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Supersymmetry, Ricci flat manifolds and the String Landscape
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.
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“Thus, out of the 28 classes, 1 is supersymmetric and stable, 26 have known bubbles of nothing, but there is one left (class G3 in [27]) for which no bubble of nothing was known.”
From Nothing is certain in string compactifications (2020) · cites this paper as [27]
In the citing paper
“Our explicit construction for the bubble of nothing of T 3 allows us to resolve a puzzle posed in [27].”
From Nothing is certain in string compactifications (2020) · cites this paper as [27]
In the citing paper
“We have constructed nulbordisms using Weierstrass fibrations (3.1) for all 27 cases; below, we will discuss explicitly the bubble for class G3, the only one left out in [27].”
From Nothing is certain in string compactifications (2020) · cites this paper as [27]
In the citing paper
“This geometry can be understood as a fibration of a T 2 over S 1 , with monodromy of the T 2 corresponding to a rotation by 2π/3 of the T 2 .”
From Nothing is certain in string compactifications (2020) · cites this paper as [27]
In the citing paper
“There are six possible geometries, labeled G1, . . .G6, each of which admits a different number of spin structures, for a total of 28 cases.”
From Nothing is certain in string compactifications (2020) · cites this paper as [27]
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Citations
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Etxebarria, I. G., Montero, M., Sousa, K., & Valenzuela, I. (2020) · Journal of High Energy Physics · doi:10.1007/jhep12(2020)032 · Cited by 87
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Cited by
Nothing is certain in string compactifications
Etxebarria, I. G., Montero, M., Sousa, K., & Valenzuela, I. (2020) · Journal of High Energy Physics · doi:10.1007/jhep12(2020)032 · Cited by 87
Gravitational memory and compact extra dimensions
Ferko, C., Satishchandran, G., & Sethi, S. (2022) · Physical Review D · doi:10.1103/physrevd.105.024072 · Cited by 20
Neutralizing topological obstructions to bubbles of nothing
Draper, P., Lillard, B., & Skye, C. (2023) · Journal of High Energy Physics · doi:10.1007/jhep10(2023)049 · Cited by 5
Metadata
- Authors
- Acharya, B. S.
- Venue
- Journal of High Energy Physics
- Published
- 2020-08
- Volume
- 2020
- Issue
- 8
- ISSN
- 1029-8479
- Cited by
- 36
- References
- 4
- Language
- en
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