New directions in bipartite field theories View Full Text


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Article Info

DATE

2013-06-10

AUTHORS

Sebastian Franco, Daniele Galloni, Rak-Kyeong Seong

ABSTRACT

We perform a detailed investigation of Bipartite Field Theories (BFTs), a general class of 4d \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 gauge theories which are defined by bipartite graphs. This class of theories is considerably expanded by identifying a new way of assigning gauge symmetries to graphs. A new procedure is introduced in order to determine the toric Calabi-Yau moduli spaces of BFTs. For graphs on a disk, we show that the matroid polytope for the corresponding cell in the Grassmannian coincides with the toric diagram of the BFT moduli space. A systematic BFT prescription for determining graph reductions is presented. We illustrate our ideas in infinite classes of BFTs and introduce various operations for generating new theories from existing ones. Particular emphasis is given to theories associated to non-planar graphs. More... »

PAGES

32

References to SciGraph publications

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    40 schema:description We perform a detailed investigation of Bipartite Field Theories (BFTs), a general class of 4d \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 gauge theories which are defined by bipartite graphs. This class of theories is considerably expanded by identifying a new way of assigning gauge symmetries to graphs. A new procedure is introduced in order to determine the toric Calabi-Yau moduli spaces of BFTs. For graphs on a disk, we show that the matroid polytope for the corresponding cell in the Grassmannian coincides with the toric diagram of the BFT moduli space. A systematic BFT prescription for determining graph reductions is presented. We illustrate our ideas in infinite classes of BFTs and introduce various operations for generating new theories from existing ones. Particular emphasis is given to theories associated to non-planar graphs.
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    46 schema:keywords Bipartite field theories
    47 Calabi-Yau moduli space
    48 bipartite graphs
    49 cells
    50 class
    51 class of theories
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    54 detailed investigation
    55 diagram
    56 direction
    57 disk
    58 emphasis
    59 field theory
    60 gauge symmetry
    61 gauge theory
    62 general class
    63 graph
    64 graph reduction
    65 idea
    66 infinite class
    67 investigation
    68 matroid polytopes
    69 moduli space
    70 new directions
    71 new procedure
    72 new theory
    73 new way
    74 non-planar graphs
    75 one
    76 operation
    77 order
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    88 schema:name New directions in bipartite field theories
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