Exact holography of the mass-deformed M2-brane theory

Abstract

We test the holographic relation between the vacuum expectation values of gauge invariant operators in N = 6 U k (N ) × U −k (N ) mass-deformed ABJM theory and the LLM geometries with Z k 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 = 1, which is given by, for large N and k = 1. Here the factor f ( ) 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 k = 1 for LLM geometries represented by rectangularshaped 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.

Holography of massive M2-brane theory with discrete torsion

“…The mass-deformed ABJM (mABJM) theory is dual to the M-theory on 11-dimensional Lin-Lunin-Maldacena (LLM) geometries with SO(2,1)×SO(4)/Z k ×SO(4)/Z k isometry [7,8]. Recently, we have made some meaningful tests of this duality [9][10][11]. We have calculated the vacuum expectation values (vevs) of chiral primary operators (CPOs) with conformal dimensions ∆ = 1 and ∆ = 2, from the classical vacuum solutions of mABJM theory and from the asymptotic expansion of the LLM solutions using the holographic methods.…”

Exact Holography of Massive M2-brane Theories and Entanglement Entropy

“…In mABJM theory, there is a unique CPO with conformal dimension one O (1) that have a nonvanishing vev [11,12]. Following the standard perturbative expansion in mABJM theory, we can calculate the one point function for such CPO and express the result as an expansion in 1/N.…”

“…In the large N limit, only the leading terms which is completely determined by the discrete Higgs vacua of the mABJM theory is relevant. See [11,12] for details. The result is…”

Mass-deformed ABJM theory and LLM geometries: exact holography

“…For the definitions of the spherical harmonics on S 7 , see appendix A. The notation (ab) means symmetrized traceless combination which is defined as 16) where g ab is a metric on S 7 . The notation [abc · · · ] means anti-symmetrization among indices, a, b, c, · · · , for instance,…”

“…In [16], we reported a summary of our work which shows an exact gauge/gravity duality relation for large N . Our analysis is based on the 3-dimensional mass-deformed Aharony-Bergman-Jafferis-Maldacena theory (mABJM) of massive M2-branes, which has N = 6 supersymmetry and U k (N )×U −k (N ) gauge symmetry, where k is the Chern-Simons level [17,18].…”