Toric Calabi–Yau supermanifolds and mirror symmetry

Belhaj, A.; Drissi, L.B.; Rasmussen, Jørgen; Saidi, E. H.; Sebbar, Ahmed

doi:10.1088/0305-4470/38/28/013

Cited by 16 publications

(18 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark A similiar phenomenon was observed [10] when the A-model target space is a crepant resolution of WCP m 1 −1|n (Q 11 ,...,Q 1m 1 |q 11 ,...,q 1n ) × · · · × WCP mn−1|n (Q n1 ,...,Qnm n |q n1 ,...,qnn) .…”

Section: A A-model Super Cy Hypersurface ⇔ B-model Quasihomogeneitymentioning

confidence: 58%

Super Landau-Ginzburg mirrors and algebraic cycles

Garavuso¹,

Katzarkov²,

Kreuzer³

et al. 2011

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

Section: A A-model Super Cy Hypersurface ⇔ B-model Quasihomogeneitymentioning

confidence: 58%

Super Landau-Ginzburg mirrors and algebraic cycles

Garavuso¹,

Katzarkov²,

Kreuzer³

et al. 2011

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Witten [5] described N = 2 nonlinear sigma models on Calabi-Yau manifolds and N = 2 Landau-Ginzburg orbifolds as being different phases of N = 2 gauged linear sigma models. Sethi's work and [6] have led others [7] to study N = 2 gauged linear sigma models which have a phase described by an N = 2 nonlinear sigma model on a Calabi-Yau supermanifold. The gauged linear sigma model framework allows the argument establishing a correspondence between the nonlinear sigma model and the Landau-Ginzburg orbifold to be made more robust.…”

Section: Introductionmentioning

confidence: 99%

Fano hypersurfaces and Calabi-Yau supermanifolds

Garavuso

Kreuzer

Noll

2009

J. High Energy Phys.

View full text Add to dashboard Cite

In this paper, we study the geometrical interpretations associated with Sethi's proposed general correspondence between N = 2 Landau-Ginzburg orbifolds with integralĉ and N = 2 nonlinear sigma models. We focus on the supervarieties associated withĉ = 3 Gepner models. In the process, we test a conjecture regarding the superdimension of the singular locus of these supervarieties. The supervarieties are defined by a hypersurface W = 0 in a weighted superprojective space and have vanishing super-first Chern class. Here, W is the modified superpotential obtained by adding as necessary to the Gepner superpotential a boson mass term and/or fermion bilinears so that the superdimension of the supervariety is equal toĉ. When Sethi's proposal calls for adding fermion bilinears, setting the bosonic part of W (denoted by W bos ) equal to zero defines a Fano hypersurface embedded in a weighted projective space. In this case, if the Newton polytope of W bos admits a nef partition, then the Landau-Ginzburg orbifold can be given a geometrical interpretation as a nonlinear sigma model on a complete intersection Calabi-Yau manifold. The complete intersection Calabi-Yau manifold should be equivalent to the Calabi-Yau supermanifold prescribed by Sethi's proposal.

show abstract

“…The supermanifold then became the Calabi-Yau supermanifold which was defined by the Calabi-Yau condition [1,25],…”

Section: Introductionmentioning

confidence: 99%

(0,2) Gauged linear sigma model on supermanifold

Okame

Hayashi

2009

Ann. Phys.

View full text Add to dashboard Cite

We construct (0, 2), D = 2 gauged linear sigma model on supermanifold with both an Abelian and non-Abelian gauge symmetry. For the purpose of checking the exact supersymmetric (SUSY) invariance of the Lagrangian density, it is convenient to introduce a new operatorÛ for the Abelian gauge group. TheÛ operator provides consistency conditions for satisfying the SUSY invariance. On the other hand, it is not essential to introduce a similar operator in order to check the exact SUSY invariance of the Lagrangian density of non-Abelian model, contrary to the Abelian one. However, we still need a new operator in order to define the (0,2) chirality conditions for the (0,2) chiral superfields. The operator U a can be defined from the conditions assuring the (0,2) supersymmetric invariance of the Lagrangian density in superfield formalism for the (0,2) U(N) gauged linear sigma model.We found consistency conditions for the Abelian gauge group which assure (0,2) supersymmetric invariance of Lagrangian density and agree with (0,2) chirality conditions for the superpotential. The supermanifold M m|n becomes the super weighted complex projective space W CP m−1|n in the U(1) case, which is considered as an example of a Calabi-Yau supermanifold. The superpotential W (φ, ξ) for the non-Abelian gauge group satisfies more complex condition for the SU(N) part, except the U(1) part of U(N), but does not satisfy a quasi-homogeneous condition. This fact implies the need for taking care of constructing the Calabi-Yau supermanifold in the SU(N) part. Because more stringent restrictions are imposed on the form of the superpotential than in the U(1) case, the superpotential seems to define a certain kind of new supermanifolds which we cannot identify exactly with one of the mathematically well defined objects.

show abstract

Toric Calabi–Yau supermanifolds and mirror symmetry

Cited by 16 publications

References 13 publications

Super Landau-Ginzburg mirrors and algebraic cycles

Super Landau-Ginzburg mirrors and algebraic cycles

Fano hypersurfaces and Calabi-Yau supermanifolds

(0,2) Gauged linear sigma model on supermanifold

Contact Info

Product

Resources

About