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Shinobu Hosono

Publications and source records attributed to Shinobu Hosono.

28 records · Page 2Linked to original sources
arXiv2005

Central charges, symplectic forms, and hypergeometric series in local mirror symmetry

We study a cohomology-valued hypergeometric series which naturally arises in the description of (local) mirror symmetry. We identify it as a central charge formula for BPS states and study its monodromy property from the viewpoint of Kontsevich's homological mirror symmetry. In the case of local mirror symmetry, we will identify a symplectic form, and will conjecture an integral and symplectic monodromy property of a relevant hypergeometric series of Gel'fand-Kapranov-Zelevinski type.

hep-th↗
arXiv2003

c=2 Rational Toroidal Conformal Field Theories via the Gauss Product

We find a concise relation between the moduli $τ, ρ$ of a rational Narain lattice $Γ(τ,ρ)$ and the corresponding momentum lattices of left and right chiral algebras via the Gauss product. As a byproduct, we find an identity which counts the cardinality of a certain double coset space defined for isometries between the discriminant forms of rank two lattices.

hep-th↗
arXiv2003

Counting Unimodular Lattices in $\R^{r,s}$

Narain lattices are unimodular lattices {\it in} $\R^{r,s}$, subject to certain natural equivalence relation and rationality condition. The problem of describing and counting these rational equivalence classes of Narain lattices in $\R^{2,2}$ has led to an interesting connection to binary forms and their Gauss products, as shown in [HLOYII]. As a sequel, in this paper, we study arbitrary rational Narain lattices and generalize some of our earlier results. In particular in the case of $\R^{2,2}$, a new interpretation of the Gauss product of binary forms brings new light to a number of related objects -- rank 4 rational Narain lattices, over-lattices, rank 2 primitive sublattices of an abstract rank 4 even unimodular lattice $U^2$, and isomorphisms of discriminant groups of rank 2 lattices.

math.QA↗
arXiv2002

Counting BPS States via Holomorphic Anomaly Equations

We study Gromov-Witten invariants of a rational elliptic surface using holomorphic anomaly equation in [HST1](hep-th/9901151). Formulating invariance under the affine $E_8$ Weyl group symmetry, we determine conjectured invariants, the number of BPS states, from Gromov-Witten invariants. We also connect our holomorphic anomaly equation to that found by Bershadsky,Cecotti,Ooguri and Vafa [BCOV1](hep-th/9302103).

hep-th↗
arXiv2002

Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations

We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge isometries of the Mukai lattice. Motivated by homological mirror symmetry we also consider the mirror counterpart, i.e. symplectic version of it. In the case of $ρ(X)=1$, we find an explicit formula which reproduces the number of Fourier-Mukai (FM) partners from the monodromy problem of the mirror K3 family. We present an explicit example in which a monodromy action does not come from an autoequivalence of the mirror side.

math.AG↗
arXiv2001

Relative Lefschetz Action and BPS State Counting

In this paper, we propose a mathematical definition of a new ``numerical invariants" of Calabi--Yau 3-folds from stable sheaves of dimension one, which is motivated by the Gopakumar-Vafa conjecture in M-theory. Moreover, we show that for any projective morphism $f:X -> Y$ of normal projective varieties, there exists a natural $sl_2 \times sl_2$ action on the intersection cohomology group $IH(X, \Q)$ which fits into the perverse Leray spectral sequence.

math.AG↗
arXiv1997

On Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3 folds

In this paper, we verify a part of the Mirror Symmetry Conjecture for Schoen's Calabi-Yau 3-fold, which is a special complete intersection in a toric variety. We calculate a part of the prepotential of the A-model Yukawa couplings of the Calabi-Yau 3-fold directly by means of a theta function and Dedekind's eta function. This gives infinitely many Gromov-Witten invariants, and equivalently infinitely many sets of rational curves in the Calabi-Yau 3-fold. Using the toric mirror construction, we also calculate the prepotential of the B-model Yukawa couplings of the mirror partner. Comparing the expansion of the B-model prepotential with that of the A-model prepotential, we check a part of the Mirror Symmetry Conjecture up to a high order.

alg-geom↗