The gauge dual of a warped product of AdS ₄ and a squashed and stretched seven-manifold

Abstract

Corrado, Pilch and Warner in 2001 have found the second 11-dimensional solution where the deformed geometry of S 7 in the lift contains S 2 × S 2 . We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. It is the U(N)×U(N)×U(N) gauge theory with two SU(2) doublet chiral fields B 1 transforming in the (N, N, 1), B 2 transforming in the (1, N, N), C 1 in the (1, N, N) and C 2 in the (N, N, 1) as well as an adjoint field Φ in the (1, adj, 1) representation.By adding the mass term for adjoint field Φ, the detailed correspondence between fields of AdS 4 supergravity and composite operators of the IR field theory is determined. Moreover, we compute the spin-2 KK modes around a warped product of AdS 4 and a squashed and stretched seven-manifold. This background with global SU(2) × SU(2) × U(1) R symmetry is related to a U(N) × U(N) × U(N) N = 2 superconformal Chern-Simons matter theory with eighth-order superpotential and Chern-Simons level (1, 1, −2). The mass-squared in AdS 4 depends on SU(2) × SU(2) × U(1) R quantum numbers and KK excitation number. The dimensions of spin-2 operators are found.√ 79 4 −1

Spin-2 spectrum of six-dimensional field theories

“…Looking back at f f = C F (−j, j + 3 + 5 2 ; 2l + 2; z) , (4. 16) we see that it has become a Jacobi polynomial (C.6) for x = 1 − 2z:…”

“…At this stage one can often be quite general, using only generic features of the class of solutions under consideration, and non-committing to a precise space M D−d . In the second stage one This fact has already been used in several cases, to infer properties of the corresponding operator spectrum, without performing the full KK reduction; see for example [14,15,16,17,18,19] for AdS 4 solutions. In particular, [17] showed in general the above statement about the spin-2 mass operator, drawing on earlier results by [20], and their arguments can be applied also to our case.…”

The free energy of $ \mathcal{N} = 2 $ supersymmetric AdS4 solutions of M-theory

“…The latter is in fact then the special case CY 3 = C 3 . Other special cases of such solutions, and their field theory duals, have been discussed recently in [29,9]. We shall discuss the general case in more detail in [14].…”

Evidence for the holographic dual ofN=3solution in massive type IIA supergravity

“…These lead to new proposals of AdS 4 /CFT 3 [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], in which the dynamics of the IR CFTs are still governed by certain superconformal Chern-Simons matter theories with more than one gauge groups. 1 In three dimensions, there exist also superconformal Chern-Simons matter systems with a single gauge group [26,27].…”

“…We first perform an explicit analysis of the Kaluza-Klein (KK) spectrum of the spin-2 fields in AdS 4 . Solving the spin-2 spectrum in a warped AdS background with inhomogeneous internal space has been encountered in previous studies [13,16,17] This paper is organized as follows. In Sec.…”