A Landau–Ginzburg/Calabi–Yau correspondence for the mirror quintic

Priddis, Nathan; Shoemaker, Mark

doi:10.5802/aif.3031

Cited by 11 publications

(11 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. The proof has been given in several places, including [7], [6], [20], so we will not give it in detail here. It consists of checking that over any geometric point (C,…”

Section: Fjrw Correlators Forẽmentioning

confidence: 99%

“…In this section, we reformulate FJRW theory in order to obtain the genus zero potential F (Ẽ 7 ,G max ) 0 from a basic CohFT. This method is also used in [7], [6], [20], so we will be brief. The details can be found in these other articles.…”

Section: Extended Fjrw Correlatorsmentioning

confidence: 99%

“…Proof. This proof is given in [7], and [20], so we only give an outline. Comparing A 3 and A 3 , we see that if m ki ∈ 1 4 , 1 2 , 3 4 for all k, i, then h 1 , .…”

Section: Extended Fjrw Correlatorsmentioning

confidence: 99%

“…Second, we give a Givental-type formula, expressing the partition function of FJRW theory of (x 4 + y 4 + z 2 , G max ) via the partition function of the so-called "untwisted theory". This step is connected to the work of [7,20,8]. The partition function of the "untwisted theory" differs from the partition function of the product of the Gromov-Witten theories of a point just by a linear change of the variables.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Givental-Type Reconstruction at a Nonsemisimple Point

Basalaev¹,

Priddis²

2018

Michigan Math. J.

Self Cite

View full text Add to dashboard Cite

In this paper we consider the orbifold curve, which is a quotient of an elliptic curve E by a cyclic group of order 4. We develop a systematic way to obtain a Givental-type reconstruction of Gromov-Witten theory of the orbifold curve via the product of the Gromov-Witten theories of a point. This is done by employing mirror symmetry and certain results in FJRW theory. In particular, we present the particular Giventals action giving the CY/LG correspondence between the Gromov-Witten theory of the orbifold curve E /Z 4 and FJRW theory of the pair defined by the polynomial x 4 + y 4 + z 2 and the maximal group of diagonal symmetries. The methods we have developed can easily be applied to other finite quotients of an elliptic curve. Using Givental's action we also recover this FJRW theory via the product of the Gromov-Witten theories of a point. Combined with the CY/LG action we get a result in pure Gromov-Witten theory with the help of modern mirror symmetry conjectures. 4,4,2 39References 40 ALEXEY BASALAEV AND NATHAN PRIDDIS pairing η. A cohomological field theory (CohFT for brevity) Λ g,n on (V, η) is a system of linear maps Λ g,n

show abstract

“…Proof. The proof has been given in several places, including [7], [6], [20], so we will not give it in detail here. It consists of checking that over any geometric point (C,…”

Section: Fjrw Correlators Forẽmentioning

confidence: 99%

Section: Extended Fjrw Correlatorsmentioning

confidence: 99%

“…Proof. This proof is given in [7], and [20], so we only give an outline. Comparing A 3 and A 3 , we see that if m ki ∈ 1 4 , 1 2 , 3 4 for all k, i, then h 1 , .…”

Section: Extended Fjrw Correlatorsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Givental-Type Reconstruction at a Nonsemisimple Point

Basalaev¹,

Priddis²

2018

Michigan Math. J.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The relation between the Gromov-Witten theory of X W and the FJRW-theory of W is the subject of the Landau-Ginzburg/Calabi-Yau correspondence, a famous duality from physics. More recently, the LG/CY correspondence has been reformulated as a precise mathematical conjecture [Rua12], and a great deal of progress has been made on this conjecture [CIR12,ChiR10,ChiR11,PS,LPS].…”

Section: Introductionmentioning

confidence: 99%