Related papers: Mirror symmetry & supersymmetry on SU(4)-structure…
We compute certain one-loop corrections to F^4 couplings of the heterotic string compactified on T^2, and show that they can be characterized by holomorphic prepotentials. We then discuss how some of these couplings can be obtained in…
Recently a very interesting three-dimensional $\mathcal{N}=2$ supersymmetric theory with $SU(3)$ global symmetry was discussed by several authors. We denote this model by $T_x$. This was conjectured to have two dual descriptions, one with…
In this work we find the first examples of (0,2) mirror symmetry on compact non-K\"ahler complex manifolds. For this we follow Borisov's approach to mirror symmetry using vertex algebras and the chiral de Rham complex. Our examples of (0,2)…
For a large class of $N=2$ SCFTs, which includes minimal models and many $\s$ models on Calabi-Yau manifolds, the mirror theory can be obtained as an orbifold. We show that in such a situation the construction of the mirror can be extended…
A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on…
A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We…
A complete embedding is a symplectic embedding $\iota:Y\to M$ of a geometrically bounded symplectic manifold $Y$ into another geometrically bounded symplectic manifold $M$ of the same dimension. When $Y$ satisfies an additional finiteness…
We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N=2, the R-symmetry is SO(2)\times SO(1,1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N=2 models…
For the base $B$ of a Maslov $0$ Lagrangian torus fibration with singularities consider the sheaf assigning to each $P\subset B$ the relative symplectic cohomology in degree $0$ of its pre-image. We compute this sheaf for nodal Lagrangian…
The relation between nilmanifolds with left-invariant complex structure and iterated principal holomorphic torus bundles is clarified and we give criteria under which deformations in the large are again of such type. As an application we…
This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by the existence of dual special Lagrangian…
The two discrete generators of the full Lorentz group $O(1,3)$ in $4D$ spacetime are typically chosen to be parity inversion symmetry $P$ and time reversal symmetry $T$, which are responsible for the four topologically separate components…
A typical large complex-structure limit for mirror symmetry consists of toric varieties glued to each other along their toric boundaries. Here we construct the mirror large volume limit space as a Weinstein symplectic manifold. We prove…
Mirror symmetry is a type of infrared duality in 3D quantum field theory that relates the low-energy dynamics of two distinct ultraviolet descriptions. Though first discovered in the supersymmetric context, it has far-reaching implications…
In this paper, we describe explicit relations in the symplectomorphism groups of toric hypersurfaces. To define the elements involved, we construct a proper stack of toric hypersurfaces with compactifying boundary representing toric…
We construct and analyze dual N=4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the…
We study Landau Ginzburg (LG) theories mirror to 2D N=2 gauged linear sigma models on toric Calabi-Yau manifolds. We derive and solve new constraint equations for Landau Ginzburg elliptic Calabi-Yau superpotentials, depending on the…
We investigate a simple class of type II string compactifications which incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual H-field and R-R fluxes. These compactifications are nongeometric analogues of the…
We revisit sigma models on target spaces given by a principal torus fibration $X\to M$, and show how treating the 2-form B as a gerbe connection captures the gauging obstructions and the global constraints on the T-duality. We show that a…
Using geometric engineering in the context of type II strings, we obtain exact solutions for the moduli space of the Coulomb branch of all N=2 gauge theories in four dimensions involving products of SU gauge groups with arbitrary number of…