Four-dimensional effective M theory on a singular<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>manifold

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We reduce M-theory on a G_2 orbifold with co-dimension four singularities, taking explicitly into account the additional gauge fields at the singularities. As a starting point, we use 11-dimensional supergravity coupled to seven-dimensional super-Yang-Mills theory, as derived in a previous paper. The resulting four-dimensional theory has N=1 supersymmetry with non-Abelian N=4 gauge theory sub-sectors. We present explicit formulae for the Kahler potential, gauge-kinetic function and superpotential. In the four-dimensional theory, blowing-up of the orbifold is described by a Higgs effect induced by continuation along D-flat directions. Using this interpretation, we show that our results are consistent with the corresponding ones obtained for smooth G_2 spaces. In addition, we consider the effects of switching on flux and Wilson lines on singular loci of the G_2 space, and we discuss the relation to N=4 SYM theory.

34 pages, Latex, v2 typos corrected

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