An supersymmetric G2-invariant flow in M-theory

Abstract

It was found that deformation of S 7 gives rise to renormalization group(RG) flow from N = 8, SO(8)-invariant UV fixed point to N = 1, G 2 -invariant IR fixed point in four-dimensional gauged N = 8 supergravity. Also BPS supersymmetric domain wall configuration interpolated between these two critical points. In this paper, we use the G 2 -invariant RG flow equations for both scalar fields and domain wall amplitude and apply them to the nonlinear metric ansatz developed by de Wit, Nicolai and Warner some time ago. We carry out the M-theory lift of the G 2 -invariant RG flow through a combinatoric use of the four-dimensional RG flow equations and eleven-dimensional Einstein-Maxwell equations. The non-trivial r(that is the coordinate transverse to the domain wall)-dependence of vacuum expectation values makes the Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric RG flow connecting two critical points. By applying an ansatz for an eleven-dimensional threeform gauge field with varying scalars, we discover an exact solution to the eleven-dimensional Einstein-Maxwell equations corresponding to the M-theory lift of the G 2 -invariant RG flow.------E-mail addresses: ahn@knu.ac.kr (C. Ahn), taichi@hepth.hanyang.ac.kr (T. Itoh)

Holographic RG flow in a new SO(3) × SO(3) sector of ω-deformed SO(8) gauged N = 8 $$ \mathcal{N}=8 $$ supergravity

“…Using the uplift ansatz (4.58), we derive the internal metric for the G 2 invariant sector This result matches with the one given in [14].…”

“…Cases that have been studied involve retaining the subset of scalar fields invariant under an SO(7), G 2 , SU(3) or SO(3) × SO(3) subgroup [3,[5][6][7][8][9], or else the seven scalars parameterising the diagonal elements of the SL(8, R)/SO(8) coset associated with the 35 self-dual scalars [10]. These various truncations are parallel to the consistent scalar-field truncations performed for the the original de Wit-Nicolai theory [11][12][13][14][15][16][17][18][19]. Consistent truncations retaining U(1) gauge fields have also been considered, giving rise to an ω-deformed version of the ST U supergravity [20], and a one-parameter extension [21] of an Einstein-Maxwell-scalar system [22] previously obtained via a reduction from eleven dimensions on a seven-dimensional Sasaki-Einstein manifold.…”

Boundary terms and three-point functions: an AdS/CFT puzzle resolved

“…In particular, the truncation will generically break SO (8) to SO(p), or perhaps even some subgroup of SO(p). 34 For early examples, see [71][72][73][74][75]. 35 The factors of p cancel between the coefficient of (C.2) and the sum in the trace.…”

Supersymmetric RG flows and Janus from type II orbifold compactification

“…t M N and t αβ are SO (6, n) and SL(2, R) generators which can be chosen as (4) with αβ = − βα and +− = 1. η M N = diag(−1, −1, −1, −1, −1, −1, 1, . .…”

“…Most of the previously studied holographic RG flows have been found within the maximal N = 8 gauged supergravities [2][3][4][5][6][7][8][9]. Many of these solutions describe various deformations of the N = 8 SCFTs arising from M2-brane world-volume proposed in [10,11].…”