295 research outputs found

    Supergravity in Twelve Dimension

    Full text link
    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

    Get PDF
    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

    Full text link
    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 DD- and EE-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

    Full text link
    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.

    Exact Renormalization of the Higgs Field

    Full text link
    Using Wilsonian renormalization, we calculate the quantum correction to observable quantities, rather than the bare parameters, of the Higgs field. A physical parameter, such as a mass-squared or a quartic coupling, at an energy scale μ\mu is obtained from that at a reference scale by integrating in the degrees of freedom in between. In this process, heavy modes decouple and the ultraviolet scale dependence is canceled in the observables. An exact renormalization group equation is parametrized by the low-energy scale μ\mu.Comment: 4 pages, 2 figures, v2: title change, published versio
    • …
    corecore