Counting Higher Genus Curves with Crosscaps in Calabi-Yau Orientifolds

Bouchard, Vincent; Florea, Bogdan; Mariño, Marcos

doi:10.1088/1126-6708/2004/12/035

Cited by 34 publications

(102 citation statements)

References 29 publications

(104 reference statements)

Supporting

Mentioning

100

Contrasting

Unclassified

Order By: Relevance

“…The implementation of this situation at the level of the topological vertex was studied in detail in [4], and will be subsummed in our formalism below. The last possibility is that σ acts in the r α -r β plane with eigenvalues (+1, −1).…”

Section: Anti-holomorphic Involutions From Symmetries Of the Toric DImentioning

confidence: 99%

“…Concerning the second point, it was recently found in [2] that the partition function of the real topological string (namely, with D-branes and O-planes at the fixed point locus of an anti-holomorphic involution [3]) on local P 2 indeed does admit a representation in the topological vertex formalism. (For previous studies of toric orientifolds after the topological vertex, see [4,5]. For recent discussions of tadpole cancellation in topological strings and their orientifolds, see [6,7].)…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The real topological vertex at work

2010

View full text Add to dashboard Cite

We develop the real vertex formalism for the computation of the topological string partition function with D-branes and O-planes at the fixed point locus of an antiholomorphic involution acting non-trivially on the toric diagram of any local toric Calabi-Yau manifold. Our results cover in particular the real vertex with non-trivial fixed leg. We give a careful derivation of the relevant ingredients using duality with Chern-Simons theory on orbifolds. We show that the real vertex can also be interpreted in terms of a statistical model of symmetric crystal melting. Using this latter connection, we also assess the constant map contribution in Calabi-Yau orientifold models.We find that there are no perturbative contributions beyond one-loop, but a non-trivial sum over non-perturbative sectors, which we compare with the non-perturbative contribution to the closed string expansion.

show abstract

Section: Anti-holomorphic Involutions From Symmetries Of the Toric DImentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The real topological vertex at work

2010

View full text Add to dashboard Cite

show abstract

“…where the superscript c denotes the contribution from Riemann surfaces with c crosscups [134][135][136]. In order to calculate the non-oriented partition function, one has to calculate…”

Section: Jhep08(2017)139mentioning

confidence: 99%

Checks of integrality properties in topological strings

Mironov¹,

Морозов²,

Морозов³

et al. 2017

J. High Energ. Phys.

View full text Add to dashboard Cite

Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arborescent knots and some non-arborescent knots. The recent results on polynomials for those knots colored by SU(N ) and SO(N ) adjoint representations [1] are useful to verify Marino's integrality conjecture up to two boxes in the Young diagram. In this paper, we review the salient aspects of the integrality properties and tabulate explicitly for an arborescent knot and a link. In our knotebook website, we have put these results for over 100 prime knots available in Rolfsen table and some links. The first application of the obtained results, an observation of the Gaussian distribution of the LMOV invariants is also reported.

show abstract

“…It is tempting to consider U q (sl N C) over C rather than C(q) by specializing q to a particular complex number z. When z is not a root of unity one obtains a Hopf algebra with generators and relations given by (31) and (32), and q replaced by z (not in q ±αi since those are names of generators). As associative algebras U z (sl N C) and U(sl N C) are isomorphic and thus have identical representation theories.…”

Section: G×g Gmentioning

confidence: 99%

“…There is also a duality involving SO(N) or Sp(N) Chern-Simons theories discussed in the physics literature [145,47,31,32].…”

Section: Construction Of Large N Dualsmentioning

confidence: 99%

Introduction to the Gopakumar–Vafa Large N Duality

Auckly¹,

Koshkin²

2007

Geometry and Topology Monographs

View full text Add to dashboard Cite

Gopakumar-Vafa Large N Duality is a correspondence between Chern-Simons invariants of a link in a 3-manifold and relative Gromov-Witten invariants of a 6-dimensional symplectic manifold relative to a Lagrangian submanifold. We address the correspondence between the Chern-Simons free energy of S 3 with no link and the Gromov-Witten invariant of the resolved conifold in great detail. This case avoids mathematical difficulties in formulating a definition of relative Gromov-Witten invariants, but includes all of the important ideas.There is a vast amount of background material related to this duality. We make a point of collecting all of the background material required to check this duality in the case of the 3-sphere, and we have tried to present the material in a way complementary to the existing literature. This paper contains a large section on Gromov-Witten theory and a large section on quantum invariants of 3-manifolds. It also includes some physical motivation, but for the most part it avoids physical terminology.

show abstract

Counting Higher Genus Curves with Crosscaps in Calabi-Yau Orientifolds

Cited by 34 publications

References 29 publications

The real topological vertex at work

The real topological vertex at work

Checks of integrality properties in topological strings

Introduction to the Gopakumar–Vafa Large N Duality

Contact Info

Product

Resources

About