Supergravity coupled to chiral matter at one loop

Abstract

We extend earlier calculations of the one-loop contributions to the effective bose Lagrangian in supergravity coupled to chiral matter. We evaluate all logarithmically divergent contributions for arbitrary background scalar fields and space-time metric. We show that, with a judicious choice of gauge fixing and of the definition of the action expansion, much of the result can be absorbed into a redefinition of the metric and a renormalization of the Kähler potential. Most of the remaining terms depend on the curvature of the Kähler metric. Further simplification occurs in models obtained from superstrings in which the Kähler Riemann tensor is covariantly constant.

Anomaly Structure of Regularized Supergravity

“…Here we approach the same problem from the point of view of the effective four dimensional supergravity theory [15]. In the following section we define our notation and display the ultraviolet divergent part of the low energy effective Lagrangian obtained from light particle loops [16]- [18] in the form of superfield operators that will be convenient for the subsequent analysis. In Section 3 we will use the results of [2] and [3], hereafter referred to as I and II, respectively, to construct invariant couplings of PV supermultiplets needed to cancel the light loop divergences.…”

“…Some calculational details are presented in a series of appendices. As discussed below, requiring the cancellation of quadratic and logarithmic UV divergences that were identified in [16]- [18] does not uniquely fix the couplings of the PV sector. In Appendix A we derive additional constraints that assure the cancellation of almost all linear divergences.…”

Pauli-Villars regularization of supergravity coupled to chiral and Yang-Mills matter

“…Since STr(2µ 2 H ′ + ν 2 ) is just the O(µ 2 ) part of STr(µ 2 + H ′ + ν) 2 , it can be read off from the general results of [4], [5], with H → H ′ + µ 2 + ν ≡H. The terms in 1 2 STrH proportional to µ 2 are:…”

“…The fermion sector Θ includes a C-odd Majorana auxiliary field α that is introduced to implement the gravitino gauge fixing condition. The full gauge fixing procedure used here is described in detail in [4], [5]. Then the one loop bosonic action is given by …”

“…The field-dependent matrices H(φ) andD µ (φ) = ∂ µ +Γ µ (φ) are given in [4], [5], where the logarithmically divergent contributions have been evaluated. Explicitly evaluating (2) with an ultraviolet cut-off Λ and a massive Pauli-Villars sector with a squared mass matrix of the form…”