19 research outputs found
Towards New Membrane Flow from de Wit-Nicolai Construction
The internal 4-form field strengths with 7-dimensional indices have been
constructed by de Wit and Nicolai in 1986. They are determined by the following
six quantities: the 56-bein of 4-dimensional N=8 gauged supergravity, the
Killing vectors on the round seven-sphere, the covariant derivative acting on
these Killing vectors, the warp factor, the field strengths with 4-dimensional
indices and the 7-dimensional metric.
In this paper, by projecting out the remaining mixed 4-form field strengths
in an SU(8) tensor that appears in the variation of spin 1/2 fermionic sector,
we also write down them explicitly in terms of some of the above quantities.
For the known critical points, the N=8 SO(8) point and the nonsupersymmetric
SO(7)^{+} point, we reproduce the corresponding 11-dimensional uplifts by
computing the full nonlinear expressions. Moreover, we find out the
11-dimensional lift of the nonsupersymmetric SO(7)^{+} invariant flow. We
decode their implicit formula for the first time and the present work will
provide how to obtain the new supersymmetric or nonsupersymmetric membrane
flows in 11-dimensions.Comment: 28 pages; the footnote 2 is added and to appear in IJMP
Are There Any New Vacua of Gauged N=8 Supergravity in Four Dimensions?
We consider the most general SU(3) singlet space of gauged N=8 supergravity
in four-dimensions. The SU(3)-invariant six scalar fields in the theory can be
viewed in terms of six real four-forms. By exponentiating these four-forms, we
eventually obtain the new scalar potential. For the two extreme limits, we
reproduce the previous results found by Warner in 1983. In particular, for the
N=1 G_2 critical point, we find the constraint surface parametrized by three
scalar fields on which the cosmological constant has the same value. We obtain
the BPS domain-wall solutions for restricted scalar submanifold. We also
describe the three-dimensional mass-deformed superconformal Chern-Simons matter
theory dual to the above supersymmetric flows in four-dimensions.Comment: 44p; the main text and appendices improved for compact
presentation;the acknowledgments added and to appear in IJMP
Perturbing Around A Warped Product Of AdS_4 and Seven-Ellipsoid
We compute the spin-2 Kaluza-Klein modes around a warped product of AdS_4 and
a seven-ellipsoid. This background with global G_2 symmetry is related to a
U(N) x U(N) N=1 superconformal Chern-Simons matter theory with sixth order
superpotential. The mass-squared in AdS_4 is quadratic in G_2 quantum number
and KK excitation number. We determine the dimensions of spin-2 operators using
the AdS/CFT correspondence. The connection to N=2 theory preserving SU(3) x
U(1)_R is also discussed.Comment: 21pp; The second and last paragraphs of section 2, the footnotes 1
and 2 added and to appear in JHE
Towards An N=1 SU(3)-Invariant Supersymmetric Membrane Flow In Eleven-Dimensional Supergravity
The M-theory lift of N=1 G_2-invariant RG flow via a combinatoric use of the
4-dimensional RG flow and 11-dimensional Einstein-Maxwell equations was found
some time ago. The 11-dimensional metric, a warped product of an asymptotically
AdS_4 space with a squashed and stretched 7-sphere, for SU(3)-invariance was
found before. In this paper, by choosing the 4-dimensional internal space as
CP^2 space, we discover an exact solution of N=1 G_2-invariant flow to the
11-dimensional field equations. By an appropriate coordinate transformation on
the three internal coordinates, we also find an 11-dimensional solution of N=1
G_2-invariant flow interpolating from N=8 SO(8)-invariant UV fixed point to N=1
G_2-invariant IR fixed point. In particular, the 11-dimensional metric and
4-forms at the N=1 G_2 fixed point for the second solution will provide some
hints for the 11-dimensional lift of whole N=1 SU(3) RG flow connecting this
N=1 G_2 fixed point to N=2 SU(3) x U(1)_R fixed point in 4-dimensions.Comment: 45 pp; Four footnotes added and corrected some statement
Domain Wall from Gauged d=4, N=8 Supergravity: Part I
By studying already known extrema of non-semi-simple Inonu-Wigner contraction
CSO(p, q)^{+} and non-compact SO(p, q)^{+}(p+q=8) gauged N=8 supergravity in
4-dimensions developed by Hull sometime ago, one expects there exists
nontrivial flow in the 3-dimensional boundary field theory. We find that these
gaugings provide first-order domain-wall solutions from direct extremization of
energy-density. We also consider the most general CSO(p, q, r)^{+} with p+q+r=8
gauging of N=8 supergravity by two successive SL(8,R) transformations of the de
Wit-Nicolai theory, that is, compact SO(8) gauged supergravity. The theory
found earlier has local SU(8)x CSO(p, q, r)^{+} gauge symmetry as well as local
N=8 supersymmetry. The gauge group CSO(p, q, r)^{+} is spontaneously reduced to
its maximal compact subgroup SO(p)^{+} x SO(q)^{+} x U(1)^{+r(r-1)/2}. The
T-tensor we obtain describes a two-parameter family of gauged N=8 supergravity
from which one can construct A_1 and A_2 tensors. The effective nontrivial
scalar potential can be written as the difference of positive definite terms.
We examine the scalar potential for critical points at which the expectation
value of the scalar field is SO(p)^{+} x SO(q)^{+} x SO(r)^{+} invariant. It
turns out that there is no new extra critical point. However, we do have flow
equations and domain-wall solutions for the scalar fields are the gradient flow
equations of the superpotential that is one of the eigenvalues of A_1 tensor.Comment: 65 pp; v2: refs added, redundant parts skipped, improvements added
and to appear in NPB; v3: the title change
N=8 Gauged Supergravity Theory and N=6 Superconformal Chern-Simons Matter Theory
By studying the previously known holographic N=4 supersymmetric
renormalization group flow(Gowdigere-Warner) in four dimensions, we find the
mass deformed Chern-Simons matter theory which has N=4 supersymmetry by adding
the four mass terms among eight adjoint fields. The geometric superpotential
from the eleven dimensions is found and provides the M2-brane probe analysis.
As second example, we consider known holographic N=8 supersymmetric
renormalization group flow(Pope-Warner) in four dimensions. The eight mass
terms are added and similar geometric superpotential is obtained.Comment: 39 pp; The footnotes 3 and 4 and the ref. added; improved the page 2
and to appear in IJMP
Supersymmetric Domain Wall and RG Flow from 4-Dimensional Gauged N=8 Supergravity
By studying various, known extrema of 1) SU(3) sectors, 2) SO(5) sectors and
3) SO(3)xSO(3) sectors of gauged N =8 supergravity in four-dimensions, one
finds that the deformation of seven sphere \S^7 gives rise to non-trivial
renormalization group(RG) flow in three-dimensional boundary conformal field
theory from UV fixed point to IR fixed point. For SU(3) sectors, this leads to
four-parameter subspace of the supergravity scalar-gravity action and we
identify one of the eigenvalues of A_1 tensor of the theory with a
superpotential of scalar potential that governs RG flows on this subspace. We
analyze some of the structure of the superpotential and discuss first-order BPS
domain-wall solutions, using some algebraic relations between superpotential
and derivatives of it with respect to fields, that determine a (super)symmetric
kink solution in four-dimensional N =8 supergravity, which generalizes all the
previous considerations. The BPS domain-wall solutions are equivalent to
vanishing of variation of spin 1/2, 3/2 fields in the supersymmetry preserving
bosonic background of gauged N=8 supergravity. For SO(5) sectors, there exist
only nontrivial nonsupersymmetric critical points that are unstable and
included in SU(3) sectors. For SO(3)xSO(3) sectors, we construct the scalar
potential(never been written) explicitly and study explicit construction of
first-order domain-wall solutions.Comment: latex, 43pages, one figure, four tables; typos corrected, ref.[24]
added, appendix shortened and to appear in Nucl.Phys.