scholarly journals Supersymmetry, Ricci flat manifolds and the String Landscape

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
B. S. Acharya
Keyword(s):  
Minkowski Spacetime ◽  
Necessary Condition ◽  
Leading Order ◽  
Special Holonomy ◽  
Ricci Flat ◽  
Simply Connected Manifolds ◽  
String Landscape ◽  
Flat Manifolds ◽  
Simply Connected

Abstract A longstanding question in superstring/M theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the mathematical conjecture that all stable, compact Ricci flat manifolds have special holonomy in dimensions below eleven. Almost equivalent is the proposal that the landscape of all geometric, stable, string/M theory compactifications to Minkowski spacetime (at leading order) are supersymmetric. For simply connected manifolds, we collect together a number of physically relevant mathematical results, emphasising some key outstanding problems and perhaps less well known results. For non-simply connected, non-supersymmetric Ricci flat manifolds we demonstrate that many cases suffer from generalised Witten bubble of nothing instabilities.

scholarly journals Stringy tachyonic instabilities of non-supersymmetric Ricci flat backgrounds

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Bobby Samir Acharya ◽  
Gerardo Aldazabal ◽  
Eduardo Andrés ◽  
Anamaría Font ◽  
Kumar Narain ◽  
...  
Keyword(s):  
Small Radius ◽  
Vacuum Energy Density ◽  
Large Radius ◽  
Spin Structures ◽  
Special Holonomy ◽  
Conformal Field ◽  
Ricci Flat ◽  
Flat Manifolds ◽  
Superstring Theories ◽  
M Theory

Abstract Superstring/M-theory compactified on compact Ricci flat manifolds have recently been conjectured to exhibit instabilities whenever the metrics do not have special holonomy. We use worldsheet conformal field theory to investigate instabilities of Type II superstring theories on compact, Ricci flat, spin 3-manifolds including a worldsheet description of their spin structures. The instabilities are signalled by the appearance of stringy tachyons at small radius and a negative (1-loop) vacuum energy density at large radius. We briefly discuss the extension to higher dimensions.

scholarly journals TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP

2021 ◽  
pp. 1-8
Author(s):  
DANIEL KASPROWSKI ◽  
MARKUS LAND
Keyword(s):  
Fundamental Group ◽  
Homotopy Equivalent ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Canonical Map ◽  
Duality Space ◽  
Simply Connected Manifolds ◽  
Simply Connected ◽  
Poincaré Duality Space

Abstract Let $\pi$ be a group satisfying the Farrell–Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$ has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby–Siebenmann invariant. If $\pi$ is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby–Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel’s conjecture, and simply connected manifolds where rigidity is a consequence of Freedman’s classification results.

scholarly journals MORE M-BRANES ON PRODUCT OF RICCI-FLAT MANIFOLDS

2012 ◽  
Vol 09 (08) ◽  
pp. 1250067 ◽  
Author(s):  
V. D. IVASHCHUK
Keyword(s):  
Ricci Flat ◽  
Flat Manifolds ◽  
Fractional Numbers

Partially supersymmetric intersecting (non-marginal) composite M-brane solutions defined on the product of Ricci-flat manifolds M0 × M1 × ⋯ × Mn in D = 11 supergravity are considered and formulae for fractional numbers of unbroken supersymmetries are derived for the following configurations of branes: M2 ∩ M2, M2 ∩ M5, M5 ∩ M5 and M2 ∩ M2 ∩ M2. Certain examples of partially supersymmetric configurations are presented.

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Grzegorz Graff ◽  
Agnieszka Kaczkowska
Keyword(s):  
Natural Number ◽  
Homotopy Class ◽  
Periodic Points ◽  
Topological Invariant ◽  
Periodic Sequence ◽  
Connected Manifold ◽  
Lefschetz Numbers ◽  
Simply Connected Manifolds ◽  
Simply Connected

AbstractLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f.In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

scholarly journals The nonuniqueness of the tangent cones at infinity of Ricci-flat manifolds

2017 ◽  
Vol 21 (5) ◽  
pp. 2683-2723
Author(s):  
Kota Hattori
Keyword(s):  
Tangent Cones ◽  
Ricci Flat ◽  
Flat Manifolds
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