Setting the quantum integrand of M-theory

Daniel S. Freed, Gregory W. Moore

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)89-132
Number of pages44
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Mar 2006

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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