Cosmological term and supersymmetry invited talk at Orbis Scientia, 1981

A persistent problem in quantum field theory is the existence of vacuum energy which is defined by the expectation value of theta/sub μν/ = 1/F2/ gμ where theta/sub μν/ is the stress-energy tensor and F is a constant. Why is this a problem. For all field theories with the exception of gravity the value of F is of no importance - it corresponds to a uniform background vacuum energy density throughout space. Since all energy levels are measured relative to the vacuum energy this quantity is unobservable. However, the Einstein equations for the gravity field know about energy in the vacuum and for F-1 approx. (GeV)2, corresponding to typical value from hadron physics, they imply that the universe curls up into a little ball about 100 meters in diameter, contrary to experience. This is the vacuum energy problem and it was first emphasized by Ya. B. Zel'dovich. One way out is to simply subtract away the vacuum energy. This ad hoc procedure - while it is what usually is done - must be viewed as unnatural because it has no basis in symmetry. The empirically observed absence of vacuum energy should have an explanation in terms of symmetry - like the absence of a photon mass is explained by a local gauge symmetry of the vacuum. Here we will show that such a symmetry of the coupled matter and gravity fields is indeed present up to terms of 0(kappa2) where kappa is the gravitational coupling constant. Our work should be viewed as a first step towards a more complete understanding of this problem