Elsevier

Nuclear Physics B

Volume 623, Issues 1–2, 18 February 2002, Pages 97-125
Nuclear Physics B

Gravity-mediated supersymmetry breaking in the brane world

https://doi.org/10.1016/S0550-3213(01)00637-XGet rights and content

Abstract

We study the transmission of supersymmetry breaking via gravitational interactions in a five-dimensional brane world compactified on S1/Z2. We assume that chiral matter and gauge fields are confined at the orbifold fixed points, where supersymmetry is spontaneously broken by effective brane superpotentials. Using an off-shell supergravity multiplet we integrate out the auxiliary fields and examine the couplings between the bulk supergravity fields and boundary matter fields. The corresponding tree-level shift in the bulk gravitino mass spectrum induces one-loop radiative masses for the boundary fields. We calculate the boundary gaugino and scalar masses for arbitrary values of the brane superpotentials, and show that the mass spectrum reduces to the Scherk–Schwarz limit for arbitrarily large values of the brane superpotentials.

Introduction

An important question in the supersymmetric standard model is how supersymmetry is spontaneously broken in the low-energy world. This question has been mainly addressed in the context of four-dimensional effective theories with limited success, but recently the idea of extra dimensions has allowed for new possibilities [1], [2], [3], [4], [5], [6], [7], [8], [9]. The extra-dimensional framework is particularly interesting because it provides a new geometrical perspective in understanding some of the problems of conventional theories. In particular, the nonlocal nature of communicating supersymmetry breaking across the compact bulk from one boundary to another can soften the divergences of the soft mass spectrum [3], [7].

The Horava–Witten scenario [2] provides the prototype model in which to study the transmission of supersymmetry breaking via an extra dimension. In this model the transmission of supersymmetry breaking can become quite involved, and to calculate boundary soft masses one requires the bulk/boundary couplings. However, the essential features can be captured by studying a simpler five-dimensional super-Yang–Mills theory coupled to chiral matter on the boundary [5]. In this toy model the couplings between five-dimensional supermultiplets and four-dimensional boundary fields are obtained by working with off-shell supermultiplets and including the auxiliary fields. As noticed in Ref. [5] the dimensional reduction of bulk fields leads to new couplings between bulk and boundary fields which are required for consistency. In particular, this allows for the construction of realistic low-energy models with bulk gauge fields in flat [7] and warped space [9].

In this work we study brane world supersymmetry breaking in the case where only gravity propagates in the bulk while the chiral matter and gauge fields are confined to the four-dimensional boundaries. We assume that due to brane dynamics supersymmetry is spontaneously broken by effective brane superpotentials. This causes the tree-level gravitino mass spectrum to shift by a constant amount depending on the values of the brane superpotential [10]. At tree-level boundary chiral matter and gauge fields are massless but due to their gravitational interactions with the bulk gravitinos they will receive a supersymmetry breaking mass at one loop. Just like the bulk gauge field case, one can use an off-shell formulation to study the bulk gravitational case as well.

Supersymmetric brane world scenarios from off-shell supergravity have been formulated in Refs. [11], [12]. We will predominantly use the results in Ref. [11] to study an off-shell formulation of supergravity in the context of supersymmetry breaking with brane superpotentials. In particular, we will show that after integrating out the auxiliary fields of the off-shell supergravity multiplet there are new couplings between bulk and boundary fields. Just like the bulk gauge field case these couplings are required in order to obtain a consistent supersymmetric limit.

The one-loop mass spectrum will continuously depend on the brane superpotential parameter, and due to the nonlocal nature of the supersymmetry breaking the masses will be finite. In fact we will see that one particular limit of our mass spectrum is the familiar Scherk–Schwarz limit [3], [13]. Actually depending on the size of the extra dimension our one-loop results can be of order the anomaly-mediated contributions [6], [14] which arise from the one-loop rescaling anomalies. Thus, although we do not discuss this issue in detail, our results could be relevant in solving the tachyonic slepton mass problem [6].

The plan of this paper is as follows: in Section 2, after briefly reviewing the bulk vector multiplet case we consider the off-shell supergravity multiplet coupled to boundary fields. In particular we show that after integrating out auxiliary fields there are new couplings between boundary gauge fields and bulk supergravity fields. Supersymmetry breaking is considered in Section 3, where we derive the unitary matrix responsible for diagonalising the Kaluza–Klein gravitino mass spectrum. This is important for determining the couplings between the boundary and bulk fields. As a further check, the same results will also be derived more directly using an explicit five-dimensional calculation. In Section 4 we calculate the one-loop gaugino and scalar masses for arbitrary values of the brane superpotential. We comment on the cancellations that are required for consistency and are satisfied by the new couplings. Again, for completeness we will present the calculation of the soft mass spectrum using both the Kaluza–Klein sum in four dimensions, and the direct five-dimensional calculation. Finally, our conclusion and comments will be presented in Section 5.

Section snippets

Off-shell bulk supergravity on S1/Z2

We start from a pure N=2 five-dimensional Poincaré supergravity [15], compactified on an orbifold S1/Z2. Our model will assume that only gravity propagates in the bulk whereas chiral matter and gauge fields will be confined to the 4D boundaries. Thus all supersymmetry breaking effects will be transmitted by gravity and in particular the gravitino mass spectrum will shift. In order to study the transmission of supersymmetry breaking effects between the 4D boundaries it is necessary to work with

Supersymmetry breaking

We now consider the case in which supersymmetry is broken. If W0+Wπ≠0 then we will see that the flat space solution spontaneously breaks supersymmetry. The supersymmetry breaking will be transmitted to matter on branes located at the orbifold fixed points via gravity. The brane action is assumed to be Sbrane=12∫d4x−πR+πRdx5e4δ(x5)L4(0)+δ(x5−πR)L4(π)+12M53δ(x5)W0+δ(x5−πR)Wπψm1σmnψn1+h.c., where L4(i) are the boundary Lagrangians describing the interaction of matter with the bulk. Expanding the

Communication of supersymmetry breaking via the bulk

As we have seen in the previous section, the introduction of a constant superpotential Wπ on the brane located at x5=πR induces a breaking of supersymmetry in the five-dimensional gravitational sector, while it remains unbroken in the visible sector living on the brane located at x5=0. The communication of supersymmetry breaking to the visible sector is then expected to arise radiatively via gravitational interactions. This is the issue which we will study below.

Conclusions and discussions

In this paper we have considered a supersymmetric five-dimensional brane world scenario where the fifth dimension is compactified on S1/Z2. In our set-up chiral matter and gauge fields are restricted to live on the boundaries while gravity propagates in the bulk. We have assumed that supersymmetry is broken at the orbifold fixed points and that supersymmetry breaking is parametrized by a constant boundary superpotential. The bulk gravitino mass spectrum is consequently shifted relative to the

Acknowledgements

We wish to thank I. Antoniadis, A. Brignole, F. Feruglio, Z. Lalak, A. Pomarol, M. Quiros, R. Rattazzi, M. Zucker and F. Zwirner for useful discussions. T.G. thanks the University of Padova Theory Group and A.R. thanks the CERN Theory Group for hospitality where part of this work was done. The work of T.G. is supported by the Swiss National Science Research Fund (FNRS) contract no. 21-55560.98.

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