Setting the quantum integrand of M-theory

Daniel S. Freed, Gregory W. Moore

Research output: Contribution to journalArticle

24 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)89-132
Number of pages44
JournalCommunications In Mathematical Physics
Volume263
Issue number1
DOIs
StatePublished - Mar 1 2006

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M-Theory
Integrand
Closed
Index Theory
Pfaffian
Functional Integral
Manifolds with Boundary
Effective Action
Dirac Operator
Quantum Field Theory
Compact Manifold
Fermions
Anomaly
Boundary conditions
theorems
fermions
anomalies
boundary conditions
Arbitrary
Term

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Setting the quantum integrand of M-theory. / Freed, Daniel S.; Moore, Gregory W.

In: Communications In Mathematical Physics, Vol. 263, No. 1, 01.03.2006, p. 89-132.

Research output: Contribution to journalArticle

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