Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3

Kovacs, Stefano and Sato, Y. and Shimada, H. (2013) Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3. Progress of Theoretical and Experimental Physics, 2014 (9). 93B01-0. ISSN 2050-3911

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We consider states with large angular momentum to facilitate the study of the M-theory regime of the AdS_4 /CFT_3 correspondence. More precisely, we study the duality between M-theory on AdS_4 × S^7/Z_k and N = 6 supersymmetric Chern–Simons-matter (ABJM) theory with gauge group U(N)×U(N) and level k, in the regime where k is of order one and N is large. In this regime the study of both sides of the duality is challenging: the lack of an explicit formulation of M-theory in AdS_4 × S^7/Z_k makes the gravity side difficult, while the CFT side is strongly coupled and the planar approximation is not applicable. In order to overcome these difficulties, we focus on states on the gravity side with large orbital angular momentum J ≫ 1 associated with a single plane of rotation in S^7 . We then identify the corresponding operators in the CFT, thereby establishing the AdS/CFT dictionary in this large angular momentum sector. We show that there are natural approximation schemes on both sides of the correspondence as a consequence of the presence of the small parameter 1/J. On the AdS side, the sector we focus on is well-approximated by the matrix model of M-theory – with matrices of size J/k – defined on the maximally supersymmetric eleven-dimensional pp-wave background. The pp-wave approximation to M-theory in AdS_4 × S^7/Z_k is justified for 1 ≪ J ≪ N^1/2 , while loop corrections in the matrix model are suppressed compared to tree-level contributions for J ≫ N^1/3 . On the CFT side, we study the ABJM theory defined on S^2 × R with large magnetic flux J/k. Using a carefully chosen gauge, we find an expansion of the Born–Oppenheimer type which arises naturally for large J in spite of the theory being strongly coupled. The energy spectra computed on the two sides agree at leading order. This provides a highly non-trivial test of the AdS_4 /CFT_3 correspondence including near-BPS observables associated with membrane degrees of freedom, therefore extending the validity of the AdS_4 /CFT_3 duality beyond the previously studied sectors corresponding to either BPS supergravity observables or the type IIA string regime.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:30
Last Modified: 26 Jul 2018 10:28

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