Combinatorial aspects of mirror symmetry

Batyrev, Victor V.; Nill, Benjamin

doi:10.1090/conm/452/08770

Cited by 69 publications

(97 citation statements)

References 27 publications

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“…Under appropriate combinatorial conditions [39,40] and for generic coefficients in the polynomials P I , the gauge theory in a geometric phase flows to an NLSM with target space a dimension k = d−1−N (quasi-smooth) Calabi-Yau complete intersection ∩ I {P I = 0} in V . We assume these conditions are satisfied, and study the linear model in the geometric phase.…”

Section: Quantum Restriction For Complete Intersectionsmentioning

confidence: 99%

Summing the instantons in half-twisted linear sigma models

McOrist

Melnikov

2009

J. High Energy Phys.

122

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We study half-twisted linear sigma models relevant to (0,2) compactifications of the heterotic string. Focusing on theories with a (2,2) locus, we examine the linear model parameter space and the dependence of genus zero half-twisted correlators on these parameters. We show that in a class of theories the correlators and parameters separate into A and B types, present techniques to compute the dependence, and apply these to some examples. These results should bear on the mathematics of (0,2) mirror symmetry and the physics of the moduli space and Yukawa couplings in heterotic compactifications.

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Section: Quantum Restriction For Complete Intersectionsmentioning

confidence: 99%

Summing the instantons in half-twisted linear sigma models

McOrist

Melnikov

2009

J. High Energy Phys.

122

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“…The construction is based on work of Batyrev and Borisov. We will follow the version presented in [17], focusing on the case of CICY threefolds. The reader should consult [17] for references to the original papers.…”

Section: Cicys and Duality Of Conesmentioning

confidence: 99%

“…The duality of these cones leads to additional examples relevant to mirror symmetry. We refer the reader to [17] for details and further reading.…”

Section: Cicys and Duality Of Conesmentioning

confidence: 99%

Mirror Symmetry and Polar Duality of Polytopes

Cox

2015

Symmetry

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“…These polytopes have several interesting properties and characterizations, for instance, a lattice polytope P is reflexive if and only if its only interior lattice point is 0 and if u and v are two lattice points on the boundary of P, then either u and v are on the same facet, or u + v is in P. This is an important concept with interesting connections to geometry and theoretical physics. For an exposition suitable for researchers with a background in discrete mathematics, we refer to Batyrev and Nill [2008].…”

Section: Betti Diagrams From Graphsmentioning

confidence: 99%

Untitled

2013

Algebra Number Theory

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This paper concerns the Weil representation of the semidirect product of the metaplectic and Heisenberg groups. First we present a canonical construction of the metaplectic group as a central extension of the symplectic group by a subquotient of the Witt group. This leads to simple formulas for the character, for the inverse Weyl transform, and for the transfer factor appearing in J. Adams's work on character lifting. Along the way, we give formulas for outer automorphisms of the metaplectic group induced by symplectic similitudes. The approach works uniformly for finite and local fields.

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Combinatorial aspects of mirror symmetry

Cited by 69 publications

References 27 publications

Summing the instantons in half-twisted linear sigma models

Summing the instantons in half-twisted linear sigma models

Mirror Symmetry and Polar Duality of Polytopes

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