More on topological vertex formalism for 5-brane webs with O5-plane

Self Cite

We construct novel web diagrams with a trivalent or quadrivalent gluing for various 6d/5d theories from certain Higgsings of 6d conformal matter theories on a circle. The theories realized on the web diagrams include 5d Kaluza-Klein theories from circle compactifications of the 6d G2 gauge theory with 4 flavors, the 6d F4 gauge theory with 3 flavors, the 6d E6 gauge theory with 4 flavors and the 6d E7 gauge theory with 3 flavors. The Higgsings also give rise to 5d Kaluza-Klein theories from twisted compactifications of 6d theories including the 5d pure SU(3) gauge theory with the Chern-Simons level 9 and the 5d pure SU(4) gauge theory with the Chern-Simons level 8. We also compute the Nekrasov partition functions of the theories by applying the topological vertex formalism to the newly obtained web diagrams.

“…The partition function (3.156) perfectly agrees with the results in [43,44,50] which were computed in different methods. We also have the extra factor and it is given by…”

Section: Jhep07(2021)128supporting

confidence: 79%

Section: Jhep07(2021)128mentioning

confidence: 99%

Section: Jhep07(2021)128mentioning

confidence: 99%

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6d/5d exceptional gauge theories from web diagrams

Hayashi

Kim

Ohmori

2021

Self Cite

“…In this subsection, we review the "topological vertex formalism with O5-plane" [29,36]. The (unrefined) topological vertex formalism [25] is a systematic algorithm to obtain the topological string partition function for a given toric-web diagram, which specifies the toric Calabi-Yau 3-fold.…”

Section: Topological Vertex Formalism For 5-brane Web With O5-planementioning

confidence: 99%

“…where the parameters Q 1 , Q 2 are exponentials of the minus of the length of the two 5-branes divided by the factor p 2 i + q 2 i respectively, the index n = p 1 q 2 + p 2 q 1 + 1. This rule is reformulated in terms of "O-vertex" in [36].…”

Section: Topological Vertex Formalism For 5-brane Web With O5-planementioning

confidence: 99%

Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane

Yagi

2021

In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-type singularities.

Discovering T-dualities of little string theories

Bhardwaj

2024

We describe a general method for deducing T-dualities of little string theories, which are dualities between these theories that arise when they are compactified on circle. The method works for both untwisted and twisted circle compactifications of little string theories and is based on surface geometries associated to these circle compactifications. The surface geometries describe information about Calabi-Yau threefolds on which M-theory can be compactified to construct the corresponding circle compactified little string theories. Using this method, we deduce at least one T-dual, and in some cases multiple T-duals, for untwisted and twisted circle compactifications of most of the little string theories that can be described on their tensor branches in terms of a 6d supersymmetric gauge theory with a simple non-abelian gauge group, which are also known as rank-0 little string theories. This includes little string theories carrying $$ \mathcal{N} $$ N = (1, 1) and $$ \mathcal{N} $$ N = (1, 0) supersymmetries. For many, but not all, circle compactifications of $$ \mathcal{N} $$ N = (1, 1) little string theories, we have T-dualities that realize Langlands dualities between affine Lie algebras. Along the way, we find another discrete theta angle distinct from 0 and π for an E-string node.