Mirror symmetry

About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.

Open-closed Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric DM stacks

Abstract: We study open-closed orbifold Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric DM stacks with respect to Lagrangian branes of Aganagic-Vafa type. We prove an open mirror theorem for toric Calabi-Yau 3-orbifolds, which expresses generating functions of orbifold disk invariants in terms of Abel-Jacobi maps of the mirror curves. This generalizes a conjecture by Aganagic-Vafa and Aganagic- Klemm-Vafa, proved by the first and the second authors, on disk invariants of smooth toric Calabi-Yau 3-folds. Open Gromov-Witten invariants of toric Calabi-Yau 3-folds have been studied extensively by both math- ematicians and physicists. They correspond to "A-model topological open string amplitudes" in the physics literature and can be interpreted as intersection numbers of certain moduli spaces of holomorphic maps from bordered Riemann surfaces to the 3-fold with boundaries in a Lagrangian submanifold. The physics prediction of these open Gromov-Witten invariants comes from string dualities: mirror symmetry relates the A-model topological string theory of a Calabi-Yau 3-fold X to the B-model topological string theory of the mirror Calabi-Yau 3-fold X ∨ ; the large N duality relates the A-model topological string theory of

On gauge/string correspondence and mirror symmetry

Abstract: We consider a mirror dual of the Berkovits-Vafa A-model for the BPS superstring on AdS5 × S5 in the form of a deformed superconifold. Via geometric transition, the theory has a dual description as the hermitian gaussian one-matrix model. We show that the A-model amplitudes of AdS2 × S4 branes, breaking the superconformal symmetry as U(2,2|4) → OSp(4*|4), are evaluated in terms of observables in the matrix model. As such, upon the usual identification gYM2 = gs, these can be expanded as Drukker-Gross circular 1/2-BPS Wilson loops in the perturbative regime of = 4 SYM.

Special geometry and the swampland

Abstract: In the context of 4d effective gravity theories with 8 supersymmetries, we propose to unify, strenghten, and refine the several swampland conjectures into a single statement: the structural criterion, modelled on the structure theorem in Hodge theory. In its most abstract form the new swampland criterion applies to all 4d $$ \mathcal{N} $$ = 2 effective theories (having a quantum-consistent UV completion) whether supersymmetry is local or rigid: indeed it may be regarded as the more general version of Seiberg-Witten geometry which holds both in the rigid and local cases. As a first application of the new swampland criterion we show that a quantum-consistent $$ \mathcal{N} $$ = 2 supergravity with a cubic pre-potential is necessarily a truncation of a higher- $$ \mathcal{N} $$ sugra. More precisely: its moduli space is a Shimura variety of ‘magic’ type. In all other cases a quantum-consistent special Kahler geometry is either an arithmetic quotient of the complex hyperbolic space SU(1, m)/U(m) or has no local Killing vector. Applied to Calabi-Yau 3-folds this result implies (assuming mirror symmetry) the validity of the Oguiso-Sakurai conjecture in Algebraic Geometry: all Calabi-Yau 3-folds X without rational curves have Picard number ρ = 2, 3; in facts they are finite quotients of Abelian varieties. More generally: the Kahler moduli of X do not receive quantum corrections if and only if X has infinite fundamental group. In all other cases the Kahler moduli have instanton corrections in (essentially) all possible degrees.

Tunneling through triple quantum dots with mirror symmetry

Abstract: Indirect exchange interactions between itinerant electrons and nanostructures with nontrivial geometrical configurations manifest a plethora of unexpected results. These configurations can be realized either in quantum dots with several potential valleys or in real complex molecules with strong correlations. Here we demonstrate that the Kondo effect may be suppressed under certain conditions in triple quantum dots with mirror symmetry at odd electron occupation. First, we show that the indirect exchange has a ferromagnetic sign in the ground state of triple quantum dots in a two-terminal cross geometry for electron occupation $N=3$. Second, we show that for electron occupation $N=1$ in three-terminal fork geometry the zero-bias anomaly in the tunnel conductance is absent (despite the presence of Kondo screening) due to the special symmetry of the dot wave function.