20,840 research outputs found
Geometric constraints in dual F-theory and heterotic string compactifications
We systematically analyze a broad class of dual heterotic and F-theory models
that give four-dimensional supergravity theories, and compare the geometric
constraints on the two sides of the duality. Specifically, we give a complete
classification of models where the heterotic theory is compactified on a smooth
Calabi-Yau threefold that is elliptically fibered with a single section and
carries smooth irreducible vector bundles, and the dual F-theory model has a
corresponding threefold base that has the form of a P^1 bundle. We formulate
simple conditions for the geometry on the F-theory side to support an
elliptically fibered Calabi-Yau fourfold. We match these conditions with
conditions for the existence of stable vector bundles on the heterotic side,
and show that F-theory gives new insight into the conditions under which such
bundles can be constructed. In particular, we find that many allowed F-theory
models correspond to vector bundles on the heterotic side with exceptional
structure groups, and determine a topological condition that is only satisfied
for bundles of this type. We show that in many cases the F-theory geometry
imposes a constraint on the extent to which the gauge group can be enhanced,
corresponding to limits on the way in which the heterotic bundle can decompose.
We explicitly construct all (4962) F-theory threefold bases for dual
F-theory/heterotic constructions in the subset of models where the common
twofold base surface is toric, and give both toric and non-toric examples of
the general results.Comment: 81 pages, 2 figures; v2, v3: references added, minor corrections; v4:
minor errors, Table 5 correcte
Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds
We propose a novel approach to obtain non-supersymmetric four-dimensional
effective actions by considering F-theory on manifolds with special holonomy
Spin(7). To perform such studies we suggest that a duality relating M-theory on
a certain class of Spin(7) manifolds with F-theory on the same manifolds times
an interval exists. The Spin(7) geometries under consideration are constructed
as quotients of elliptically fibered Calabi-Yau fourfolds by an
anti-holomorphic and isometric involution. The three-dimensional minimally
supersymmetric effective action of M-theory on a general Spin(7) manifold with
fluxes is determined and specialized to the aforementioned geometries. This
effective theory is compared with an interval Kaluza-Klein reduction of a
non-supersymmetric four-dimensional theory with definite boundary conditions
for all fields. Using this strategy a minimal set of couplings of the
four-dimensional low-energy effective actions is obtained in terms of the
Spin(7) geometric data. We also discuss briefly the string interpretation in
the Type IIB weak coupling limit.Comment: 39 pages, 4 figures, v2: improvements and clarifications on the 4d
interpretation and weak coupling limit; typos correcte
Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics
We construct asymptotically AdS_5 solutions to 5-dimensional Einstein-Maxwell
theory with Chern-Simons term which are dual to 4-dimensional gauge theories,
including N=4 SYM theory, in the presence of a constant background magnetic
field B and a uniform electric charge density \rho. For the solutions
corresponding to supersymmetric gauge theories, we find numerically that a
small magnetic field causes a drastic decrease in the entropy at low
temperatures. The near-horizon AdS_2 \times R^3 geometry of the purely
electrically charged brane thus appears to be unstable under the addition of a
small magnetic field. Based on this observation, we propose a formulation of
the third law of thermodynamics (or Nernst theorem) that can be applied to
black holes in the AdS/CFT context.
We also find interesting behavior for smaller, non-supersymmetric, values of
the Chern-Simons coupling k. For k=1 we exhibit exact solutions corresponding
to warped AdS_3 black holes, and show that these can be connected to
asymptotically AdS_5 spacetime. For k\leq 1 the entropy appears to go to a
finite value at extremality, but the solutions still exhibit a mild singularity
at strictly zero temperature. In addition to our numerics, we carry out a
complete perturbative analysis valid to order B^2, and find that this
corroborates our numerical results insofar as they overlap.Comment: 45 pages v2: added note about subsequent results found in
arXiv:1003.130
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