TY - JOUR

T1 - M-theory, the signature theorem, and geometric invariants

AU - Sati, Hisham

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/6/22

Y1 - 2011/6/22

N2 - The equations of motion and the Bianchi identity of the C-field in M-theory are encoded in terms of the signature operator. We then reformulate the topological part of the action in M-theory using the signature, which leads to connections to the geometry of the underlying manifold, including positive scalar curvature. This results in a variation on the miraculous cancellation formula of Alvarez-Gaumé and Witten in 12 dimensions and leads naturally to the Kreck-Stolz s-invariant in 11 dimensions. Hence M-theory detects the diffeomorphism type of 11-dimensional (and seven-dimensional) manifolds and in the restriction to parallelizable manifolds classifies topological 11 spheres. Furthermore, requiring the phase of the partition function to be anomaly-free imposes restrictions on allowed values of the s-invariant. Relating to string theory in ten dimensions amounts to viewing the bounding theory as a disk bundle, for which we study the corresponding phase in this formulation.

AB - The equations of motion and the Bianchi identity of the C-field in M-theory are encoded in terms of the signature operator. We then reformulate the topological part of the action in M-theory using the signature, which leads to connections to the geometry of the underlying manifold, including positive scalar curvature. This results in a variation on the miraculous cancellation formula of Alvarez-Gaumé and Witten in 12 dimensions and leads naturally to the Kreck-Stolz s-invariant in 11 dimensions. Hence M-theory detects the diffeomorphism type of 11-dimensional (and seven-dimensional) manifolds and in the restriction to parallelizable manifolds classifies topological 11 spheres. Furthermore, requiring the phase of the partition function to be anomaly-free imposes restrictions on allowed values of the s-invariant. Relating to string theory in ten dimensions amounts to viewing the bounding theory as a disk bundle, for which we study the corresponding phase in this formulation.

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U2 - 10.1103/PhysRevD.83.126010

DO - 10.1103/PhysRevD.83.126010

M3 - Article

AN - SCOPUS:79960797866

VL - 83

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 12

M1 - 126010

ER -