Setting the Quantum Integrand of M-Theory |
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Authors: | Daniel S Freed Gregory W Moore |
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Institution: | (1) Department of Mathematics, University of Texas at Austin, 1 University Station, Austin, TX 78712-0257, USA;(2) Department of Physics, Rutgers University, Piscataway, NJ, 08855-0849, USA |
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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 E8-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.
The work of D.F. is supported in part by NSF grant DMS-0305505. The work of G.M. is supported in part by DOE grant DE-FG02-96ER40949 |
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