Transmission of Supersymmetry Breaking from a 4-Dimensional Boundary

TL;DR

The paper develops a tractable 5D field-theoretic toy model in which bulk 5D super-Yang-Mills fields couple to wall-localized chiral multiplets, enabling controlled study of SUSY-breaking mediation across a fifth dimension. By working with off-shell multiplets, it provides a concrete algorithm to couple bulk and boundary fields, revealing two distinct channels for transmitting SUSY breaking between boundaries and calculating the resulting soft masses. It also analyzes the Casimir energy associated with SUSY breaking, deriving both FI-term–driven and loop-mediated contributions and their asymptotic behaviors, which suggest possibilities for stabilizing the inter-boundary distance. Furthermore, the work connects these 5D results to Hořava–Witten's SUSY-breaking structure and discusses how a reduction to lower dimensions captures the essence of the proposed mechanisms, pointing toward a broader generalization to full supergravity and unification scenarios.

Abstract

In the strong-coupling limit of the heterotic string theory constructed by Horava and Witten, an 11-dimensional supergravity theory is coupled to matter multiplets confined to 10-dimensional mirror planes. This structure suggests that realistic unification models are obtained, after compactification of 6 dimensions, as theories of 5-dimensional supergravity in an interval, coupling to matter fields on 4-dimensional walls. Supersymmetry breaking may be communicated from one boundary to another by the 5-dimensional fields. In this paper, we study a toy model of this communication in which 5-dimensional super-Yang-Mills theory in the bulk couples to chiral multiplets on the walls. Using the auxiliary fields of the Yang-Mills multiplet, we find a simple algorithm for coupling the bulk and boundary fields. We demonstrate two different mechanisms for generating soft supersymmetry breaking terms in the boundary theory. We also compute the Casimir energy generated by supersymmetry breaking.

Figures (7)

• Figure 1: Feynman diagrams contributing to the scattering process $\phi\phi\to \phi\phi$.
• Figure 2: Feynman diagrams contributing to the $\phi$ self-energy at one-loop order.
• Figure 3: Feynman diagrams contributing to the mass shift of a scalar $\phi$ on one wall due to loop effects of the supermultiplet on the other wall.
• Figure 4: The basic integral which appears in the two-loop contribution to the scalar field mass.
• Figure 5: Behavior of the induced supersymmetry breaking mass for scalars at $x^5 = 0$ as a function of $\ell$. We plot $m_\phi^2$ in units of $2 C_2(R) C(R') (g^2/(4\pi)^2)^2 )\cdot (m^2/\ell^2))$.