Computing amplitudes in topological M-theory

• We define a topological quantum membrane theory on a seven dimensionalmanifold of G2 holonomy. We describe in detail the path integral evaluation for membranegeometries given by circle bundles over Riemann surfaces. We show that when the targetspace is CY3 × S 1 quantum amplitudes of non-local observables of membranes wrappingthe circle reduce to the A-model amplitudes. In particular for genus zero we show thatour model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrappingcalibrated homology spheres in the CY3 , we find that the amplitudes of our model arerelated to Joyce invariants.

Subject headings

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Keyword

Topological Field Theories

Topological Strings

M-Theory.

Physics

Fysik

Publication and Content Type

ref (subject category)

art (subject category)