Quantum Cohomology and Periods

Iritani, Hiroshi

doi:10.5802/aif.2798

Cited by 46 publications

(59 citation statements)

References 83 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to also classify the corresponding singularity types using table 3.1, we still need to determine the polarisation η. This can be done by evaluating the negative of the Mukai pairing [41,[43][44][45]. On the K-theory space the Mukai pairing of branes ξ and ξ is defined by…”

Section: The Large Complex Structure and Large Volume Pointmentioning

confidence: 99%

Infinite distance networks in field space and charge orbits

Grimm

Palti

2019

J. High Energ. Phys.

145

400

View full text Add to dashboard Cite

The Swampland Distance Conjecture proposes that approaching infinite distances in field space an infinite tower of states becomes exponentially light. We study this conjecture for the complex structure moduli space of Calabi-Yau manifolds. In this context, we uncover significant structure within the proposal by showing that there is a rich spectrum of different infinite distance loci that can be classified by certain topological data derived from an associated discrete symmetry. We show how this data also determines the rules for how the different infinite distance loci can intersect and form an infinite distance network. We study the properties of the intersections in detail and, in particular, propose an identification of the infinite tower of states near such intersections in terms of what we term charge orbits. These orbits have the property that they are not completely local, but depend on data within a finite patch around the intersection, thereby forming an initial step towards understanding global aspects of the distance conjecture in field spaces. Our results follow from a deep mathematical structure captured by the so-called orbit theorems, which gives a handle on singularities in the moduli space through mixed Hodge structures, and is related to a local notion of mirror symmetry thereby allowing us to apply it also to the large volume setting. These theorems are general and apply far beyond Calabi-Yau moduli spaces, leading us to propose that similarly the infinite distance structures we uncover are also more general.

show abstract

Section: The Large Complex Structure and Large Volume Pointmentioning

confidence: 99%

Infinite distance networks in field space and charge orbits

Grimm

Palti

2019

J. High Energ. Phys.

145

400

View full text Add to dashboard Cite

show abstract

“…The quantum Z-variation of Hodge structure. -Following [CK,§8] and [Ir,§5], we now introduce a weight 3 variation of Hodge structure on V O = V ⊗ O((∆ * ) r−1 ), where the ∆ * are punctured disks with coordinates q j = e 2πiτ j , j = 0, . .…”

Section: A-modelmentioning

confidence: 99%

Local mirror symmetry and the sunset Feynman integral

Bloch¹,

Kerr

Vanhove

2017

Advances in Theoretical and Mathematical Physics

116

150

View full text Add to dashboard Cite

We study the sunset Feynman integral defined as the scalar two-point self-energy at two-loop order in a two dimensional space-time.We firstly compute the Feynman integral, for arbitrary internal masses, in terms of the regulator of a class in the motivic cohomology of a 1-parameter family of open elliptic curves. Using an Hodge theoretic (B-model) approach, we show that the integral is given by a sum of elliptic dilogarithms evaluated at the divisors determined by the punctures.Secondly we associate to the sunset elliptic curve a local non-compact Calabi-Yau 3-fold, obtained as a limit of elliptically fibered compact Calabi-Yau 3-folds. By considering the limiting mixed Hodge structure of the Batyrev dual A-model, we arrive at an expression for the sunset Feynman integral in terms of the local Gromov-Witten prepotential of the del Pezzo surface of degree 6. This expression is obtained by proving a strong form of local mirror symmetry which identifies this prepotential with the second regulator period of the motivic cohomology class.

show abstract

“…This paper arose out of our previous works [Iri11,MM11] on quantum D-modules of (toric) complete intersections. The embedding of QDM amb (Z) into QDM(E ∨ ) appeared in [Iri11,Remark 6.14] in the case where X is a weak Fano toric orbifold and E ∨ = K X ; in [MM11, Theorem 1.1], QDM amb (Z) was presented as the quotient QDM (e,E) (X) by Ker(e(E)∪) when E is a direct sum of ample line bundles. We would also like to draw attention to a recent work of Borisov-Horja [BH13] on the duality of better behaved GKZ systems.…”

Section: Introductionmentioning

confidence: 99%

Quantum Serre Theorem as a Duality Between QuantumD-Modules: Table 1.

Iritani

Mann²,

Mignon³

2015

Int Math Res Notices

Self Cite

View full text Add to dashboard Cite

We give an interpretation of quantum Serre theorem of Coates and Givental as a duality of twisted quantum D-modules. This interpretation admits a non-equivariant limit, and we obtain a precise relationship among (1) the quantum D-module of X twisted by a convex vector bundle E and the Euler class, (2) the quantum D-module of the total space of the dual bundle E ∨ → X, and (3) the quantum D-module of a submanifold Z ⊂ X cut out by a regular section of E.When E is the anticanonical line bundle K −1 X , we identify these twisted quantum D-modules with second structure connections with different parameters, which arise as Fourier-Laplace transforms of the quantum D-module of X. In this case, we show that the duality pairing is identified with Dubrovin's second metric (intersection form).

show abstract

Quantum Cohomology and Periods

Cited by 46 publications

References 83 publications

Infinite distance networks in field space and charge orbits

Infinite distance networks in field space and charge orbits

Local mirror symmetry and the sunset Feynman integral

Quantum Serre Theorem as a Duality Between QuantumD-Modules: Table 1.

Contact Info

Product

Resources

About