Hilbert series for moduli spaces of instantons on ℂ2/ℤn View Full Text


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Article Info

DATE

2014-01-31

AUTHORS

Anindya Dey, Amihay Hanany, Noppadol Mekareeya, Diego Rodríguez-Gómez, Rak-Kyeong Seong

ABSTRACT

We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p + 4) system with the D(p + 4) branes (with or without O(p + 4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic An−1 ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected. More... »

PAGES

182

References to SciGraph publications

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    http://scigraph.springernature.com/pub.10.1007/jhep01(2014)182

    DOI

    http://dx.doi.org/10.1007/jhep01(2014)182

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    33 schema:description We study chiral gauge-invariant operators on moduli spaces of G instantons for any classical group G on A-type ALE spaces using Hilbert Series (HS). Moduli spaces of instantons on an ALE space can be realized as Higgs branches of certain quiver gauge theories which appear as world-volume theories on Dp branes in a Dp-D(p + 4) system with the D(p + 4) branes (with or without O(p + 4) planes) wrapping the ALE space. We study in detail a list of quiver gauge theories which are related to G-instantons of arbitrary ranks and instanton numbers on a generic An−1 ALE space and discuss the corresponding brane configurations. For a large class of theories, we explicitly compute the Higgs branch HS which reveals various algebraic/geometric aspects of the moduli space such as the dimension of the space, generators of the moduli space and relations connecting them. In a large number of examples involving lower rank instantons, we demonstrate that HS for equivalent instantons of isomorphic gauge groups but very different quiver descriptions do indeed agree, as expected.
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    39 schema:keywords ALE spaces
    40 DP
    41 Dp-branes
    42 G-instantons
    43 Higgs branch
    44 Higgs branch Hilbert series
    45 Hilbert series
    46 arbitrary rank
    47 aspects
    48 branches
    49 brane
    50 brane configurations
    51 class
    52 classical group G
    53 configuration
    54 description
    55 detail
    56 dimensions
    57 example
    58 gauge group
    59 gauge theory
    60 gauge-invariant operators
    61 generator
    62 geometric aspects
    63 group
    64 group G
    65 instanton number
    66 instantons
    67 large class
    68 large number
    69 list
    70 moduli space
    71 number
    72 operators
    73 quiver description
    74 quiver gauge theories
    75 rank
    76 relation
    77 series
    78 space
    79 system
    80 theory
    81 world-volume theory
    82 schema:name Hilbert series for moduli spaces of instantons on ℂ2/ℤn
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