Deformed 4D, N=2 Vector Multiplets and Partial Supersymmetry Breaking in OffShell Supergravity
Core Concepts
The authors elaborate on the deformation of offshell vector multiplets in 4D, N=2 supergravity, both in components and superspace, to engineer an offshell model that exhibits partial local supersymmetry breaking with a zero cosmological constant.
Abstract
The paper focuses on the deformation of offshell vector multiplets in 4D, N=2 supergravity. Key highlights:

The authors introduce the standard Weyl multiplet, abelian vector multiplet, linear multiplet, and hyperdilaton Weyl multiplet in superspace and components. These are the building blocks for constructing offshell supergravity models.

They elaborate on the deformation of the offshell abelian vector multiplet, including the introduction of electric and magnetic FayetIliopoulos (FI) terms. The magnetic FI term induces a deformation of the offshell field transformations.

Using the hyperdilaton Weyl multiplet, the authors engineer an offshell model that exhibits partial local supersymmetry breaking with a zero cosmological constant. This model consists of one physical and one compensating vector multiplet, with the physical one magnetically deformed.

The authors show that by tuning the electric and magnetic FI terms appropriately, the determinant of the matrix governing the fermion shifts and mass terms can be made zero, leading to partial supersymmetry breaking in a Minkowski vacuum. This is similar to the mechanism in the global AntoniadisPartoucheTaylor (APT) model.

The simplicity of the construction, with all steps being offshell, allows for the potential addition of other couplings, including higherderivative ones, in a straightforward manner.
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On 4D, ${\mathcal{N}=2}$ deformed vector multiplets and partial supersymmetry breaking in offshell supergravity
Stats
The determinant of the matrix Mij = 2cξij + iζij must be zero to achieve partial supersymmetry breaking, where c is a nonzero real constant, and ξij and ζij are the electric and magnetic FI terms, respectively.
Quotes
"Electric and magnetic FayetIlioupulous (FI) terms are used to engineer partial breaking of N = 2 global supersymmetry for systems of vector multiplets."
"The magnetic FI term induces a deformation of the offshell field transformations associated with an imaginary constant shift of the triplet of auxiliary fields of the vector multiplet."
Deeper Inquiries
How can the offshell model be extended to include additional matter multiplets while maintaining the partial supersymmetry breaking mechanism?
The offshell model presented in the context of 4D, N = 2 supergravity can be extended to include additional matter multiplets by carefully incorporating them into the existing framework without disrupting the delicate balance that allows for partial supersymmetry breaking. One approach is to introduce additional vector multiplets or hypermultiplets that couple to the hyperdilaton Weyl multiplet. These additional multiplets can be engineered to interact with the existing magnetically deformed vector multiplet and the compensating vector multiplet, ensuring that the overall structure remains consistent with the superconformal algebra.
To maintain the partial supersymmetry breaking mechanism, it is crucial that the new matter multiplets do not introduce additional degrees of freedom that could lead to full supersymmetry restoration. This can be achieved by ensuring that the new multiplets are either onshell or constrained in such a way that they do not contribute to the supersymmetry algebra's closure. For instance, one could utilize composite linear multiplets derived from the hypermultiplet sector to generate additional electric or magnetic FayetIliopoulos (FI) terms, which can be tuned to preserve the zero determinant condition of the matrix associated with the supersymmetry breaking.
Moreover, the introduction of additional matter multiplets should be accompanied by a thorough analysis of the resulting scalar potential and vacuum structure to ensure that the desired phenomenological features, such as stability and the existence of viable vacua, are preserved. This careful balancing act allows for a richer structure while still adhering to the principles of partial supersymmetry breaking.
What are the potential phenomenological implications of the proposed offshell partial supersymmetry breaking mechanism in supergravity?
The proposed offshell partial supersymmetry breaking mechanism in supergravity has several intriguing phenomenological implications. Firstly, it provides a framework for understanding how supersymmetry can be broken at high energy scales while still allowing for a lowenergy effective theory that retains N = 1 supersymmetry. This is particularly relevant in the context of particle physics, where such mechanisms could help explain the hierarchy problem and the stability of the Higgs boson.
Additionally, the presence of both electric and magnetic FayetIliopoulos (FI) terms in the model allows for a rich vacuum structure, potentially leading to a variety of cosmological scenarios. The ability to engineer scalar potentials with both positive and negative cosmological constants could have implications for inflationary models and the dynamics of the early universe. The zero cosmological constant condition achieved in the model may also provide insights into the nature of dark energy and its role in cosmic acceleration.
Furthermore, the offshell nature of the model allows for the inclusion of higherderivative terms and additional couplings, which could lead to novel predictions for supersymmetric particle spectra and interactions. This flexibility may enable the exploration of new physics beyond the Standard Model, including the possibility of discovering new particles or interactions at future collider experiments.
Can the deformation of offshell vector multiplets be generalized to other extended supergravity theories, such as 5D or 6D, and what new insights would that provide?
Yes, the deformation of offshell vector multiplets can be generalized to other extended supergravity theories, such as 5D or 6D supergravity. The principles underlying the deformation, particularly the use of electric and magnetic FayetIliopoulos (FI) terms, are not confined to 4D, N = 2 supergravity but can be adapted to higherdimensional theories with extended supersymmetry.
In 5D and 6D supergravity, the introduction of offshell vector multiplets can lead to new insights regarding the structure of the supersymmetry algebra and the nature of supersymmetry breaking. For instance, the interplay between electric and magnetic deformations in these higherdimensional contexts could reveal additional symmetries or dualities that are not apparent in 4D models. This could enhance our understanding of the relationship between different supergravity theories and their compactifications.
Moreover, the generalization of these deformations may provide a pathway to explore the implications of partial supersymmetry breaking in the context of string theory and Mtheory. The resulting models could offer new perspectives on the landscape of vacua in string theory, potentially leading to a better understanding of moduli stabilization and the emergence of effective field theories in lower dimensions.
Overall, extending the deformation of offshell vector multiplets to higherdimensional supergravity theories could yield significant advancements in our understanding of supersymmetry, its breaking mechanisms, and the implications for both particle physics and cosmology.