https://doi.org/10.1140/epjc/s10052-017-4909-3
Regular Article - Theoretical Physics
Exact holography of the mass-deformed M2-brane theory
1
Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea
2
University College, Sungkyunkwan University, Suwon, 440-746, South Korea
* e-mail: okab@skku.edu
Received:
19
April
2017
Accepted:
10
May
2017
Published online:
23
May
2017
We test the holographic relation between the vacuum expectation values of gauge invariant operators in 
U
mass-deformed ABJM theory and the LLM geometries with 
orbifold in 11-dimensional supergravity. To do so, we apply the Kaluza–Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vacuum expectation values of the chiral primary operator with conformal dimension 
, which is given by 
, for large N and 
. Here the factor 
is independent of N. Our results involve an infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a non-trivial test of gauge/gravity duality away from the conformal fixed point. We extend our results to the case of 
for LLM geometries represented by rectangular-shaped Young diagrams. We also discuss the exact mapping of the gauge/gravity at finite N for classical supersymmetric vacuum solutions in field theory side and corresponding classical solutions in gravity side.
© The Author(s), 2017
