Supersymmetric Three-cycles Research Articles

Towards geometric D6-brane model building on non-factorisable toroidal ℤ 4-orbifolds

We present a geometric approach to D-brane model building on the non-factorisable torus backgrounds of $T^6/\mathbb{Z}_4$, which are $A_3 \times A_3$ and $A_3 \times A_1 \times B_2$. Based on the counting of `short' supersymmetric three-cycles per complex structure {\it vev}, the number of physically inequivalent lattice orientations with respect to the anti-holomorphic involution ${\cal R}$ of the Type IIA/$\Omega\cal{R}$ orientifold can be reduced to three for the $A_3 \times A_3$ lattice and four for the $A_3 \times A_1 \times B_2$ lattice. While four independent three-cycles on $A_3 \times A_3$ cannot accommodate phenomenologically interesting global models with a chiral spectrum, the eight-dimensional space of three-cycles on $A_3 \times A_1 \times B_2$ is rich enough to provide for particle physics models, with several globally consistent two- and four-generation Pati-Salam models presented here. We further show that for fractional {\it sLag} three-cycles, the compact geometry can be rewritten in a $(T^2)^3$ factorised form, paving the way for a generalisation of known CFT methods to determine the vector-like spectrum and to derive the low-energy effective action for open string states.

Effects of brane-flux transition on black holes in string theory

Extremal N=2 black holes in four dimensions can be described by an ensemble of D3-branes wrapped on internal supersymmetric three-cycles of Calabi-Yau threefolds on which type IIB superstring theory is compactified. We construct a similar configuration, with extra RR and NS-NS three-form fluxes being turned on. We can avoid the Freed-Witten anomaly on the D3-branes by enforcing the pullback of these extra fluxes to the D3-branes to vanish at the classical level. In the setup the D3-brane charge is not conserved since it is classified as a trivial class in twisted K-theory. Consequently, the D3-branes may disappear by encountering an instantonic D5-brane localized in time. We discuss what happens on the black hole described by such disappearing D3-branes, relying mainly on topological arguments. Especially, we argue that another RR three-form flux will be left as a lump of remnant which is localized in the uncompactified four-dimensional space-time and that it may carry the same amount of degrees of freedom to describe a black hole, in cooperation with the original NS-NS flux, after this transition of the D3-branes.

Supersymmetric intersecting D6-branes and fluxes in massive Type IIA string theory

We study N=1 supersymmetric four-dimensional solutions of massive Type IIA supergravity with intersecting D6-branes in the presence NS–NS three-form fluxes. We derive N=1 supersymmetry conditions for the D6-brane and flux configurations in an internal manifold X 6 and derive the intrinsic torsion (or SU(3)-structure) related to the fluxes. In the absence of fluxes, N=1 supersymmetry implies that D6-branes wrap supersymmetric three-cycles of X 6 that intersect at angles of SU(3) rotations and the geometry is deformed by SU(3)-structures. The presence of fluxes breaks the SU(3) structures to SU(2) and the D6-branes intersect at angles of SU(2) rotations; non-zero mass parameter corresponds to D8-branes which are orthogonal to the common cycle of all D6-branes. The anomaly inflow indicates that the gauge theory on intersecting (massive) D6-branes is not chiral.

More supersymmetric standardlike models from intersecting D6-branes on type IIA orientifolds

We present new classes of supersymmetric Standard-like models from type IIA $\IT^6/(\IZ_2\times \IZ_2)$ orientifold with intersecting D6-branes. D6-branes can wrap general supersymmetric three-cycles of $\IT^6=\IT^2\times \IT^2\times \IT^2$, and any $\IT^2$ is allowed to be tilted. The models still suffer from additional exotics, however we obtained solutions with fewer Higgs doublets, as well as models with all three families of left-handed quarks and leptons arising from the same intersecting sector, and examples of a genuine left-right symmetric model with three copies of left-handed and right-handed families of quarks and leptons.

Calibrated geometries and non-perturbative superpotentials in M-theory

We consider non perturbative effects in M-theory compactifications on a seven-manifold of G_2 holonomy arising from membranes wrapped on supersymmetric three-cycles. When membranes are wrapped on associative submanifolds they induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification on a seven-manifold, to four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity with non vanishing expectation value of the four-form field strength.

Mirror symmetry for open strings

We discuss the generation of superpotentials in four-dimensional, N = 1 supersymmetric field theories arising from type IIA D6-branes wrapped on supersymmetric three-cycles of a Calabi-Yau threefold. In general, nontrivial superpotentials arise from sums over disc instantons. We find several examples of special Lagrangian three-cycles with nontrivial topology which are mirror to obstructed rational curves, conclusively demonstrating the existence of such instanton effects. In addition, we present explicit examples of disc instantons ending on the relevant three-cycles. Finally, we give a preliminary construction of a mirror map for the open string moduli, in a large-radius limit of the type IIA compactification.

Supersymmetric three-cycles and (super)symmetry breaking

We describe physical phenomena associated with a class of transitions that occur in the study of supersymmetric three-cycles in Calabi-Yau (CY) threefolds. The transitions in question occur at real codimension one in the complex structure moduli space of the Calabi-Yau manifold. In type-IIB string theory, these transitions can be used to describe the evolution of a Bogomol'nyi-Prasad-Sommerfeld (BPS) state as one moves through a locus of marginal stability: at the transition point the BPS particle becomes degenerate with a supersymmetric two-particle state, and after the transition the lowest energy state carrying the same charges is a nonsupersymmetric two-particle state. In the IIA theory, wrapping the cycles in question with D6 branes leads to a simple realization of the Fayet model: for some values of the CY modulus gauge symmetry is spontaneously broken, while for other values supersymmetry is spontaneously broken.

Aspects of NT ⩾ 2 topological gauge theories and D-branes

We comment on various aspects of topological gauge theories possessing N T ⩾ 2 topological symmetry: (1) We show that the construction of Vafa-Witten and Dijkgraaf-Moore of ‘balanced’ topological field theories is equivalent to an earlier construction in terms of N T = 2 superfields inspired by supersymmetric quantum mechanics. (2) We explain the relation between topological field theories calculating signed and unsigned sums of Euler numbers of moduli spaces. (3) We show that the topological twist of N = 4 d = 4 Yang-Mills theory recently constructed by Marcus is formally a deformation of four-dimensional super-BF theory. (4) We construct a novel N T = 2 topological twist of N = 4 d = 3 Yang-Mills theory, a ‘mirror’ of the Casson invariant model, with certain unusual features (e.g. no bosonic scalar field and hence no underlying equivariant cohomology) (5) We give a complete classification of the topological twists of N = 8 d = 3 Yang-Mills theory and show that they are realised as world-volume theories of Dirichlet two brane instantons wrapping supersymmetric three-cycles of Calabi-Yau three-folds and G 2-holonomy Joyce manifolds. (6) We describe the topological gauge theories associated to D-string instantons on holomorphic curves in K3's and Calabi-Yau 3-folds.