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 D-type singularities
    50 Nekrasov partition function
    51 Nf flavors
    52 O5-plane
    53 Seiberg-Witten curve
    54 Web
    55 agreement
    56 boundary conditions
    57 cases
    58 conditions
    59 curves
    60 cycle integrals
    61 diagram
    62 dual graph
    63 equations
    64 evidence
    65 flavor
    66 formalism
    67 function
    68 further evidence
    69 gauge theory
    70 graph
    71 hand
    72 integrals
    73 light
    74 limit
    75 mirror symmetry
    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
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