Exoflops in two dimensions

Aspinwall, Paul S.

doi:10.1007/jhep07(2015)104

Cited by 6 publications

(4 citation statements)

References 35 publications

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“…Notably, when we study geodesic motion in the extended Kähler cone in Section III, it will be sufficient to consider only the vector multiplet moduli space, which receives no quantum corrections in the interior of the Kähler cone. Moreover, in contrast to four-dimensional N = 1 or N = 2 models [26], where a rich structure of non-geometric or hybrid phases can occur [18,[27][28][29][30], the moduli space of five-dimensional N = 1 supergravity is simpler and ends at the boundary of the extended Kähler cone, missing all non-geometric phases [31].…”

Section: E M-theory On Cy Threefoldsmentioning

confidence: 99%

Swampland Conjectures and Infinite Flop Chains

Brodie,

Constantin,

Lukas

et al. 2021

Preprint

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We investigate swampland conjectures for quantum gravity in the context of M-theory compactified on Calabi-Yau threefolds which admit infinite sequences of flops. Naively, the moduli space of such compactifications contains paths of arbitrary geodesic length traversing an arbitrarily large number of Kähler cones, along which the low-energy spectrum remains virtually unchanged. In cases where the infinite chain of Calabi-Yau manifolds involves only a finite number of isomorphism classes, the moduli space has an infinite discrete symmetry which relates the isomorphic manifolds connected by flops. This is a remnant of the 11D Poincare symmetry and consequently gauged, as it has to be by the no-global symmetry conjecture. The apparent contradiction with the swampland distance conjecture is hence resolved after dividing by this discrete symmetry. If the flop sequence involves infinitely many non-isomorphic manifolds, this resolution is no longer available. However, such a situation cannot occur if the Kawamata-Morrison conjecture for Calabi-Yau threefolds is true. Conversely, the swampland distance conjecture, when applied to infinite flop chains, implies the Kawamata-Morrison conjecture under a plausible assumption on the diameter of the Kähler cones.

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Section: E M-theory On Cy Threefoldsmentioning

confidence: 99%

Swampland Conjectures and Infinite Flop Chains

Brodie,

Constantin,

Lukas

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…. 2 This assumption sacrifices some generality but simplifies the formulas and is sufficient for the purpose of comparison with previous works. We leave the details of the most general case to the interested reader.…”

Section: Examples and Comparisonsmentioning

confidence: 99%

“…GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds [33], as examples of noncommutative crepant resolutions [43,2], and as intermediate spaces appearing in wall crossing and correspondence results [50,41,26]. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory.…”

Section: Introductionmentioning

confidence: 99%

Towards a mirror theorem for GLSMs

Shoemaker

2021

Preprint

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We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model (V, G, θ, w). We show that certain derivatives of I-functions of quasimap invariants of [V θ G] produce I-functions (appropriately defined) of the GLSM. When G is an algebraic torus we obtain an explicit formula for an I-function, and check that it agrees with previously computed I-functions in known special cases. Our approach is based on a new construction of GLSM invariants which applies whenever the evaluation maps from the moduli space are proper, and includes insertions from light marked points. CONTENTS 1. Introduction 1 2. GLSM setup and the state space 6 3. Compact type GLSM invariants 10 4. Genus zero, two marked points 21 5. Adding light points 23 6. Generating functions 27 7. Examples and comparisons 36 Appendix A. Proof of Theorem 5.6 43 References 48 * (j 1 c * β 1 ) ∪ • • • ∪ ev c n * (j n c * β n ) in Proposition 3.15 is equal to ev *

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“…The intermediate space T has appeared previously in the context of Landau-Ginzburg models. After adding an appropriate superpotential w : T → C, the corresponding LG model is known as an exoflop, and was studied in [3]. In the context of derived categories, the category of matrix factorizations on the LG model w : T → C was used to prove an equivalence of categories between the derived categories arising from different Berglund-H übsch-Krawitz mirrors [21].…”

Section: 3mentioning

confidence: 99%

Extremal transitions via quantum Serre duality

Mi¹,

Shoemaker²

2020

Preprint

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Two varieties Z and Z are said to be related by extremal transition if there exists a degeneration from Z to a singular variety Z and a crepant resolution Z → Z. In this paper we compare the genus-zero Gromov-Witten theory of toric hypersurfaces related by extremal transitions arising from toric blow-up. We show that the quantum D-module of Z, after analytic continuation and restriction of a parameter, recovers the quantum D-module of Z. The proof provides a geometric explanation for both the analytic continuation and restriction parameter appearing in the theorem. CONTENTS 1. Introduction 1 2. Gromov-Witten theory preliminaries 6 3. Toric preliminaries 15 4. Geometric setup for extremal transitions 21 5. The total spaces 29 6. Crepant transformation conjecture 35 7. D-module of the partial compactification 41 8. Main theorem 46 References 51

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Exoflops in two dimensions

Cited by 6 publications

References 35 publications

Swampland Conjectures and Infinite Flop Chains

Swampland Conjectures and Infinite Flop Chains

Towards a mirror theorem for GLSMs

Extremal transitions via quantum Serre duality

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