Discrete R symmetries and anomalies

Abstract

Abstract:We comment on aspects of discrete anomaly conditions focussing particularly on R symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We provide examples in open string theories of non-universal discrete anomalies at low energies. We then consider the fact that R symmetries are necessarily broken at low energies. We exhibit dynamical models, in which fields charged under the Standard Model gauge group (for example, a doublet and a triplet) gain roughly equal masses, but where the doublet and the triplet possess different discrete charges and the low-energy anomaly conditions fail.

R parity violation from discrete R symmetries

“…By allowing for different couplings of the axion a to the field strengths of SU(3) C , SU(2) L and U(1) Y , it is always possible to cancel the anomalies with the Green-Schwarz mechanism [18,19]. However, if one is to preserve gauge coupling unification in a natural way, the anomalies need to be universal, i.e.…”

“…On the other hand, as pointed out in [18], universality of the anomaly coefficients is, strictly speaking, not a consistency condition, even though one may impose it in order not to spoil precision gauge unification [13]. Precision gauge unification may also be preserved, for example, if the scalar partner of the axion a has an expectation value that is much smaller than the axion decay constant f a , or by an accidental cancellation of unrelated effects [19].…”

Superstring perturbation theory via super Riemann surfaces: an overview

“…At the nonperturbative level, the global U (1) symmetry is broken (at least down to a subgroup of finite order) by spacetime instanton effects. For a recent analysis, see [10].…”

Gravity mediation retrofitted

“…But even for these, if there are light scalars, anomalies can be canceled by a Green-Schwarz mechanism. In heterotic string examples, when this occurs, one often finds that all anomalies can be cancelled by couplings to a single field [27].A priori, in the presence of multiple moduli, anomalies not only need not vanish, but need not be equal [28,29]. But there is a simpler, more macroscopic reason, that one should not impose anomaly constraints.…”