Relating U(N) x U(N) to SU(N) x SU(N) Chern-Simons membrane theories

Neil Lambert; Constantinos Papageorgakis

doi:10.1007/JHEP04(2010)104

Relating U(N) x U(N) to SU(N) x SU(N) Chern-Simons membrane theories

Neil Lambert, Constantinos Papageorgakis

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

By integrating out the U(1) B gauge field, we show that the U(n) x U(n) ABJM theory at level k is equivalent to a Z(k) identification of the (SU(n) x SU(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)x SU(2))/Z(2) theory. We also conjecture that the U(2) x U(2) ABJM model at k = 2 is equivalent to the N = 8 SU(2) x SU(2)-theory.

Original language	English
Article number	104
Journal	Journal of High Energy Physics
Issue number	4
Early online date	27 Apr 2010
DOIs	https://doi.org/10.1007/JHEP04(2010)104
Publication status	Published - Apr 2010

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10.1007/JHEP04(2010)104

Cite this

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title = "Relating U(N) x U(N) to SU(N) x SU(N) Chern-Simons membrane theories",

abstract = "By integrating out the U(1) B gauge field, we show that the U(n) x U(n) ABJM theory at level k is equivalent to a Z(k) identification of the (SU(n) x SU(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)x SU(2))/Z(2) theory. We also conjecture that the U(2) x U(2) ABJM model at k = 2 is equivalent to the N = 8 SU(2) x SU(2)-theory.",

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AU - Papageorgakis, Constantinos

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AB - By integrating out the U(1) B gauge field, we show that the U(n) x U(n) ABJM theory at level k is equivalent to a Z(k) identification of the (SU(n) x SU(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)x SU(2))/Z(2) theory. We also conjecture that the U(2) x U(2) ABJM model at k = 2 is equivalent to the N = 8 SU(2) x SU(2)-theory.

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