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Journal of High Energy Physics

, 2015:132 | Cite as

Hilbert series for theories with Aharony duals

  • Amihay Hanany
  • Chiung Hwang
  • Hyungchul Kim
  • Jaemo Park
  • Rak-Kyeong Seong
Open Access
Regular Article - Theoretical Physics

Abstract

The algebraic structure of moduli spaces of 3d \( \mathcal{N}=2 \) supersymmetric gauge theories is studied by computing the Hilbert series which is a generating function that counts gauge invariant operators in the chiral ring. These U(N c ) theories with N f flavors have Aharony duals and their moduli spaces receive contributions from both mesonic and monopole operators. In order to compute the Hilbert series, recently developed techniques for Coulomb branch Hilbert series in 3d \( \mathcal{N}=4 \) are extended to 3d \( \mathcal{N}=2 \). The Hilbert series computation leads to a general expression of the algebraic variety which represents the moduli space of the U(N c ) theory with N f flavors and its Aharony dual theory. A detailed analysis of the moduli space is given, including an analysis of the various components of the moduli space.

Keywords

Supersymmetric gauge theory D-branes Differential and Algebraic Geometry Superstring Vacua 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Amihay Hanany
    • 1
  • Chiung Hwang
    • 2
  • Hyungchul Kim
    • 2
  • Jaemo Park
    • 2
    • 3
  • Rak-Kyeong Seong
    • 4
  1. 1.Theoretical Physics Group, Blackett LaboratoryImperial College LondonLondonUnited Kingdom
  2. 2.Department of PhysicsPOSTECHPohangKorea
  3. 3.Postech Center for Theoretical Physics (PCTP)POSTECHPohangKorea
  4. 4.School of PhysicsKorea Institute for Advanced StudySeoulKorea

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