Built on

D. R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories
1997
Earlier work this paper cites.
M. R. Douglas, S. H. Katz, and C. Vafa, Small instantons, Del Pezzo surfaces and type I-prime theory
1997
Earlier work this paper cites.
N. C. Leung and C. Vafa, Branes and toric geometry
1998
Earlier work this paper cites.
O. Aharony, A. Hanany, and B. Kol, Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams
1998
Earlier work this paper cites.
A. Hanany and A. Zaffaroni, Issues on orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry
1999
Earlier work this paper cites.
M. Aganagic, A. Klemm, M. Marino, and C. Vafa, The Topological vertex
2005
Earlier work this paper cites.
D.-E. Diaconescu and B. Florea, The Ruled vertex and D-E degenerations
2005
Earlier work this paper cites.
A. Iqbal and A.-K. Kashani-Poor, The Vertex on a strip
2006
Earlier work this paper cites.
D.-E. Diaconescu, B. Florea, and N. Saulina, A Vertex formalism for local ruled surfaces
2006
Earlier work this paper cites.
D.-E. Diaconescu and B. Florea, The Ruled vertex and nontoric del Pezzo surfaces
2006
Earlier work this paper cites.
A. Okounkov, N. Reshetikhin, and C. Vafa, Quantum Calabi-Yau and classical crystals
2006
Earlier work this paper cites.
A. Iqbal, C. Kozcaz, and C. Vafa, The Refined topological vertex
2009
Earlier work this paper cites.
H. Awata and H. Kanno, Refined BPS state counting from Nekrasov’s formula and Macdonald functions
Original
2009
Earlier work this paper cites.
F. Benini, S. Benvenuti, and Y. Tachikawa, Webs of five-branes and N=2 superconformal field theories
Original
2009
Earlier work this paper cites.
J. Walcher, Evidence for Tadpole Cancellation in the Topological String
Original
2009
Earlier work this paper cites.

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C. Hwang, J. Kim, S. Kim, and J. Park, General instanton counting and 5d SCFT
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2017

Topological vertex formalism with O5-plane

Kim, Sung-Soo, Yagi, Futoshi

Understand

We propose new topological vertex formalism for Type IIB $(p,q)$ 5-brane web with an O5-plane.

We apply our proposal to 5d $\mathcal{N}=1$ Sp(1) gauge theory with $N_f=0,1,8$ flavors to compute the topological string partition functions and check the agreement with the known results.
Especially for the $N_f=8$ case, which corresponds to E-string theory on a circle, we obtain a new, yet simple, expression of the partition function with two Young diagram sum.

Built on

D. R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories
1997
Earlier work this paper cites.
M. R. Douglas, S. H. Katz, and C. Vafa, Small instantons, Del Pezzo surfaces and type I-prime theory
1997
Earlier work this paper cites.
N. C. Leung and C. Vafa, Branes and toric geometry
1998
Earlier work this paper cites.
O. Aharony, A. Hanany, and B. Kol, Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams
1998
Earlier work this paper cites.
A. Hanany and A. Zaffaroni, Issues on orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry
1999
Earlier work this paper cites.
M. Aganagic, A. Klemm, M. Marino, and C. Vafa, The Topological vertex
2005
Earlier work this paper cites.
D.-E. Diaconescu and B. Florea, The Ruled vertex and D-E degenerations
2005
Earlier work this paper cites.
A. Iqbal and A.-K. Kashani-Poor, The Vertex on a strip
2006
Earlier work this paper cites.
D.-E. Diaconescu, B. Florea, and N. Saulina, A Vertex formalism for local ruled surfaces
2006
Earlier work this paper cites.
D.-E. Diaconescu and B. Florea, The Ruled vertex and nontoric del Pezzo surfaces
2006
Earlier work this paper cites.
A. Okounkov, N. Reshetikhin, and C. Vafa, Quantum Calabi-Yau and classical crystals
2006
Earlier work this paper cites.
A. Iqbal, C. Kozcaz, and C. Vafa, The Refined topological vertex
2009
Earlier work this paper cites.
H. Awata and H. Kanno, Refined BPS state counting from Nekrasov’s formula and Macdonald functions
Original
2009
Earlier work this paper cites.
F. Benini, S. Benvenuti, and Y. Tachikawa, Webs of five-branes and N=2 superconformal field theories
Original
2009
Earlier work this paper cites.
J. Walcher, Evidence for Tadpole Cancellation in the Topological String
Original
2009
Earlier work this paper cites.