We generalize the known method for explicit construction of mirror pairs of $(2,2)$-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, these theories are realized as Calabi-Yau hypersurfaces in weighted projective spaces. This generalization makes it possible to construct the mirror partners of many manifolds for which the mirror was not previously known.
We study B-brane superpotentials depending on several closed- and open- moduli on Calabi-Yau hypersurfaces and complete intersections. By blowing up the ambient space along a curve wrapped by B-branes in a Calabi-Yau manifold, we obtain a blow-up new manifold and the period integral satisfying the GKZ-system. Via mirror symmetry to A-model, we calculate the superpotentials and extract Ooguri-Vafa invariants for concrete examples of several open-closed moduli in Calabi-Yau manifolds.
Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
研究了超对称循环对磁通背景的纤维化。对于具有静态SU（2）结构和镜像\hat{M}的内部六维流形M，证明了乘积M x \hat{M}被超对称三环面双纤维化，两组纤维都横截于M和\hat{M} .镜像映射是通过对纤维进行T-对偶来实现的。的磁通量，几何和非几何的对称性，示出同意与以前的progratures的基础上的镜像对称的要求杀死prepotential。在一般的SU（3）xSU（3）背景下，纤维被通量破坏，尽管它们可能在类型跳跃点处存活。使幸存的纤维T-对偶确保了在镜像对称下纯旋量的交换。
On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds
我们得到了N=2标量势的完整超引力描述，它实现了Calabi-Yau流形（广义几何）上的一般通量紧化。Berglund和Mayr不久前提出的有效势V_{eff} = V_{(\partial_Z V=0)} $, obtained by integrating out the massive axionic fields of the special quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with respect to {\rm Sp}(2 h_2+2)\times {\rm Sp}(2 h_1+2) and their exchange, being h_1, h_2 the complex dimensions of the underlying special geometries. {\Scr V}_{eff} has a manifestly N=1 form in terms of a mirror symmetric superpotential $ W$。
The goal of the present paper is to calculate the complex structure moduli space Kähler potentials for hypersurfaces in weighted projective spaces and compare with the partition functions of their mirror GLSMs. We explicitly perform the Kähler potential computation and show that the corresponding formula is well-defined in case of quasismooth hypersurfaces. We then construct the mirror GLSM with an appropriate number of Kähler parameters and discuss the interpretation of its partition function in terms of mirror symmetry. Namely, it is shown that different contributions to the partition functi…
We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups $G_2$ and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to twisted connected sum $G_2$ manifolds, mirrors of such Spin(7) manifolds can be found by applying mirror symmetry to the pair of non-compact manifolds they are glued from. To provide non-trivial checks for such geometric mirror constructions, we give a CFT analysis of mirror maps for Joyce orbifolds in several new instances for both the Spin(7) and the $G_2$ ca…
The Argyres-Douglas (AD) theories of type $(D_n,D_m)$, realized by type IIB geometrical engineering on a single hypersurface singularity, are studied. We analyze their conformal manifolds and propose the 3d mirror theories of all theories in this class upon reduction on a circle. A subclass of the AD theories in question that admits marginal couplings is found to be $\mathrm{SO}$ or $\mathrm{USp}$ gaugings of certain $D_p(\mathrm{SO}(2N))$ and $D_p(\mathrm{USp}(2N))$ theories. For such theories, we develop a method to derive this weakly-coupled description from the Newton polygon associated to…
We present a new construction of mirror pairs of Calabi-Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi-Yau fibrations using recent conjectures about Landau-Ginzburg models. Utilizing this notion, we give pairs of normal crossing varieties and show that the pairs of smoothed Calabi-Yau manifolds satisfy the Hodge number relations of mirror symmetry. We consider quasi-Fano threefolds that are some blow-ups of Gorenstein toric Fano threefolds and build 6518 mirror…
We study the new case of the application of the JKLMR conjecture on the connection between the exact partition functions of $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on $S^2$ and special Kähler geometry on the moduli spaces of Calabi-Yau manifold $Y$. The last ones arise as manifolds of the supersymmetric vacua of the GLSM. We establish this correspondence using the Mirror symmetry in Batyrev's approach. Namely, starting from the two-moduli non-Fermat Calabi-Yau manifold $X$ we construct the dual GLSM with the supersymmetric vacua $Y$, which is the mirror for $X$. Kn…
Argyres-Douglas theories constitute an important class of superconformal field theories in $4$d. The main focus of this paper is on two infinite families of such theories, known as $D^b_p(\mathrm{SO}(2N))$ and $(A_m, D_n)$. We analyze in depth their conformal manifolds. In doing so we encounter several theories of class $\mathcal{S}$ of twisted $A_{\text{odd}}$, twisted $A_{\text{even}}$ and twisted $D$ types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include $D_p(G)$ theories, with $G$ non-simply-laced algebras. A number of new …
We find that for many Calabi-Yau threefolds with elliptic or genus one fibrations mirror symmetry factorizes between the fiber and the base of the fibration. In the simplest examples, the generic CY elliptic fibration over any toric base surface $B$ that supports an elliptic Calabi-Yau threefold has a mirror that is an elliptic fibration over a dual toric base surface $\tilde{B}$ that is related through toric geometry to the line bundle $-6K_B$. The Kreuzer-Skarke database includes all these examples and gives a wide range of other more complicated constructions where mirror symmetry also fact…
