5,406 research outputs found
Emergent Calabi-Yau Geometry
We show how the smooth geometry of Calabi-Yau manifolds emerges from the
thermodynamic limit of the statistical mechanical model of crystal melting
defined in our previous paper arXiv:0811.2801. In particular, the thermodynamic
partition function of molten crystals is shown to be equal to the classical
limit of the partition function of the topological string theory by relating
the Ronkin function of the characteristic polynomial of the crystal melting
model to the holomorphic 3-form on the corresponding Calabi-Yau manifold.Comment: 4 pages; v2: revised discussion on wall crossing; v3: typos
corrected, published versio
Topological quantum D-branes and wild embeddings from exotic smooth R^4
This is the next step of uncovering the relation between string theory and
exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges
in IIA string theory. We construct wild embeddings of spheres and relate them
to a class of topological quantum Dp-branes as well to KK theory. These branes
emerge when there are non-trivial NS-NS H-fluxes where the topological classes
are determined by wild embeddings S^2 -> S^3. Then wild embeddings of higher
dimensional -complexes into S^n correspond to Dp-branes. These wild
embeddings as constructed by using gropes are basic objects to understand
exotic smoothness as well Casson handles. Next we build C*-algebras
corresponding to the embeddings. Finally we consider topological quantum
D-branes as those which emerge from wild embeddings in question. We construct
an action for these quantum D-branes and show that the classical limit agrees
with the Born-Infeld action such that flat branes = usual embeddings.Comment: 18 pages, 1 figur
Constructions of generalized complex structures in dimension four
Four-manifold theory is employed to study the existence of (twisted)
generalized complex structures. It is shown that there exist (twisted)
generalized complex structures that have more than one type change loci. In an
example-driven fashion, (twisted) generalized complex structures are
constructed on a myriad of four-manifolds, both simply and non-simply
connected, which are neither complex nor symplectic
Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry
Assuming the standard framework of mirror symmetry, a conjecture is
formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y
should act by families of Fourier-Mukai transforms over the complex moduli
space of the mirror X. The conjecture generalizes a proposal of Kontsevich
relating monodromy transformations and self-equivalences. Supporting evidence
is given in the case of elliptic curves, lattice-polarized K3 surfaces and
Calabi-Yau threefolds. A relation to the global Torelli problem is discussed.Comment: Approx. 20 pages LaTeX. One reference adde
Remarks on the naturality of quantization
Hamiltonian quantization of an integral compact symplectic manifold M depends
on a choice of compatible almost complex structure J. For open sets U in the
set of compatible almost complex structures and small enough values of Planck's
constant, the Hilbert spaces of the quantization form a bundle over U with a
natural connection. In this paper we examine the dependence of the Hilbert
spaces on the choice of J, by computing the semi-classical limit of the
curvature of this connection. We also show that parallel transport provides a
link between the action of the group Symp(M) of symplectomorphisms of M and the
Schrodinger equation.Comment: 20 page
A risk assessment for visual only meat inspection of both indoor and outdoor pigs within the UK
The current system of post-mortem inspection using the typical macroscopic inspection techniques is ineffective identifying the most common foodborne illenss risks, e.g. Salmonella or Campylobacter. Therefore, there is a need to adopt a more appropriate, risk-based approach to meat inspection
Microfold (M) cells: important immunosurveillance posts in the intestinal epithelium
This article suggest that technopreneurship subject should no longer be offered to ITB student as an optional subject but a compulsory one. The reason is that this subject may enable ITB's graduates to be technopreneurs when they graduate. In his opinion, a technopreneur is regarded as a critical success factor in increasing both Growth National Product (GNP). Therefore, their role in resolving Indonesia's current multi dimensional crises and enhancing Indonesia's development will be very significant. The writer also claims that this subject is relevant for ITB's student-who will become engineers and specialists in arts when they graduate-since technopreneurship subject teaches the students how to do business in the field of engineering and art and train the students to acquire technopreneur's qualities such as being critical, innovative, reasonable, positive thinking, risk taking person
A note on monopole moduli spaces
We discuss the structure of the framed moduli space of Bogomolny monopoles
for arbitrary symmetry breaking and extend the definition of its stratification
to the case of arbitrary compact Lie groups. We show that each stratum is a
union of submanifolds for which we conjecture that the natural metric is
hyperKahler. The dimensions of the strata and of these submanifolds are
calculated, and it is found that for the latter, the dimension is always a
multiple of four.Comment: 17 pages, LaTe
On semistable principal bundles over a complex projective manifold, II
Let (X, \omega) be a compact connected Kaehler manifold of complex dimension
d and E_G a holomorphic principal G-bundle on X, where G is a connected
reductive linear algebraic group defined over C. Let Z (G) denote the center of
G. We prove that the following three statements are equivalent: (1) There is a
parabolic subgroup P of G and a holomorphic reduction of the structure group of
E_G to P (say, E_P) such that the bundle obtained by extending the structure
group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat
connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The
principal G-bundle E_G is pseudostable, and the degree of the charateristic
class c_2(ad(E_G) is zero.Comment: 15 page
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