Mirror symmetry

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

Special Lagrangian m-folds in C m with symmetries

Abstract: This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones in C^m invariant under a subgroup G in SU(m) isomorphic to U(1)^{m-2}. By writing the special Lagrangian equation as an o.d.e. in G-orbits and solving the o.d.e., we find a large family of distinct, G-invariant special Lagrangian cones on T^{m-1} in C^m. These examples are interesting as local models for singularities of special Lagrangian submanifolds of Calabi-Yau manifolds. Such models will be needed to understand Mirror Symmetry and the SYZ conjecture.

The effective action of D6-branes in $ \mathcal{N} = 1 $ type IIA orientifolds

Abstract: We use a Kaluza-Klein reduction to compute the low-energy effective action for the massless modes of a spacetime-filling D6-brane wrapped on a special Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold. The modifications to the characteristic data of the $ \mathcal{N} = 1 $ bulk orientifold theory in the presence of a D6-brane are analysed by studying the underlying Type IIA supergravity coupled to the brane world volume in the democratic formulation and performing a detailed dualisation procedure. The $ \mathcal{N} = 1 $ chiralcoordinates are found to be in agreement with expectations from mirror symmetry. We work out the Kahler potential for the chiral superfields as well as the gauge kinetic functions for the bulk and the brane gauge multiplets including the kinetic mixing between the two. The scalar potential resulting from the dualisation procedure can be formally interpreted in terms of a superpotential. Finally, the gauging of the Peccei-Quinn shift symmetries of the complex structure multiplets reproduces the D-term potential enforcing the calibration condition for special Lagrangian 3-cycles.

Partition functions of 3d D ^ $$ \widehat{D} $$ -quivers and their mirror duals from 1d free fermions

Abstract: We study the matrix models calculating the sphere partition functions of 3d gauge theories with $$ \mathcal{N}=4 $$ supersymmetry and a quiver structure of a $$ \widehat{D} $$ Dynkin diagram (where each node is a unitary gauge group). As in the case of necklace (Â) quivers, we can map the problem to that of free fermion quantum mechanics whose complicated Hamiltonian we find explicitly. Many of these theories are conjectured to be dual under mirror symmetry to certain unitary linear quivers with extra Sp nodes or antisymmetric hypermultiplets. We show that the free fermion formulation of such mirror pairs are related by a linear symplectic transformation. We then study the large N expansion of the partition function, which as in the case of the  quivers is given to all orders in 1/N by an Airy function. We simplify the algorithm to calculate the numerical coefficients appearing in the Airy function and evaluate them for a wide class of $$ \widehat{D} $$ -quiver theories.

Matrix Factorizations And Mirror Symmetry: The Cubic Curve

Abstract: We revisit open string mirror symmetry for the elliptic curve, using matrix factorizations for describing D-branes on the B-model side. We show how flat coordinates can be intrinsically defined in the Landau-Ginzburg model, and derive the A-model partition function counting disk instantons that stretch between three D-branes. In mathematical terms, this amounts to computing the simplest Fukaya product m_2 from the LG mirror theory. In physics terms, this gives a systematic method for determining non-perturbative Yukawa couplings for intersecting brane configurations.