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


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Article Info

DATE

2021-06-01

AUTHORS

Xiaobin Li, Futoshi Yagi

ABSTRACT

In this paper, we study 5d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 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. More... »

PAGES

4

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    41 schema:description In this paper, we study 5d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 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.
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    49 Nekrasov partition function
    50 Nf flavors
    51 O5-plane
    52 Seiberg-Witten curve
    53 Web
    54 agreement
    55 boundary conditions
    56 cases
    57 conditions
    58 curves
    59 cycle integrals
    60 diagram
    61 dual graph
    62 equations
    63 evidence
    64 flavor
    65 formalism
    66 function
    67 further evidence
    68 gauge theory
    69 graph
    70 hand
    71 integrals
    72 light
    73 limit
    74 mirror symmetry
    75 non-toric Calabi-Yau
    76 orientifold planes
    77 paper
    78 partition function
    79 plane
    80 point equation
    81 profile function
    82 relation
    83 resolvent
    84 saddle-point equations
    85 singularity
    86 symmetry
    87 terms
    88 theory
    89 thermodynamic limit
    90 topological vertex formalism
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