295 research outputs found
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 - and -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.
Exact Renormalization of the Higgs Field
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 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 .Comment: 4 pages, 2 figures, v2: title change, published versio
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