: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <i>h</i> obeying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>+</mo><mn>2</mn><mi>h</mi><mo>≠</mo><mn>0</mn></mrow></semantics></math></inline-formula>. …”
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Mirror symmetry in emergent gravity by Hyun Seok Yang

“…In particular, the doubling for the variety of emergent Calabi–Yau manifolds allows us to arrange a pair of Calabi–Yau manifolds such that they are mirror to each other. …”
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Duality Between the Webs of Heterotic and Type II Vacua by Candelas, P, Font, A

“…We discuss how transitions in the space of heterotic K3*T^2 compactifications are mapped by duality into transitions in the space of Type II compactifications on Calabi-Yau manifolds. We observe that perturbative symmetry restoration, as well as non-perturbative processes such as changes in the number of tensor multiplets, have at least in many cases a simple description in terms of the reflexive polyhedra of the Calabi-Yau manifolds. …”

Lectures on special Lagrangian geometry by Joyce, D

“…We introduce special Lagrangian submanifolds in C^m and in (almost) Calabi-Yau manifolds, and survey recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. …”

Comments on A,B,C Chains of Heterotic and Type II Vacua by Candelas, P, Perevalov, E, Rajesh, G

“…We construct, as hypersurfaces in toric varieties, Calabi-Yau manifolds corresponding to F-theory vacua dual to E8*E8 heterotic strings compactified to six dimensions on K3 surfaces with non-semisimple gauge backgrounds. …”

Toric geometry and dualities of string theory by Candelas, P

“…The (0,2) vacua require an understanding of vector bundles on Calabi-Yau manifolds and these are much less well understood than the Calabi-Yau manifolds themselves. …”

Toric geometry and dualities of string theory by Candelas, P

“…The (0,2) vacua require an understanding of vector bundles on Calabi-Yau manifolds and these are much less well understood than the Calabi-Yau manifolds themselves. …”

RELATION BETWEEN THE WEIL-PETERSSON AND ZAMOLODCHIKOV METRICS by Candelas, P, Hubsch, T, Schimmrigk, R

“…We derive the Weil-Petersson metric on the moduli space of Calabi-Yau manifolds from that of Zamolodchikov, as the limit where the coupling tensors of the corresponding non-linear σ-model depend only on constant modes of the string coordinates.…”

Triadophilia: A Special Corner in the Landscape by Candelas, P, Ossa, X, He, Y, Szendroi, B

“…We draw attention to the fact that there appear to be very few Calabi--Yau manifolds with the Hodge numbers h^{11} and h^{21} both small. …”

Relationship between two Calabi–Yau orbifolds arising as hyper–surfaces in a quotient of the same weighted projective space by A. Belavin, D. Gepner

“…In this article we consider a question: what is the relation between two Calabi-Yau manifolds of two different Berglund–Hubsch types if they appear as hyper–surfaces in the quotient of the same weighted projective space. …”
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Hodge numbers for all CICY quotients by Constantin, A, Gray, J, Lukas, A

“…We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. …”

Hyperconifold Transitions, Mirror Symmetry, and String Theory by Davies, R

“…The new hyperconifold transitions are also used to construct a small number of new Calabi-Yau manifolds, with small Hodge numbers and fundamental group Z_3 or Z_5. …”

Singularities of special Lagrangian submanifolds by Joyce, D

“…We survey what is known about singularities of special Lagrangian submanifolds (SL $m$-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's work [18-22] on SL $m$-folds $X$ with isolated conical singularities. …”

ROLLING AMONG CALABI-YAU VACUA by Candelas, P, Green, P, Hubsch, T

“…For a very large number of Calabi-Yau manifolds of many different numerical invariants and hence distinct homotopy types, the relevant moduli spaces can be assembled into a connected web. …”

Type IIB flux compactifications with h 1,1 = 0 by Jacob Bardzell, Eduardo Gonzalo, Muthusamy Rajaguru, Danielle Smith, Timm Wrase

“…Abstract We revisit flux compactifications of type IIB string theory on ‘spaces’ dual to rigid Calabi-Yau manifolds. This rather unexplored part of the string landscapes harbors many interesting four-dimensional solutions, namely supersymmetric N $$ \mathcal{N} $$ = 1 Minkowski vacua without flat direction and infinite families of AdS vacua, some potentially with unrestricted rank for the gauge group. …”
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Tops as building blocks for G2 manifolds by Braun, A

“…These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes. In particular, this enables us to prove combinatorial formulas for the Hodge numbers and other relevant topological data.…”

Singularities of special Lagrangian submanifolds by Joyce, D

“…We survey what is known about singularities of special Lagrangian submanifolds (SL m-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356, math.DG/0303272 on SL m-folds X with isolated conical singularities. …”

Classification of base geometries in F-theory by Wang, Yinan, Ph. D. Massachusetts Institute of Technology

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Heterotic compactification, an algorithmic approach by Anderson, L, He, Y, Lukas, A

“…This is done in the context of complete intersection Calabi-Yau manifolds in a single projective space where we classify positive monad bundles. …”

Non-perturbative topological string theory on compact Calabi-Yau 3-folds by Jie Gu, Amir-Kian Kashani-Poor, Albrecht Klemm, Marcos Mariño

“…We obtain analytic and numerical results for the non-perturbative amplitudes of topological string theory on arbitrary, compact Calabi-Yau manifolds. Our approach is based on the theory of resurgence and extends previous special results to the more general case. …”
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