Supergravity in Twelve Dimension

We consider supergravity in twelve dimension, whose dimensional reduction yields eleven-dimensional, IIA, and IIB supergravities. This also provides the effective field theory of F-theory. We must take one direction as a compact circle, so that the Poincar\'e symmetry and the zero-mode field contents are identical to those of eleven-dimensional supergravity. We also have a tower of massive Kaluza-Klein states to be viewed as the wrapping modes of M2-branes. The twelfth dimension decompactifies only if other two directions are compactified on a torus, restoring different ten dimensional Poincar\'e symmetry of IIB supergravity, whose missing graviton is provided by components of the rank three tensor field. This condition prevents us from violating the condition on the maximal number of real supercharges, which should be thirty-two. The self-duality condition of the IIB four-form fields is understood from twelve-dimensional Hodge duality. In this framework T-duality is re-interpreted as taking different compactification routes.Comment: 33+1 page

On the Standard Model Group in F-theory

We analyze the Standard Model gauge group SU(3) x SU(2) x U(1) constructed in F-theory. The non-Abelian part SU(3) x SU(2) is described by singularities of Kodaira type. It is distinguished to naive product of SU(3) and SU(2), revealed by blow-up analysis, since the resolution procedures cannot be done separately to each group. The Abelian part U(1) is constructed by obtaining a desirable global two-form harboring it, using `factorization method' similar to the decomposition method of the spectral cover; It makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU(5) is achieved, without threshold correction from the flux along hypercharge direction.Comment: 29 page

E(lementary) Strings in Six-Dimensional Heterotic F-Theory

Using E-strings, we can analyze not only six-dimensional superconformal field theories but also probe vacua of non-perturabative heterotic string. We study strings made of D3-branes wrapped on various two-cycles in the global F-theory setup. We claim that E-strings are elementary in the sense that various combinations of E-strings can form M-strings as well as heterotic strings and new kind of strings, called G-strings. Using them, we show that emissions and combinations of heterotic small instantons generate most of known six-dimensional superconformal theories, their affinizations and little string theories. Taking account of global structure of compact internal geometry, we also show that special combinations of E-strings play an important role in constructing six-dimensional theories of $D$- and $E$-types. We check global consistency conditions from anomaly cancellation conditions, both from five-branes and strings, and show that they are given in terms of elementary E-string combinations.Comment: 58 pages, 16 figures; v2. version to appear in JHE

Supersymmetric three family chiral SU(6) grand unification model from F-theory

We obtain a supersymmetric three family chiral SU(6) grand unification model with the global family symmetry SU(3)[family] from F-theory. This model has nice features such as all the fermion masses are reasonably generated and there results only one pair of Higgs doublets, realizing the doublet-triplet splitting from the family symmetry SU(3)[family]. The proton hexality is realized toward the proton stability problem. There is a room to fit the three gauge couplings using the F-theory flux idea and we obtain the proton lifetime in the 10^{36-37} yr region.Comment: 5 pages, to be published in Phys. Rev.

Non-thermal WIMP baryogenesis

We propose a WIMP baryogensis achieved by the annihilation of non-thermally produced WIMPs from decay of heavy particles, which can result in low reheating temerature. Dark matter (DM) can be produced non-thermally during a reheating period created by the decay of long-lived heavy particle, and subsequently re-annihilate to lighter particles even after the thermal freeze-out. The re-annihilation of DM provides the observed baryon asymmetry as well as the correct relic density of DM. We investigate how wahout effects can affect the generation of the baryon asymmetry and study a model suppressing them. In this scenario, we find that DM can be heavy enough and its annihilation cross section can also be larger than that adopted in the usual thermal WIMP baryogenesis.Comment: 5 pages, 6 figure