Anomaly mediation from unbroken supergravity

Abstract

When supergravity (SUGRA) is spontaneously broken, it is well known that anomaly mediation generates sparticle soft masses proportional to the gravitino mass. Recently, we showed that one-loop anomaly-mediated gaugino masses should be associated with unbroken supersymmetry (SUSY). This counterintuitive result arises because the underlying symmetry structure of (broken) SUGRA in flat space is in fact (unbroken) SUSY in antide Sitter (AdS) space. When quantum corrections are regulated in a way that preserves SUGRA, the underlying AdS curvature (proportional to the gravitino mass) necessarily appears in the regulated action, yielding soft masses without corresponding goldstino couplings. In this paper, we extend our analysis of anomaly mediation to sfermion soft masses. Already at tree-level we encounter a number of surprises, including the fact that zero soft masses correspond to broken (AdS) SUSY. At one-loop, we explain how anomaly mediation appears when regulating SUGRA in a way that preserves super-Weyl invariance. We find that recent claims in the literature about the non-existence of anomaly mediation were based on a Wilsonian effective action with residual gauge dependence, and the gauge-invariant 1PI effective action contains the expected anomaly-mediated spectrum. Finally, we calculate the sfermion spectrum to all orders, and use supertrace relations to derive the familiar two-loop soft masses from minimal anomaly mediation, as well as unfamiliar tree-level and one-loop goldstino couplings consistent with renormalization group invariance.

Anomaly mediation in local effective theories

“…The second puzzle concerns the goldstino couplings. The XW 2 α interaction contains a goldstino coupling, which is not expected in strict gravitino mediation [6,7]. The resolution is that the microscopic theory breaks SUSY by a small amount F Q ∼ vW 0 .…”

“…[6,7] have analyzed anomaly mediation in detail and demonstrated that there are several distinct mechanisms at work, physically separable by the JHEP02(2014)069 goldstino coupling to the supercurrent. The gaugino mass contributions we will identify correspond to pure gravitino mediation in the language of [6,7], although as we will see the issue of the goldstino coupling is somewhat subtle. The masses we study are bulk AdS masses, which are equivalent to the flat-space masses when the SUSY-breaking is sequestered from the visible sector (see also footnote 1.)…”

“…They can also be obtained by manipulating the conformal compensator of certain supergravity formalisms [2,3]. In a more broadly-applicable field theoretic approach, they can be associated with supersymmetric completions of non-local couplings [4][5][6][7]. In certain circumstances, they are associated with local interactions [4].…”

(Non-)decoupled supersymmetric field theories

“…As emphasized above, the form of this coupling is fixed by some contact terms in the correlators of the energy-momentum tensor multiplet and it is necessary even if supergravity is non-dynamical. It has to be included when analyzing supersymmetric theories in curved space (for a discussion from a different point of view in the case of AdS 4 , see also [17,18]). In flat space, if SUSY is broken in the hidden sector B, we need to turn on a VEV for M in order to cancel the cosmological constant.…”

“…If the vacuum is supersymmetric, it is eventually canceled by infrared dynamics. In [17,18] the central idea is that the anomaly mediated contribution (for example, the gaugino mass or the A-term) is actually supersymmetric under a deformed SUSY algebra characteristic of AdS 4 space. Several aspects of these derivations have to be contrasted with the main features of our approach, which we now summarize:…”