We discuss an N = 2 supergravity model that interpolates the full and the partial supersymmetry breakings. In particular, we find the conditions for an N = 0 Minkowski vacuum, which is continuously connected to the partialbreaking (N = 1 preserving) one. The model contains multiple (Abelian) vector multiplets and a single hypermultiplet, and is constructed by employing the embedding tensor technique. We compute the mass spectrum on the Minkowski vacuum, and find some non-trivial mass relations among the massive fields. Our model allows us to choose the two supersymmetry-breaking scales independently, and to discuss the cascade supersymmetry breaking for the applications to particle phenomenology and cosmology. * the prepotential exists) leads to the breaking of the whole N = 2 supersymmetries, 1 and some fields acquire masses by (super) higgs mechanism. However, it generally leads to a degenerate mass spectrum due to a single supersymmetry-breaking scale. Therefore, it is impossible to realize the above mentioned N = 1 models within this framework. In order to incorporate such phenomenological models, the N = 2 supersymmetries need to be broken by two different breaking scales. Then, an approximate N = 1 supersymmetry appears between these scales. Furthermore, when they are hierarchical, the situation approaches to the partial breaking of the supersymmetries.The possibility of the partial breaking in N = 2 supergravity was found in Refs. [7][8][9], and there, it was shown that the partial breaking occurs by gauging a matter (hyper) sector in a specific frame where the prepotential does not exist. The systematic analysis for the partial breaking conditions based on the so-called embedding tensor [10,11] can be found in Ref. [12] (see also [13][14][15]). These models are studied in connection with the partial breaking in the global N = 2 models [16] by taking the rigid supersymmetry limit [8,[17][18][19]. Also, there are various discussions related to the D-brane effective actions, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The partial supersymmetry breaking in non-Abelian gauge theories are discussed in both of the global [36][37][38] and the local supersymmetry cases [39] (see also [40] for review).In this paper, we interpolate the full and the partial supersymmetry breaking to obtain the approximate partial breaking of N = 2 supersymmetries. 2 Then, the spectrum should be characterized by two independent breaking scales of the N = 2 supersymmetries. In Ref. [7], the model realizes the full or the partial supersymmetry breaking, and the parameter spaces for those vacua are continuously connected. For phenomenological applications, we need matter multiplets, in addition to the goldstino multiplets. Therefore, we generalize the model in such a way that it has multiple vector multiplets, more general prepotential, and larger class of the gauging of the isometries, including the model of Ref.[7] as a special case. Then, we investigate the conditions for the supersymmetry breakings at two ...

We study the supersymmetry breaking patterns in four-dimensional N = 2 gauged supergravity. The model contains multiple (Abelian) vector multiplets and a single hypermultiplet which parametrizes SO(4, 1)/SO(4) coset. We derive the expressions of two gravitino masses under general gaugings and prepotential based on the embedding tensor formalism, and discuss their behaviors in some concrete models. Then we show that in a single vector multiplet case, the partial breaking always occurs when the third derivative of the prepotential exists at the vacuum, but we can have several breaking patterns otherwise.

We formulate a six dimensional U (1) gauge theory compactified on a (two dimensional) sphere S 2 with flux and localized brane sources. Profiles of the lowest Kaluza-Klein (KK) wavefunctions and their masses are derived analytically. In contrast to ordinary sphere compactifications, the above setup can lead to the degeneracy of and the sharp localizations of the linearly independent lowest KK modes, depending on the number of branes and their tensions. Moreover, it can naturally accommodate CP violation in Yukawa interactions. *

We provide N = 1 superfield description of BPS backgrounds in sixdimensional supergravity (6D SUGRA) with 3-branes, which is compactified on a twodimensional space. The brane terms induce the localized fluxes. We find a useful gauge in which the background equations become significantly simple. This is not the Wess-Zumino gauge, and the relation to the usual component-field expression of 6D SUGRA is not straightforward. One of the equations reduces to the Liouville equation. By moving to the Wess-Zumino gauge, we check that our expressions reproduce the known results of the previous works, which are expressed in the component fields. Our results help us develop the systematic derivation of four-dimensional effective theories that keeps the N = 1 SUSY structure.