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Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories

Neil Lambert, Constantinos Papageorgakis

Abstract

By integrating out the U(1)_B gauge field, we show that the U(n)xU(n) ABJM theory at level k is equivalent to a Z_k identification of the (SU(n)xSU(n))/Z_n Chern-Simons theory, but only when n and k are coprime. As a consequence, the k=1 ABJM model for two M2-branes in R^8 can be identified with the N=8 (SU(2)xSU(2))/Z_2 theory. We also conjecture that the U(2)xU(2) ABJM model at k=2 is equivalent to the N=8 SU(2)xSU(2)-theory.

Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories

Abstract

By integrating out the U(1)_B gauge field, we show that the U(n)xU(n) ABJM theory at level k is equivalent to a Z_k identification of the (SU(n)xSU(n))/Z_n Chern-Simons theory, but only when n and k are coprime. As a consequence, the k=1 ABJM model for two M2-branes in R^8 can be identified with the N=8 (SU(2)xSU(2))/Z_2 theory. We also conjecture that the U(2)xU(2) ABJM model at k=2 is equivalent to the N=8 SU(2)xSU(2)-theory.

Paper Structure

This paper contains 9 sections, 65 equations.

Table of Contents

  1. Introduction
  2. ${\cal N}=6$ Chern-Simons theories from 3-algebras
  3. From 3-algebras to the ABJM theory
  4. Dual Photon Formulation
  5. Moduli Space of $n=2$ theories
  6. Moduli Space In General
  7. The moduli space of the $k=2$ $\mathrm{SU}(2)\times\mathrm{SU}(2)$-theory
  8. Summary
  9. Acknowledgements