E8 Gauge Theory, and a Derivation of K-Theory from M-Theory

Duiliu-Emanuel Diaconescu; Edward Witten; Gregory Moore

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E8 Gauge Theory, and a Derivation of K-Theory from M-Theory

Duiliu-Emanuel Diaconescu, Gregory Moore, Edward Witten

High Energy Physics - Theory · Submitted 10 May 2000

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

The authors' main claim We analyze the detailed phase factors on the two sides and show that they agree, thereby testing M-theory/Type IIA duality as well as the K-theory formalism in an interesting way.

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arXiv IDhep-th/0005090 (version 3)

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CitationDuiliu-Emanuel Diaconescu, Edward Witten, Gregory Moore. "E8 Gauge Theory, and a Derivation of K-Theory from M-Theory." arXiv:hep-th/0005090 (2000). https://pith.science/paper/B52PKIFL

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The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the RR fields to K-theory. The analogous partition function of M-theory on X x S1 contains subtle phases that are similarly associated with E8 gauge theory. We analyze the detailed phase factors on the two sides and show that they agree, thereby testing M-theory/Type IIA duality as well as the K-theory formalism in an interesting way. We also show that certain D-brane states wrapped on nontrivial homology cycles are actually unstable, that (-1)^{F_L} symmetry in Type IIA superstring theory depends in general on a cancellation between a fermion anomaly and an anomaly of RR fields, and that Type IIA superstring theory with no wrapped branes is well-defined only on a spacetime with W_7=0.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the RR fields to K-theory.	background 1.00	0.10	0.06	asserted 0.99
s1	The analogous partition function of M-theory on X x S1 contains subtle phases that are similarly associated with E8 gauge theory.	background 0.72	0.26	0.07	asserted 0.99
s2	We analyze the detailed phase factors on the two sides and show that they agree, thereby testing M-theory/Type IIA duality as well as the K-theory formalism in an interesting way.	contribution 0.70	0.96	0.58	asserted 1.00
s3	We also show that certain D-brane states wrapped on nontrivial homology cycles are actually unstable, that (-1)^{F_L} symmetry in Type IIA superstring theory depends in general on a cancellation between a fermion anomaly and an anomaly of RR fields, and that Type IIA superstring theory with no wrapped branes is well-defined only on a spacetime with W_7=0.	result 0.96	0.92	0.19	asserted 1.00

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Original abstract

The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the RR fields to K-theory. The analogous partition function of M-theory on X x S1 contains subtle phases that are similarly associated with E8 gauge theory. We analyze the detailed phase factors on the two sides and show that they agree, thereby testing M-theory/Type IIA duality as well as the K-theory formalism in an interesting way. We also show that certain D-brane states wrapped on nontrivial homology cycles are actually unstable, that (-1)^{F_L} symmetry in Type IIA superstring theory depends in general on a cancellation between a fermion anomaly and an anomaly of RR fields, and that Type IIA superstring theory with no wrapped branes is well-defined only on a spacetime with W_7=0.

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60 later papers cite it

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2 later papers by other authors are listed below: 1 built on it and 1 cited it as support.

Builds on it 1 of 4 papers with this label

Derived a constraint on degree twelve Chern numbers that generalizes the constraint on degree ten Chern numbers in this paper.

M-Theory with Framed Corners and Tertiary Index Invariants (2012) · 0.96 · paraphrased: the licence does not allow quoting

Cites it as support 1 paper

Reduced compatibility of F4 with ten-dimensional type IIA at the topological level to that of E8, which follows from this paper.

On the geometry of the supermultiplet in M-theory (2009) · 0.97 · paraphrased: the licence does not allow quoting

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61 arXiv papers cite this in 153 sentences

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Papers citing it · 121 sentences without a confident label

Contests it 1 paper

Indeed, despite wideheld beliefs within the string theory community, there is as of yet no definitive mathematically rigorous argument for twisted K-theory being the right coefficients for D-brane charge: the purported derivation of [ref] is rather a consistency check on the sign of the partition function over K-theory fields—a priori many other (twisted) cohomology theories could yield the same sign rule; the arguments of [ref] are differential form computations, hence cannot capture any torsion information; and there are moreover persistent conceptual issues with the proposal that D-brane charge is classified by twisted K-theory (see for example [ref] ).

Parametrised Homotopy Theory and Gauge Enhancement · Conclusion · contest 0.77

Builds on it 4 papers

In particular the question of extension of the $_2$ invariant $f(a+b)- f(a) -f(b)$ of [ref] becomes a question of extension on String manifolds of $MString_10 ( Z)$ rather than $MSpin(Z)$ for the Spin case, where $Z$ is $K(, 4 ) ×K(, 4)$ or $K(, 4) ∧K(, 4)$.

Anomalies of E8 gauge theory on String manifolds · Introduction · 0.90
This results in a constraint on degree twelve Chern numbers that generalize the constraint on degree ten Chern numbers in [ref] , and gives rise to a cup product composite Chern–Simons theory.

M-Theory with Framed Corners and Tertiary Index Invariants · Introduction · 0.96
This is the orbifold generalization of the Freed-Witten condition [ref] formulated in terms of obstruction classes in Bredon cohomology.

Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory · Consistency conditions · 0.99

Uses its method or tool 3 papers

The analysis follows that of [ref] .

Anomalies of E8 gauge theory on String manifolds · Refinement of the M-theory/IIA partition Function · 0.87
This approach has been used in [ref] , and is the approach we will use to determine the duality anomaly of type IIB string theory.

The anomaly that was not meant IIB · Bordism groups and anomalies · 0.96
We will analyze the first system in a way that is similar to the analysis of the latter in [ref] .

Topological aspects of the NS5-brane · Introduction · 0.80

Compares with it 6 papers

Thus that makes a departure from the discussion of [ref] in two respects: We are looking at the phase in eleven dimensions, involving the eta invariant, instead of the phase in twelve dimensions, involving the index, and the expression is a ten-dimensional integral.

Geometry of Spin and Spin^c structures in the M-theory partition function · Introduction and Summary · 1.00
We show that it reproduces the relevant properties of previous models, mainly [ref] , and refines them in the following ways. * All three gauge fields are dynamical (gravity, C-field, $E_8$-field), none is fixed background.

The E8 moduli 3-stack of the C-field in M-theory · Introduction · 0.83
This allows for more general boundary conditions than those of Atiyah-Patodi-Singer (APS) [ref] used in [ref] .

Corners in M-theory · Introduction · 0.87

Cites it as support 1 paper

Hence at the topological level, compatibility of $F_4$ with ten-dimensional type IIA is reduced to that of $E_8$, which follows from [ref] [ref] [ref] .

On the geometry of the supermultiplet in M-theory · Compatibility with ten-dimensional superstring theories · 0.97

Cites it as background 12 papers

The DMW anomaly [ref] in the comparison of the partition functions of M-theory and type IIA string theory is given by the vanishing of the seventh integral Stiefel-Whitney class $W_7(X)$ of spacetime $X$.

Anomalies of E8 gauge theory on String manifolds · Introduction · 0.90
We start by recalling the setting and the results that we need from [ref] .

Geometry of Spin and Spin^c structures in the M-theory partition function · The phase of M-theory in the $Spin^c$ case. · 0.98
It has been tradition to describe the expected M-brane charge quantization via ordinary cohomology equipped with an incremental sequence of constraints (e.g. [ref] [ref] [ref] [ref] ).

M/F-Theory as Mf-Theory · Introduction · 0.97

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