Corners in M-theory

Hisham Sati

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Corners in M-theory

Hisham Sati

High Energy Physics - Theory · Submitted 14 Jan 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As an extension, we show that manifolds with corners appear naturally in M-theory.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

M-theory can be defined on closed manifolds as well as on manifolds with boundary. As an extension, we show that manifolds with corners appear naturally in M-theory. We illustrate this with four situations: The lift to bounding twelve dimensions of M-theory on Anti de Sitter spaces, ten-dimensional heterotic string theory in relation to twelve dimensions, and the two M-branes within M-theory in the presence of a boundary. The M2-brane is taken with (or as) a boundary and the worldvolume of the M5-brane is viewed as a tubular neighborhood. We then concentrate on (variant) of the heterotic theory as a corner and explore analytical and geometric consequences. In particular, we formulate and study the phase of the partition function in this setting and identify the corrections due to the corner(s). The analysis involves considering M-theory on disconnected manifolds, and makes use of the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners and the b-calculus of Melrose.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	M-theory can be defined on closed manifolds as well as on manifolds with boundary.	background 1.00	0.08	0.05	asserted 0.99
s1	As an extension, we show that manifolds with corners appear naturally in M-theory.	contribution 0.59	0.92	0.74	asserted 1.00
s2	We illustrate this with four situations: The lift to bounding twelve dimensions of M-theory on Anti de Sitter spaces, ten-dimensional heterotic string theory in relation to twelve dimensions, and the two M-branes within M-theory in the presence of a boundary.	contribution 0.90	0.76	0.18	asserted 0.98
s3	The M2-brane is taken with (or as) a boundary and the worldvolume of the M5-brane is viewed as a tubular neighborhood.	method 0.48	0.69	0.06	asserted 0.94
s4	We then concentrate on (variant) of the heterotic theory as a corner and explore analytical and geometric consequences.	contribution 0.98	0.84	0.15	asserted 0.88
s5	In particular, we formulate and study the phase of the partition function in this setting and identify the corrections due to the corner(s).	contribution 0.55	0.94	0.25	asserted 1.00
s6	The analysis involves considering M-theory on disconnected manifolds, and makes use of the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners and the b-calculus of Melrose.	method 0.99	0.70	0.08	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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The paper

Original abstract

M-theory can be defined on closed manifolds as well as on manifolds with boundary. As an extension, we show that manifolds with corners appear naturally in M-theory. We illustrate this with four situations: The lift to bounding twelve dimensions of M-theory on Anti de Sitter spaces, ten-dimensional heterotic string theory in relation to twelve dimensions, and the two M-branes within M-theory in the presence of a boundary. The M2-brane is taken with (or as) a boundary and the worldvolume of the M5-brane is viewed as a tubular neighborhood. We then concentrate on (variant) of the heterotic theory as a corner and explore analytical and geometric consequences. In particular, we formulate and study the phase of the partition function in this setting and identify the corrections due to the corner(s). The analysis involves considering M-theory on disconnected manifolds, and makes use of the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners and the b-calculus of Melrose.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Perturbative Anomaly Inflow on Orbifolds
hep-th 2026-08 conditional novelty 7.0 of 10

The non-identity ALE fixed-point contribution on the M9 wall reproduces the Kac-label-dependent remainder of the tensor-branch anomaly polynomial for A-type orbi-instanton theories.
Framed M-branes, corners, and topological invariants
hep-th 2013-10 conditional novelty 5.0 of 10

M-brane worldvolumes, when framed or given corners, carry Hopf, Kervaire, f, and nu invariants, and the C-field plus its dual are proposed to be captured by maps into the 4-sphere.

How the literature uses it

9 arXiv papers cite this in 23 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 18 sentences without a confident label

Uses its method or tool 2 papers

In the presence of corners, the Melrose $b$-calculus is used to replace the eta-invariant with the $b$-eta-invariant [ref] .

M-Theory with Framed Corners and Tertiary Index Invariants · Introduction · 0.88
This involves using a type of Stokes formula for various faces in codimension $k$, in the setting advocated in [ref] .

Extended higher cup-product Chern-Simons theories · Final remarks · 0.91

Cites it as background 3 papers

The latter has been studied in the dual context of M-theory [ref] [ref] .

On global anomalies in type IIB string theory · Introduction · 0.81
The most important concepts from b-geometry for the ensuing formalism are summarised in Appendix [ref]; a detailed introduction can be found in [ref] , see also [ref] for a more physics oriented introduction.

Extended quantum field theory, index theory and the parity anomaly · Extended quantum field theory and the parity anomaly · 0.99
Some aspects of behavior of ends in M-theory are discussed in [ref] .

Constraints on heterotic M-theory from s-cobordism · Compactification · 0.87

What it cites · 43 sentences without a confident label

Builds on 2 papers

This is a global extension of the [ref] [ref] “upstairs" and “downstairs" notions, respectively, to corners.

Heterotic and Type I String Dynamics from Eleven Dimensions · Formulation using the signature operator · 1.00
This is a global extension of the [ref] [ref] “upstairs" and “downstairs" notions, respectively, to corners.

Eleven-Dimensional Supergravity on a Manifold with Boundary · Formulation using the signature operator · 1.00

Compares with 2 papers

This allows for more general boundary conditions than those of Atiyah-Patodi-Singer (APS) [ref] used in [ref] .

E8 Gauge Theory, and a Derivation of K-Theory from M-Theory · Introduction · 0.87
For comparison, let us briefly recall the case with no corners [ref] .

Two nontrivial index theorems in odd dimensions · Formulation using Dirac operators · 0.89

Cites as background 3 papers

These spaces appear as the near horizon limits of the M2-brane and the M5-brane, respectively, via the AdS/CFT correspondence which relates quantum supergavity on the AdS factor to the conformal field theory on the boundary $∂AdS$ [ref] .

The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 0.80
Note that $D_M^+$ is the operator appearing in Horava-Witten theory [ref] [ref] .

Eleven-Dimensional Supergravity on a Manifold with Boundary · Formulation using Dirac operators · 0.88
Note that $D_M^+$ is the operator appearing in Horava-Witten theory [ref] [ref] .

Heterotic and Type I String Dynamics from Eleven Dimensions · Formulation using Dirac operators · 0.88

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