Soft Supersymmetry Breaking from Gaugino Condensation

We study the structure of soft breaking terms in the context of a gaugino condensation scenario. Assuming that the Supergravity Lagrangian is the correct quantum field theory limit, at some momentum scale $μ_{UV}$, of a more fundamental one, we demonstrate that the correct result is obtained simply by substituting, in the tree level Supergravity Lagrangian, $λλ$ (the gaugino condensate) by its vacuum expectation value $Λ^3$. In string inspired scenarios this implies, in particular, that the scalar masses are vanishing at the string tree-level and receive a contribution, at the one loop level, which is proportional to the Green Schwarz coefficient $δ_{GS}$. Our results do not agree with the ones obtained in the effective Lagrangian approach. We study in detail the origin of this discrepancy, and we argue that the use of the supertrace anomaly to determine the effective theory for the condensate does not fix its gravitational interactions, leaving the soft breaking terms and the vacua of the theory unspecified.

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