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

Abstract

We present the full calculation of the divergent one-loop contribution to the effective boson Lagrangian for supergravity, including the Yang-Mills sector and the helicity-odd operators that arise from integration over fermion fields. The only restriction is on the Yang-Mills kinetic energy normalization function, which is taken diagonal in gauge indices, as in models obtained from superstrings. ͓S0556-2821͑97͒01002-3͔

Anomaly Structure of Regularized Supergravity

“…Given that it is not trivial to identify all the total derivatives that were dropped in [16] and [17], we cannot guarantee that there are no other such D-term anomalies, so for present purposes we will subsume these into an operator that we will call Ω ′ D . In order to preserve the correct form of the anomaly, we require that PV chiral supermultiplet mass terms have well-defined modular weights.…”

“…with S transforming under modular and U (1) X transformations as 17) so that the dilaton Kähler potential…”

“…is the helicity-odd part, 17 where N is the helicity-odd part of −i D + M Θ . T − is not invariant under chiral transformations because, unlike the the other operators appearing in (A.1), N cannot be recast in invariant form; it explicitly contains the axial current.…”

“…Terms linear in gauge charges and modular weights are fixed by the requirement that quadratic divergences cancel; this uniquely fixes the PV contribution to the coefficient of r µνρσr µνρσ as given in (C.43), but terms cubic in these parameters are not fixed by the requirement of cancellation of quadratic (or logarithmic) UV divergences. However the expansion of the parity odd part of the fermion determinant [see (B.1)], given explicitly in [17], has, in addition to a linear divergence proportional to TrA that generates an r µνρσr µνρσ term in the anomaly, a linear divergence proportional to TrA 3 , where A is the axial current in the fermion connection. This contains the U (1) K connection as well as the (symmetric) YM gauge connections and the (axial part of the) scalar reparameterization connections for chiral fermions.…”

“…As has been recently emphasized [19], in supergravity the fermion connections and corresponding field strengths contain many more operators than the Yang-Mills [8]- [13] and space-time curvature [20]- [22] terms that have been studied previously in the context of anomaly cancellation. These additional operators include [21,16,17] the Kähler U (1) K connection for all fermions, the reparameterization connection for chiral fermions, an axion coupling in the gaugino connection and a (matrix-valued) connection [17] linear in the Yang-Mills field strength in the gaugino-gravitino sector. 1 In addition, besides the spin connection common to all fermions, the gravitino connection includes a term proportional to the affine connection, and the gauginos have an additional connection that involves the dilaton and its axionic superpartner.…”