Supergravity coupled to chiral and Yang-Mills matter at one loop

Abstract

We present the full result for the divergent one-loop contribution to the effective boson Lagrangian for supergravity coupled to chiral and Yang-Mills supermultiplets. We also consider the specific case of dilaton couplings in effective supergravity Lagrangians from superstrings, for which the one-loop result is considerably simplified.

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

“…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…”

“…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 choice used above is "supersymmetric" in the sense that it corresponds to analogous matrix elements [5] in the bosonic and ghost sectors, yielding the cancellation of the F 2 terms. Now we introduce the dilaton; that is, we couple the Yang-Mills sector to a holomorphic function of the chiral multiplets: f ab = δ ab f, f = x + iy.…”

“…The "supersymmetric" choice, which matches corresponding matrix elements [5] in the bosonic and ghost sectors, is γ = δ = 1 2 , ǫ = 0, ζ = 1. Then the F 2 terms again cancel, and the remaining terms:…”