Implications of decoupling effects for one-loop corrected effective actions from superstring theory

We study the decoupling effects in one-loop corrected N = 1 supersymmetric theory with gauge neutral chiral superfields, by calculating the one-loop corrected effective Lagrangian that involves light and heavy fields with the mass scale M , and subsequently eliminating heavy fields by their equations of motion. In addition to new nonrenormalizable couplings, we determine the terms that grow as logM and renormalize the fields and couplings in the effective field theory, in accordance with the decoupling theorem. However, in a theory derived from superstring theory, these terms can significantly modify low energy predictions for the effective couplings of light fields. For example, in a class of heterotic superstring vacua with an anomalous U(1) the vacuum restabilization introduces such decoupling effects which in turn correct the low energy predictions for certain couplings by 10-50%. In principle the decoupling effects of heavy fields in field theory are well understood. According to the decoupling theorem [1] (for additional references see, e.g., [2]) in field theory of interacting light (with masses m) and heavy fields (with masses M) the heavy fields decouple; the effective Lagrangian of the light fields can be written in terms of the original classical Lagrangian of light fields with the loop effects of heavy fields absorbed into redefinitions of new light fields, masses and couplings, and the only new terms in this effective Lagrangian are non-renormalizable ones, proportional to inverse powers of M (both at treeand loop-levels). When field theory is an effective description of phenomena at certain energies, the rescaling of the fields and couplings due to the heavy fields does not affect the structure of couplings, since those are free parameters whose values are determined by experiments. On the other hand if the field theory is describing an effective theory of an underlying fundamental theory, like superstring theory, where the couplings at the string scale are calculable, the decoupling effects of the heavy field can be important and can significantly affect the low energy predictions for the couplings of light fields at low energies. Therefore the quantitative study of decoupling effects at the loop-level in effective supersymmetric theories is important; it should improve our understanding of such effects for the effective Lagrangians from superstring theory and provide us with calculable corrections for the low energy predictions of the theory. Effective theories of N = 1 supersymmetric four-dimensional perturbative superstring vacua can be obtained by employing techniques of two-dimensional conformal field theory [3]. In particular the kählerian and the chiral (super-) potential can be calculated explicitly at the tree level. (For a representative work on the subject see, e.g., [4, 5], and references therein.) 1 One of the compelling motivations for a detailed study of decoupling effects is the phenomenon of vacuum restabilization [6] for a class of four-dimensional (quasi-realistic) superstring vacua with an “anomalous” U(1). For such string vacua of perturbative heterotic string theory, the Fayet-Iliopoulos (FI) Dterm is generated at genus-one [7], thus triggering certain fields to acquire vacuum expectation values (VEV’s) of order MString ∼ ggaugeMP lanck ∼ ×10 GeV along Dand F flat directions of the effective N = 1 supersymmetric theory. 2 (Here ggauge is the gauge coupling and MP lanck the Planck scale.) Due to these large stringscale VEV’s a number of additional fields obtain large string-scale masses. Some of them in turn couple through (renormalizable) interactions to the remaining light fields, and thus While the superpotential terms calculated at the string tree-level are protected from higher genus corrections, the kählerian potential is not. Such higher genus corrections to the kählerian potential could be significant, however, their structure has not been studied very much. On the open Type I string side these effects are closely related to the blowing-up procedure of Type I orientifolds and were recently studied in [8].