Abstract
We study the partition function \( \mathcal{N}=1 \) 5D U(N) gauge theory with g adjoint hypermultiplets and show that for massless adjoint hypermultiplets it is equal to the partition function of a two dimensional topological field on a genus g Riemann surface. We describe the topological field theory by its amplitudes associated with cap, propagator and pair of pants. These basic amplitudes are open topological string amplitudes associated with certain Calabi-Yau threefolds in the presence of Lagrangian branes.
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A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d Topological QFT, JHEP 03 (2010) 032 [arXiv:0910.2225] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The Superconformal Index of the E 6 SCFT, JHEP 08 (2010) 107 [arXiv:1003.4244] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The 4d Superconformal Index from q-deformed 2d Yang-Mills, Phys. Rev. Lett. 106 (2011) 241602 [arXiv:1104.3850] [INSPIRE].
A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, Gauge Theories and Macdonald Polynomials, Commun. Math. Phys. 319 (2013) 147 [arXiv:1110.3740] [INSPIRE].
Y. Fukuda, T. Kawano and N. Matsumiya, 5D SYM and 2D q-Deformed YM, Nucl. Phys. B 869 (2013) 493 [arXiv:1210.2855] [INSPIRE].
Y. Tachikawa, 4d partition function on S 1 × S 3 and 2d Yang-Mills with nonzero area, PTEP 2013 (2013) 013B01 [arXiv:1207.3497] [INSPIRE].
J. Bryan and R. Pandharipande, The Local Gromov-Witten theory of curves, math/0411037 [INSPIRE].
M. Aganagic, H. Ooguri, N. Saulina and C. Vafa, Black holes, q-deformed 2d Yang-Mills and non-perturbative topological strings, Nucl. Phys. B 715 (2005) 304 [hep-th/0411280] [INSPIRE].
D.-E. Diaconescu, B. Florea and N. Saulina, A Vertex formalism for local ruled surfaces, Commun. Math. Phys. 265 (2006) 201 [hep-th/0505192] [INSPIRE].
S.H. Katz, D.R. Morrison and M.R. Plesser, Enhanced gauge symmetry in type-II string theory, Nucl. Phys. B 477 (1996) 105 [hep-th/9601108] [INSPIRE].
E. Witten, Phase transitions in M-theory and F-theory, Nucl. Phys. B 471 (1996) 195 [hep-th/9603150] [INSPIRE].
W.y. Chuang, D.E. Diaconescu and G. Pan, BPS states and the P=W conjecture, arXiv:1202.2039 [INSPIRE].
H. Nakajima and K. Yoshioka, Instanton counting on blowup. 1., Invent. Math. 162 (2005) 313 [math/0306198] [INSPIRE].
C. Vafa, Two dimensional Yang-Mills, black holes and topological strings, hep-th/0406058 [INSPIRE].
N.C. Leung and C. Vafa, Branes and toric geometry, Adv. Theor. Math. Phys. 2 (1998) 91 [hep-th/9711013] [INSPIRE].
M. Aganagic, A. Klemm, M. Mariño and C. Vafa, The topological vertex, Commun. Math. Phys. 254 (2005) 425 [hep-th/0305132] [INSPIRE].
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [INSPIRE].
M. Aganagic and C. Vafa, Mirror symmetry, D-branes and counting holomorphic discs, hep-th/0012041 [INSPIRE].
A. Iqbal and C. Kozcaz, Refined Hopf Link Revisited, JHEP 04 (2012) 046 [arXiv:1111.0525] [INSPIRE].
M. Aganagic and S. Shakirov, Refined Chern-Simons Theory and Topological String, arXiv:1210.2733 [INSPIRE].
A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex, JHEP 10 (2009) 069 [hep-th/0701156] [INSPIRE].
A. Iqbal, C. Kozcaz and K. Shabbir, Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory, Nucl. Phys. B 838 (2010) 422 [arXiv:0803.2260] [INSPIRE].
A. Iqbal and B.A. Qureshi, A N−1 Fibration and q-deformed Yang-Mills, to appear.
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ArXiv ePrint: 1507.02662
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Iqbal, A., Khan, A.Z., Qureshi, B.A. et al. Topological field theory amplitudes for A N−1 fibration. J. High Energ. Phys. 2015, 1–22 (2015). https://doi.org/10.1007/JHEP12(2015)017
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DOI: https://doi.org/10.1007/JHEP12(2015)017