39 research outputs found
4D, N = 1 Supersymmetry Genomics (I)
Presented in this paper the nature of the supersymmetrical representation
theory behind 4D, N = 1 theories, as described by component fields, is
investigated using the tools of Adinkras and Garden Algebras. A survey of
familiar matter multiplets using these techniques reveals they are described by
two fundamental valise Adinkras that are given the names of the cis-Valise
(c-V) and the trans-Valise (t-V). A conjecture is made that all off-shell 4D, N
= 1 component descriptions of supermultiplets are associated with two integers
- the numbers of c-V and t-V Adinkras that occur in the representation.Comment: 53 pages, 19 figures, Report-II of SSTPRS 2008 Added another chapter
for clarificatio
Hodge Numbers from Picard-Fuchs Equations
Given a variation of Hodge structure over P¹ with Hodge numbers (1,1,…,1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin-Kontsevich-Möller-Zorich, by using the local exponents of the corresponding Picard-Fuchs equation. This allows us to compute the Hodge numbers of Zucker's Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi-Yau threefolds
Riemann-Hilbert problem for Hurwitz Frobenius manifolds: regular singularities
In this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy)
problem corresponding to Frobenius structures on Hurwitz spaces. We find a
solution to this Riemann-Hilbert problem in terms of integrals of certain
meromorphic differentials over a basis of an appropriate relative homology
space, study the corresponding monodromy group and compute the monodromy
matrices explicitly for various special cases.Comment: final versio
Supersymmetric Intersecting Branes on the Type IIA T^6/Z_4 orientifold
We study supersymmetric intersecting D6-branes wrapping 3-cycles in the Type
IIA T^6/Z_4 orientifold background. As a new feature, the 3-cycles in this
orbifold space arise both from the untwisted and the Z_2 twisted sectors. We
present an integral basis for the homology lattice, H_3(M,Z), in terms of
fractional 3-cycles, for which the intersection form involves the Cartan matrix
of E8. We show that these fractional D6-branes can be used to construct
supersymmetric brane configurations realizing a three generation Pati-Salam
model. Via brane recombination processes preserving supersymmetry, this GUT
model can be broken down to a standard-like model.Comment: 48 pages, TeX, harvmac, 8 figures, v4: some signs correcte
Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
We investigate orientifolds of type II string theory on K3 and Calabi-Yau
3-folds with intersecting D-branes wrapping special Lagrangian cycles. We
determine quite generically the chiral massless spectrum in terms of
topological invariants and discuss both orbifold examples and algebraic
realizations in detail. Intriguingly, the developed techniques provide an
elegant way to figure out the chiral sector of orientifold models without
computing any explicit string partition function. As a new example we derive a
non-supersymmetric Standard-like Model from an orientifold of type IIA on the
quintic Calabi-Yau 3-fold with wrapped D6-branes. In the case of supersymmetric
intersecting brane models on Calabi-Yau manifolds we discuss the D-term and
F-term potentials, the effective gauge couplings and the Green-Schwarz
mechanism. The mirror symmetric formulation of this construction is provided
within type IIB theory. We finally include a short discussion about the lift of
these models from type IIB on K3 to F-theory and from type IIA on Calabi-Yau
3-folds to M-theory on G_2 manifolds.Comment: 82 pages, harvmac, 5 figures. v2: references added. v3: T^6
orientifold corrected, JHEP versio
Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
We present the most complete list of mirror pairs of Calabi-Yau complete
intersections in toric ambient varieties and develop the methods to solve the
topological string and to calculate higher genus amplitudes on these compact
Calabi-Yau spaces. These symplectic invariants are used to remove redundancies
in examples. The construction of the B-model propagators leads to compatibility
conditions, which constrain multi-parameter mirror maps. For K3 fibered
Calabi-Yau spaces without reducible fibers we find closed formulas for all
genus contributions in the fiber direction from the geometry of the fibration.
If the heterotic dual to this geometry is known, the higher genus invariants
can be identified with the degeneracies of BPS states contributing to
gravitational threshold corrections and all genus checks on string duality in
the perturbative regime are accomplished. We find, however, that the BPS
degeneracies do not uniquely fix the non-perturbative completion of the
heterotic string. For these geometries we can write the topological partition
function in terms of the Donaldson-Thomas invariants and we perform a
non-trivial check of S-duality in topological strings. We further investigate
transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2
quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur
Supersymmetry, G-flux and Spin(7) manifolds
In this note we study warped compactifications of M-theory on manifolds of
Spin(7) holonomy in the presence of background 4-form flux. The explicit form
of the superpotential can be given in terms of the self -dual Cayley
calibration on the Spin(7) manifold, in agreement with the general formula
propsed in hep-th/9911011
Recent developments in the techniques of controlling and measuring suction in unsaturated soils
Calabi-Yau Volumes and Reflexive Polytopes
We study various geometrical quantities for Calabi–Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the Sasaki–Einstein base of the corresponding Calabi–Yau cone are calculated. By doing so, we conjecture new bounds for the Sasaki–Einstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence