Setting the quantum integrand of M-theory

Details Setting the quantum integrand of M-theory Setting the quantum integrand of M-theory

2004-09-14

arxiv.org/abs/hep-th/0409135v3

Commun.Math.Phys. 263 (2006) 89-132

Physics

High Energy Physics

High Energy Physics - Theory

52 pages; revised version for publication in Commun. Math. Phys. corrects a few typos

Scientific paper

10.1007/s00220-005-1482-7

In anomaly-free quantum field theories the integrand in the bosonic functional integral--the exponential of the effective action after integrating out fermions--is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-theory the E(8)-model for the C-field allows us to set the quantum integrand using geometric index theory. We derive mathematical results of independent interest about pfaffians of Dirac operators in 8k+3 dimensions, both on closed manifolds and manifolds with boundary. These theorems are used to set the quantum integrand of M-theory for closed manifolds and for compact manifolds with either temporal (global) or spatial (local) boundary conditions. In particular, we show that M-theory makes sense on arbitrary 11-manifolds with spatial boundary, generalizing the construction of heterotic M-theory on cylinders.

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