Supersymmetry breaking by constant superpotentials and O'Raifeartaigh model in warped space

Supersymmetry breaking together by constant boundary superpotentials and by the O'Raifeartaigh model is studied in a warped space model. It is shown that the contribution of constant boundary superpotentials enables the moduli of chiral supermultiplets to be stabilized and that the vacuum at the stationary point has zero cosmological constant in a wide region of parameters.Comment: 13 pages, sections restructured, typos correcte

Pin^-(2)-monopole equations and intersection forms with local coefficients of 4-manifolds

We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and give its applications to intersection forms with local coefficients of 4-manifolds. The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients. The second is a local coefficient version of Furuta's 10/8-inequality. As a corollary, we construct nonsmoothable spin 4-manifolds satisfying Rohlin's theorem and the 10/8-inequality.Comment: 23 page

Gauge and Yukawa couplings in 6D supersymmetric SU(6) models

We study six-dimensional (6D) SU(6) supersymmetric models where the doublet-triplet splitting, quark-lepton mass relations and gaugino-mediated supersymmetry breaking are taken into account. We find that effective 4D gauge coupling constants have highly nontrivial behavior between two compactification scales. It is shown that realistic patterns of Yukawa coupling constants are obtained for valid values of parameters and that hierarchical numbers are generated via suppression by extra-dimensional effects.Comment: 56 pages, 5 figure

On the boundary components of central streams

Foliations on the space of $p$-divisible groups were studied by Oort in 2004. In his theory, special leaves called central stream play an important role. In this paper, we give a complete classification of the boundary components of the central streams for an arbitrary Newton polygon in the unpolarized case. Hopefully this classification would help us to know the boundaries of other leaves and more detailed structure of the boundaries of central streams

Examples of compact minitwistor spaces and their moduli space

In a paper (math.DG/0403528) we obtained explicit examples of Moishezon twistor spaces of some compact self-dual four-manifolds admitting a non-trivial Killing field, and also determined their moduli space. In this note we investigate minitwistor spaces associated to these twistor spaces. We determine their structure, minitwistor lines and also their moduli space, by using a double covering structure of the twistor spaces. In particular, we find that these minitwistor spaces have different properties in many respects, compared to known examples of minitwistor spaces. Especially, we show that the moduli space of the minitwistor spaces is identified with the configuration space of different 4 points on a circle divided by the standard PSL(2, R)-action.Comment: 10 pages. V2: title slightly changed, presentation improved, errors correcte

Geomety of generic Moishezon twistor spaces on 4CP^2

In this paper we investigate a family of Moishezon twistor spaces on the connected sum of 4 complex projective planes, which can be regarded as a direct generalization of the twistor spaces on 3CP^2 of double solid type studied by Poon and Kreussler-Kurke. These twistor spaces have a natural structure of double covering over a scroll of 2-planes over a conic. We determine the defining equations of the branch divisors in an explicit form, which are very similar to the case of 3CP^2. Using these explicit description we compute the dimension of the moduli spaces of these twistor spaces. Also we observe that similarly to the case of 3CP^2, these twistor spaces can also be considered as generic Moishezon twistor spaces on 4CP^2. We obtain these results by analyzing the anticanonical map of the twistor spaces in detail, which enables us to give an explicit construction of the twistor spaces, up to small resolutions.Comment: 31 pages, 5 figure

Bauer-Furuta invariants under Z_2-actions

S.Bauer and M.Furuta defined a stable cohomotopy refinement of the Seiberg-Witten invariants. In this paper, we prove a vanishing theorem of Bauer-Furuta invariants for 4-manifolds with smooth Z/2-actions. As an application, we give a constraint on smooth Z/2-actions on homotopy K3#K3, and construct a nonsmoothable locally linear Z/2-action on K3#K3. We also construct a nonsmoothable locally linear Z/2-action on $K3$.Comment: 21 pages, typos corrected, several descriptions change

Pin−(2)\mathrm{Pin}^-(2)-monopole invariants

We introduce a diffeomorphism invariant of $4$-manifolds, the $\mathrm{Pin}^-(2)$-monopole invariant, defined by using the $\mathrm{Pin}^-(2)$-monopole equations. We compute the invariants of several $4$-manifolds, and prove gluing formulae. By using the invariants, we construct exotic smooth structures on the connected sum of an elliptic surface $E(n)$ with arbitrary number of the $4$-manifolds of the form of $S^2\times\Sigma$ or $S^1\times Y$ where $\Sigma$ is a compact Riemann surface with positive genus and $Y$ is a closed $3$-manifold. As another application, we give an estimate of the genus of surfaces embedded in a $4$-manifold $X$ representing a class $\alpha\in H_2(X;l)$, where $l$ is a local coefficient on $X$.Comment: 48 pages, minor revisio

Smoothability of Z\times Z-actions on 4-manifolds

We construct a nonsmoothable Z\times Z-action on the connected sum of an Enriques surface and S^2\times S^2, such that each of generators is smoothable. We also construct a nonsmoothable self-homeomorphism on an Enriques surface.Comment: 6 page

Self-dual metrics and twenty-eight bitangents

We consider self-dual metrics on 3CP^2 of positive scalar curvature admitting a non-trivial Killing field, but which is not conformally isometric to LeBrun's metrics. Firstly, we determine defining equations of the twistor spaces of such self-dual metrics. Next we prove that conversely, the complex threefolds defined by the equations always become twistor spaces of self-dual metrics on 3CP^2 of the above kind. As a corollary, we determine a global structure of the moduli spaces of these self-dual metrics; namely we show that the moduli space is non-empty and isomorphic to R^3/G, where G is an involution of R^3 having one-dimensional fixed locus. Combined with works of LeBrun, this settles a moduli problem of self-dual metrics on 3CP^2 of positive scalar curvature admitting a non-trivial Killing field. In our proof, a key role is played by a classical result in algebraic geometry that a smooth plane quartic always possesses twenty-eight bitangents.Comment: 71 pages. V2; errors corrected. V3; 15 figures adde