477 research outputs found
Mirror Symmetry and Landau Ginzburg Calabi-Yau Superpotentials in F-theory Compactifications
We study Landau Ginzburg (LG) theories mirror to 2D N=2 gauged linear sigma
models on toric Calabi-Yau manifolds. We derive and solve new constraint
equations for Landau Ginzburg elliptic Calabi-Yau superpotentials, depending on
the physical data of dual linear sigma models. In Calabi-Yau threefolds case,
we consider two examples. First, we give the mirror symmetry of the canonical
line bundle over the Hirzebruch surfaces . Second, we find a special
geometry with the affine so(8) Lie algebra toric data extending the geometry of
elliptically fibered K3. This geometry leads to a pure N=1 six dimensional
SO(8) gauge model from the F-theory compactification. For Calabi-Yau fourfolds,
we give a new algebraic realization for ADE hypersurfaces.Comment: 27 pages, latex. To appear in Journal of Physics A: Mathematical and
Genera
NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration
Using the algebraic geometry method of Berenstein and Leigh (BL),
hep-th/0009209 and hep-th/0105229), and considering singular toric varieties
with NC irrational torus fibration, we construct NC extensions
of complex d dimension Calabi-Yau (CY) manifolds embedded
in . We give realizations of the NC toric group, derive the constraint eqs for NC Calabi-Yau (NCCY) manifolds
embedded in and work out solutions for
their generators. We study fractional branes at singularities and show
that, due to the complete reducibility property of group
representations, there is an infinite number of non compact fractional branes
at fixed points of the NC toric group.Comment: 12 pages, LaTex, no figur
On ADE Quiver Models and F-Theory Compactification
Based on mirror symmetry, we discuss geometric engineering of N=1 ADE quiver
models from F-theory compactifications on elliptic K3 surfaces fibered over
certain four-dimensional base spaces. The latter are constructed as
intersecting 4-cycles according to ADE Dynkin diagrams, thereby mimicking the
construction of Calabi-Yau threefolds used in geometric engineering in type II
superstring theory. Matter is incorporated by considering D7-branes wrapping
these 4-cycles. Using a geometric procedure referred to as folding, we discuss
how the corresponding physics can be converted into a scenario with D5-branes
wrapping 2-cycles of ALE spaces.Comment: 21 pages, Latex, minor change
Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case
Using Katz, Klemm and Vafa geometric engineering method of
supersymmetric QFTs and results on the classification of generalized
Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of
CFTs based on \textit{indefinite} singularities. We show
that the vanishing condition for the general expression of holomorphic beta
function of quiver gauge QFTs coincides exactly with the
fundamental classification theorem of KM algebras. Explicit solutions are
derived for mirror geometries of CY threefolds with \textit{% hyperbolic}
singularities.Comment: 23 pages, 4 figures, minor change
Classification of N=2 supersymmetric CFT_{4}s: Indefinite Series
Using geometric engineering method of 4D quiver gauge
theories and results on the classification of Kac-Moody (KM) algebras, we show
on explicit examples that there exist three sectors of infrared
CFTs. Since the geometric engineering of these CFTs involve type II
strings on K3 fibered CY3 singularities, we conjecture the existence of three
kinds of singular complex surfaces containing, in addition to the two standard
classes, a third indefinite set. To illustrate this hypothesis, we give
explicit examples of K3 surfaces with H and E hyperbolic
singularities. We also derive a hierarchy of indefinite complex algebraic
geometries based on affine and T algebras going beyond the
hyperbolic subset. Such hierarchical surfaces have a remarkable signature that
is manifested by the presence of poles.Comment: 12 pages, 2 figure
On Thermodynamics of AdS Black Holes in M-Theory
Motivated by a recent work on asymptotically AdS_4 black holes in M-theory,
we investigate the thermodynamics and thermodynamical geometry of AdS black
holes from M2 and M5-branes. Concretely, we consider AdS black holes in
AdS_{p+2}\times S^{11-p-2}, where p=2,5 by interpreting the number of M2 (and
M5-branes) as a thermodynamical variable. We study the corresponding phase
transition to examine their stabilities by calculating and discussing various
thermodynamical quantities including the chemical potential. Then, we compute
the thermodynamical curvatures from the Quevedo metric for M2 and M5-branes
geometries to reconsider the stability of such black objects. The Quevedo
metric singularities recover similar stability results provided by the phase
transition program.Comment: 16 pages, 12 figures. Late
Ehrenfest Scheme of Higher Dimensional Topological AdS Black Holes in The Third Order Lovelock-Born-Infeld Gravity
Interpreting the cosmological constant as a thermodynamic pressure and its
conjugate quantity as a thermodynamic volume, we reconsider the investigation
of P-V critical behaviors of (1+n)-dimensional topological AdS black holes in
Lovelock-Born-Infeld gravity. In particular, we give an explicit expression of
the universal number \chi=\frac{P_c v_c}{T_c} in terms of the space dimension
. Then, we examine the phase transitions at the critical points of such
topological black holes for 6 \leq n \leq 11 as required by the physical
condition of the thermodynamical quantities. More precisely, the Ehrenfest
equations have been checked revealing that the black hole system undergoes a
second phase transition at the critical points.Comment: 18 pages, latex with 10 figures, titled modified, section added,
typos corrected, accepted for publication in International Journal of
Geometric Methods in Modern Physics (2015
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