2,580 research outputs found
Complex projective surfaces and infinite groups
The paper contains a general construction which produces new examples of non
simply-connected smooth projective surfaces. We analyze the resulting surfaces
and their fundamental groups. Many of these fundamental groups are expected to
be non-residually finite. Using the construction we also suggest a series of
potential counterexamples to the Shafarevich conjecture which claims that the
universal covering of smooth projective variety is holomorphically convex. The
examples are only potential since they depend on group theoretic questions,
which we formulate, but we do not know how to answer. At the end we formulate
an arithmetic version of the Shafarevich conjecture.Comment: 29 pages, some comments and examples added LaTeX 2.0
Triadophilia: A Special Corner in the Landscape
It is well known that there are a great many apparently consistent vacua of
string theory. We draw attention to the fact that there appear to be very few
Calabi--Yau manifolds with the Hodge numbers h^{11} and h^{21} both small. Of
these, the case (h^{11}, h^{21})=(3,3) corresponds to a manifold on which a
three generation heterotic model has recently been constructed. We point out
also that there is a very close relation between this manifold and several
familiar manifolds including the `three-generation' manifolds with \chi=-6 that
were found by Tian and Yau, and by Schimmrigk, during early investigations. It
is an intriguing possibility that we may live in a naturally defined corner of
the landscape. The location of these three generation models with respect to a
corner of the landscape is so striking that we are led to consider the
possibility of transitions between heterotic vacua. The possibility of these
transitions, that we here refer to as transgressions, is an old idea that goes
back to Witten. Here we apply this idea to connect three generation vacua on
different Calabi-Yau manifolds.Comment: 41 pages 4 pdf figures, one is large. Improved discussion of the
Gross-Popescu manifolds, Figure 4 added, additions to Table 1 and other minor
correction
Holomorphic Vector Bundles and Non-Perturbative Vacua in M-Theory
We review the spectral cover formalism for constructing both U(n) and SU(n)
holomorphic vector bundles on elliptically fibered Calabi-Yau three-folds which
admit a section. We discuss the allowed bases of these three-folds and show
that physical constraints eliminate Enriques surfaces from consideration.
Relevant properties of the remaining del Pezzo and Hirzebruch surfaces are
presented. Restricting the structure group to SU(n), we derive, in detail, a
set of rules for the construction of three-family particle physics theories
with phenomenologically relevant gauge groups. We show that anomaly
cancellation generically requires the existence of non-perturbative vacua
containing five-branes. We illustrate these ideas by constructing four explicit
three-family non-perturbative vacua.Comment: 44 pages, Latex 2e with amsmath, typos correcte
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