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Constraints on heterotic M-theory from s-cobordism
High Energy Physics - Theory · Submitted 6 Feb 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group-- a quotient of algebraic K-theory of the integral group ring of the fundamental group-- and a distinguished element, the Whitehead torsion.
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The abstract, sentence by sentence
We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homtopy equivalence. In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group-- a quotient of algebraic K-theory of the integral group ring of the fundamental group-- and a distinguished element, the Whitehead torsion. We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homtopy equivalence. | contribution 0.56 | 0.69 | 0.15 | asserted 1.00 |
| s1 | In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. | interpretation 0.65 | 0.58 | 0.11 | asserted 1.00 |
| s2 | This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group-- a quotient of algebraic K-theory of the integral group ring of the fundamental group-- and a distinguished element, the Whitehead torsion. | result 0.68 | 0.76 | 0.73 | asserted 0.99 |
| s3 | We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications. | contribution 0.93 | 0.80 | 0.04 | unclear 0.51 |
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The paper
Original abstract
We interpret heterotic M-theory in terms of h-cobordism, that is the eleven-manifold is a product of the ten-manifold times an interval is translated into a statement that the former is a cobordism of the latter which is a homtopy equivalence. In the non-simply connected case, which is important for model building, the interpretation is then in terms of s-cobordism, so that the cobordism is a simple-homotopy equivalence. This gives constraints on the possible cobordisms depending on the fundamental groups and hence provides a characterization of possible compactification manifolds using the Whitehead group-- a quotient of algebraic K-theory of the integral group ring of the fundamental group-- and a distinguished element, the Whitehead torsion. We also consider the effect on the dynamics via diffeomorphisms and general dimensional reduction, and comment on the effect on F-theory compactifications.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 24 sentences without a confident label
Compares with 1 paper
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While this solves the parity problem it uses boundary conditions which lead to a Bianchi identity for the C-field which is different from the one in [ref] .
Eleven-Dimensional Supergravity on a Manifold with Boundary · Automorphisms · 0.87
Cites as support 1 paper
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This is strengthened by the fact that in a class of models which admit perturbative heterotic duals, the F-theory and heterotic computations match [ref] .
Model Building with F-Theory · Automorphisms · 1.00
Cites as background 9 papers
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This includes constructing the standard model via string compactifications [ref] , most notably via heterotic M-theory [ref] [ref] .
Eleven-Dimensional Supergravity on a Manifold with Boundary · Introduction · 0.99
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This includes constructing the standard model via string compactifications [ref] , most notably via heterotic M-theory [ref] [ref] .
Heterotic and Type I String Dynamics from Eleven Dimensions · Introduction · 0.99
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The case when $π_1(Y^11)$ is nontrivial is discussed extensively in [ref] in relation the partition functions and to type IIA string theory.
Geometry of Spin and Spin^c structures in the M-theory partition function · Introduction · 0.91
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