More CFTs and RG flows from deforming M2/M5-brane horizon

Abstract

Near-horizon geometry of coincident M2-branes at a conical singularity is related to M-theory on AdS 4 times an appropriate seven-dimensional manifold X 7 . For X 7 = N 0,1,0 , squashing deformation is known to lead to spontaneous (super)symmetry breaking from N = (3, 0) to N = (0, 1) in gauged AdS 4 supergravity. Via AdS/CFT correspondence, it is interpreted as renormalization group flow of strongly coupled three-dimensional field theory with SU(3) × SU(2) global symmetry. The flow interpolates between N = (0, 1) fixed point in the UV to N = (3, 0) fixed point in the IR. Evidences for the interpretation are found both from critical points of the supergravity scalar potential and from conformal dimension of relevant chiral primary operators at each fixed point. We also analyze cases with X 7 = SO(5)/SO(3) max , V 5,2 (R), and find that there is no nontrivial renormalization group flows. We extend the analysis to Englert type vacua of M-theory. By analyzing de Wit-Nicolai potential, we find that deformation of S 7 gives rise to renormalization group flow from N = 8, SO(8) invariant UV fixed point to N = 1, G 2 invariant IR fixed point. For AdS 7 supergravity relevant for near-horizon geometry of coincident M5-branes, we also point out a nontrivial renormalization group flow from N = 1 superconformal UV fixed point to non-supersymmetric IR fixed point.Few examples are known for three-dimensional interacting conformal field theories or for renormalization group flows among themselves, mainly due to strong coupling dynamics in the infrared limit. For example, N = 1 superconformal field theories, which arise in various situations involving D-brane dynamics, do not have any continuous R-symmetries, holomorphy constraints or any known non-renormalization theorems. In the previous paper [1], as an alternative route, we have proposed to classify three-dimensional (super)conformal field theories by utilizing the AdS/CFT correspondence [2,3,4] and earlier, exhaustive study of the Kaluza-Klein supergravity [5]. The simplest spontaneous compactification of the eleven-dimensional supergravity [6] is the Freund-Rubin [7] compactification 2 to a product of AdS 4 spacetime and an arbitrary compact seven-dimensional Einstein manifold X 7 of positive scalar curvature. Continuous deformations among X 7 's is of interest 3 , as they would be interpreted, in the strongly interacting d = 3 quantum field theory dual to the AdS 4 supergravity, to renormalization group flows among interacting (super)conformal fixed points. The best known example is provided by round and squashed S 7 . The standard Einstein metric of the round S 7 yields a vacuum with SO(8) gauge symmetry and N = 8 supersymmetry. The S 7 also admits the second, squashed Einstein metric [8], yielding a vacuum with SO(5) × SO(3) gauge symmetry and N = 1 or N = 0 supersymmetry, depending on the orientation of the S 7 [9].In [1], we have shown that the well-known spontaneous (super)symmetry breaking deformation from round-to squashed-S 7 is mapped to a renormalization group fl...

Domain wall from gauged d=4, supergravity: part I

“…Moreover, α and β in (46) consist of α t that was defined as (26) and (27)(we replace α by α t ) and α s as (29) and (30). We also replace α ′ with α s .…”

“…Among them, round S 7 -and G 2 -invariant vacua are stable, while SO (7) ± -invariant ones are known to be unstable [24]. In [25,26] three dimensional conformal field theories were classified by using AdS/CFT correspondence. In particular, researchers [27] have studied the SU (3) × U (1) critical point, from the point of higher dimensional analysis, which does not belong to the classification [19] but is a supersymmetric critical point of four-dimensional gauged supergravity.…”

Supersymmetric AdS $$_2\times \Sigma _2$$ 2 × Σ 2 solutions from tri-sasakian trunc

“…It is a theory of interacting three hypermultiplets transforming in a triplet of the SU (3) flavor symmetry, and each hypermultiplet transforms as a bifundamental under the SU (N ) × SU (N ) gauge group and as a doublet of the SU (2) R ∼ SO(3) R Rsymmetry. There are also a number of previous works giving holographic studies of this theory both in 11-dimensional context and in the effective N = 3 and N = 4 gauged supergravities [19,[27][28][29][30][31]. Solutions given in these works are holographic RG flows, Janus solutions and supersymmetric AdS 2 × 2 solutions with magnetic charges.…”

Three-dimensional SCFTs, supersymmetric domain wall and renormalization group flow

“…In the previous papers [1,2], threedimensional (super)conformal field theories were classified by utilizing the AdS/CFT correspondence [3,4,5] and earlier, exhaustive study of the Kaluza-Klein supergravity [6].…”

“…In this paper, we will continue to analyze a vacuum of N = 8 supergravity with SU(3) × U(1) symmetry, studied earlier by Nicolai and Warner [17], that was considered very briefly in [2]. In section 2, by explicitly constructing 28-beins u, v fields, that are an element of fundamental 56-dimensional representation of E 7 , in terms of scalar and pseudo-scalar fields of N = 8 supergravity, we get A 1 , A 2 tensors (7), (9).…”