### Abstract

The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams e-invariant. If the eleven-dimensional manifold itself has a boundary, the resulting ten-dimensional manifold can be viewed as a codimension two corner. The partition function in this context has been studied by the author in relation to index theory for manifolds with corners, essentially on the product of two intervals. In this paper, we focus on the case of framed manifolds (which are automatically Spin) and provide a formulation of the refined partition function using a tertiary index invariant, namely the f-invariant introduced by Laures within elliptic cohomology. We describe the context globally, connecting the various spaces and theories around M-theory, and providing a ptic corner. The analysis for type IIA leads to a physical identification of various components of eta-forms appearing in the formula for the phase of the partition function.

Original language | English (US) |
---|---|

Article number | 024 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 10 |

DOIs | |

State | Published - Mar 27 2014 |

### Fingerprint

### Keywords

- Anomalies
- Elliptic genera
- Eta-forms
- M-theory
- Manifolds with corners
- Partition functions
- Tertiary index invariants

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

**M-theory with framed corners and tertiary index invariants.** / Sati, Hisham.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - M-theory with framed corners and tertiary index invariants

AU - Sati, Hisham

PY - 2014/3/27

Y1 - 2014/3/27

N2 - The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams e-invariant. If the eleven-dimensional manifold itself has a boundary, the resulting ten-dimensional manifold can be viewed as a codimension two corner. The partition function in this context has been studied by the author in relation to index theory for manifolds with corners, essentially on the product of two intervals. In this paper, we focus on the case of framed manifolds (which are automatically Spin) and provide a formulation of the refined partition function using a tertiary index invariant, namely the f-invariant introduced by Laures within elliptic cohomology. We describe the context globally, connecting the various spaces and theories around M-theory, and providing a ptic corner. The analysis for type IIA leads to a physical identification of various components of eta-forms appearing in the formula for the phase of the partition function.

AB - The study of the partition function in M-theory involves the use of index theory on a twelve-dimensional bounding manifold. In eleven dimensions, viewed as a boundary, this is given by secondary index invariants such as the Atiyah-Patodi-Singer eta-invariant, the Chern-Simons invariant, or the Adams e-invariant. If the eleven-dimensional manifold itself has a boundary, the resulting ten-dimensional manifold can be viewed as a codimension two corner. The partition function in this context has been studied by the author in relation to index theory for manifolds with corners, essentially on the product of two intervals. In this paper, we focus on the case of framed manifolds (which are automatically Spin) and provide a formulation of the refined partition function using a tertiary index invariant, namely the f-invariant introduced by Laures within elliptic cohomology. We describe the context globally, connecting the various spaces and theories around M-theory, and providing a ptic corner. The analysis for type IIA leads to a physical identification of various components of eta-forms appearing in the formula for the phase of the partition function.

KW - Anomalies

KW - Elliptic genera

KW - Eta-forms

KW - M-theory

KW - Manifolds with corners

KW - Partition functions

KW - Tertiary index invariants

UR - http://www.scopus.com/inward/record.url?scp=84897899719&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897899719&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2014.024

DO - 10.3842/SIGMA.2014.024

M3 - Article

AN - SCOPUS:84897899719

VL - 10

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 024

ER -