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arXiv · hep-th/0409135

Setting the quantum integrand of M-theory

Daniel S. Freed·Gregory W. Moore
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Abstract

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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Daniel S. Freed, Gregory W. Moore. 2005-12-22. Setting the quantum integrand of M-theory. https://doi.org/10.1007/s00220-005-1482-7

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