Vanishing Str M 2 in the presence of anomalous U A ( 1 ) Jorge

We show that the presence of an anomalous UA(1) factor in the gauge group of string-derived models may have the new and important phenomenological consequence of allowing the vanishing of StrM2 in the “shifted” vacuum, that results in the process of cancelling the anomalous UA(1). The feasibility of this effect seems to be enhanced by a vanishing vacuum energy, and by a “small” value of StrM2 in the original vacuum. In the class of free-fermionic models with vanishing vacuum energy that we focus on, a necessary condition for this mechanism to be effective is that StrM2 > 0 in the original vacuum. A vanishing StrM2 ameliorates the cosmological constant problem and is a necessary element in the stability of the no-scale mechanism. CTP-TAMU-37/95 DOE/ER/40717–16 ACT-12/95 September 1995 Many realistic string models built to date, especially all those constructed within the free-fermionic formulation, contain U(1) factors in their gauge groups with non-vanishing traces. These so-called anomalous U(1)’s may be understood as the result of truncating the string spectrum to the massless sector (over which the traces are taken), and do not imply an anomaly in the full string model. Nonetheless, the low-energy effective theory takes notice of this effect in the form of a FayetIliopoulos contribution to the D-term of the anomalous UA(1). This contribution can be calculated by examining the conditions under which the anomaly will cancel in the full theory, and is given by a one-loop string calculation [1] DA → DA + ǫ ; DA = ∑ i q A|φi| , ǫ = gM 192π2 TrUA , (1) where q A is the charge of the φi field under UA(1), and M ≈ 10GeV is the relevant mass scale (or reduced Planck mass). The non-zero shift in DA, if not compensated, has the dire consequence of breaking supersymmetry at the Planck scale. Interestingly enough, in all instances where anomalous U(1)’s have been reported in consistent models, it has been always possible to give vacuum expectation values (vevs) to some scalar fields charged under UA(1), such that DA + ǫ vanishes at the nearby vacuum determined by these vevs. This shifted vacuum is “nearby” because typically 〈φ〉 ∼ √ǫ = O( 1 10 M). The vacuum shift needed to cancel the anomalous U(1) is not without consequence. Indeed, one now has to consider carefully other pieces of the scalar potential that in the absence of UA(1) would have vanished automatically, with all vevs equal to zero. These are the usual Fand D-flatness conditions