Flop Invariance of the Topological Vertex

The closed topological vertex is the simplest "off-strip" case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an "on-strip" subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive q-difference equations for generating functions of special subsets of the amplitudes. These q-difference equations may be interpreted as the defining equation of a quantum mirror curve.

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“…Note that (6.6) is consistent with (6.3). These matching rules of parameters agree with the known result for the partition functions [2,5,31].…”

Section: Flop Transitionsupporting

confidence: 89%

Open string amplitudes of closed topological vertex

Takasaki

Nakatsu

2015

J. Phys. A: Math. Theor.

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“…If we introduce a regularization corresponding to the flop transition [32,36,37] for a certain part of web diagram, 22) JHEP01 (2017)093 we obtain the perturbative contribution 23) which is analogous to the known result for N f ≤ 2N [40]. However, for later purpose, it is convenient to transform in such a way that negative powers of A 1 never appear when we eliminate A 3 by the traceless condition.…”

Section: Jhep01(2017)093mentioning

confidence: 89%

Equivalence of several descriptions for 6d SCFT

Hayashi

Kim

Lee

et al. 2017

J. High Energ. Phys.

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We show that the three different looking BPS partition functions, namely the elliptic genus of the 6d N = (1, 0) Sp(1) gauge theory with 10 flavors and a tensor multiplet, the Nekrasov partition function of the 5d N = 1 Sp(2) gauge theory with 10 flavors, and the Nekrasov partition function of the 5d N = 1 SU(3) gauge theory with 10 flavors, are all equal to each other under specific maps among gauge theory parameters. This result strongly suggests that the three gauge theories have an identical UV fixed point. Type IIB 5-brane web diagrams play an essential role to compute the SU(3) Nekrasov partition function as well as establishing the maps.

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“…This Hodge integral is well-known [18], and one obtains 24) where B 2g are the Bernoulli numbers. These are precisely the coefficients of the asymptotic expansion of the MacMahon function at g s = − log q → 0 (see appendix E of [19]):…”

Section: Constant Map Contribution In Orientifoldsmentioning

confidence: 97%

The real topological vertex at work

2010

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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.

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Flop Invariance of the Topological Vertex

Abstract: Abstract. We prove transformation formulae for generating functions of GromovWitten invariants on general toric Calabi-Yau threefolds under flops. Our proof is based on a combinatorial identity on the topological vertex and analysis of fans of toric CalabiYau threefolds.

Cited by 34 publications

References 17 publications

Open string amplitudes of closed topological vertex

Open string amplitudes of closed topological vertex

Equivalence of several descriptions for 6d SCFT

The real topological vertex at work

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