The Eleven-Dimensional Uplift of Four-Dimensional Supersymmetric RG Flow

The squashed and stretched 7-dimensional internal metric preserving U(1) x U(1) x U(1)_R symmetry possesses an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein L^{p, q, r} space. The r(transverse to the domain wall)-dependence of the two 4-dimensional supergravity fields, that play the role of geometric parameters for squashing and stretching, makes the 11-dimensional Einstein-Maxwell equations consistent not only at the two critical points but also along the whole N=2 supersymmetric RG flow connecting them. The Ricci tensor of the solution has common feature with the previous three 11-dimensional solutions. The 4-forms preserve only U(1)_R symmetry for other generic parameters of the metric. We find an exact solution to the 11-dimensional Einstein-Maxwell equations corresponding to the lift of the 4-dimensional supersymmetric RG flow.Comment: 16 p

More on Meta-Stable Brane Configuration by Quartic Superpotential for Fundamentals

For the case where the gauge theory superpotential has a quartic term as well as the mass term for quarks, the nonsupersymmetric meta-stable brane configuration was found recently. By adding the orientifold 6-planes and the extra fundamental flavors to this brane configuration, we describe the meta-stable nonsupersymmetric vacua of the gauge theory with antisymmetric flavor as well as fundamental flavors in type IIA string theory.Comment: 16 pp, 4 figures; second paragraph of section 1, figures 2, 3, 4, the last paragraph of page 5, the equation (2.1) and the footnote 2 are improved and to appear in PL

Other Meta-Stable Brane Configuration by Adding an Orientifold 6-Plane to Giveon-Kutasov

Giveon and Kutasov have found the type IIA intersecting nonsupersymmetric meta-stable brane configuration where the electric gauge theory superpotential has a quartic term as well as the mass term for quarks. In this paper, by adding the orientifold 6-plane to this brane configuration, we describe the brane configuration corresponding to the meta-stable nonsupersymmetric vacua of the supersymmetric unitary gauge theory with symmetric flavor as well as fundamental flavors.Comment: 16 pp, 3 figures; The mirrors of Figures 2 and 3 corrected; the footnote 5 added and to appear in PL

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

The Gauge Dual of Gauged N=8 Supergravity Theory

The most general SU(3)-singlet space of gauged N=8 supergravity in four-dimensions is studied recently. The SU(3)-invariant six scalar fields are realized by six real four-forms. A family of holographic N=1 supersymmetric RG flows on M2-branes in three-dimensions is described. This family of flows is driven by three independent mass parameters from the N=8 SO(8) theory and is controlled by two IR fixed points, N=1 G_2-invariant one and N=2 SU(3) x U(1)-invariant one. The generic flow with arbitrary mass parameters is N=1 supersymmetric and reaches to the N=2 SU(3) x U(1) fixed point where the three masses become identical. A particular N=1 supersymmetric SU(3)-preserving RG flow from the N=1 G_2-invariant fixed point to the N=2 SU(3) x U(1)-invariant fixed point is also discussed.Comment: 19pp; added the footnote 1, improved the conclusion and to appear in IJMP

N=1 Supersymmetric Boundary Bootstrap

We investigate the boundary bootstrap programme for finding exact reflection matrices of integrable boundary quantum field theories with N=1 boundary supersymmetry. The bulk S-matrix and the reflection matrix are assumed to take the form S=S_1S_0, R=R_1R_0, where S_0 and R_0 are the S-matrix and reflection matrix of some integrable non-supersymmetric boundary theory that is assumed to be known, and S_1 and R_1 describe the mixing of supersymmetric indices. Under the assumption that the bulk particles transform in the kink and boson/fermion representations and the ground state is a singlet we present rules by which the supersymmetry representations and reflection factors for excited boundary bound states can be determined. We apply these rules to the boundary sine-Gordon model, to the boundary a_2^(1) and a_4^(1) affine Toda field theories, to the boundary sinh-Gordon model and to the free particle.Comment: 43 pages, LaTex, 14 eps figures, minor correction

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

Meta-Stable Brane Configurations by Higher Order Polynomial Superpotential

We construct the type IIA nonsupersymmetric meta-stable brane configuration consisting of (2k+1) NS5-branes and D4-branes where the electric gauge theory superpotential has an order (2k+2) polynomial for the bifundamentals. We find a rich pattern of nonsupersymmetric meta-stable states as well as the supersymmetric stable ones. By adding the orientifold 4-plane to this brane configuration, we also describe the intersecting brane configuration of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of corresponding gauge theory.Comment: 27pp, 8 figures; some footnotes added; to appear in IJMP

c=5/2 Free Fermion Model of WB_{2} Algebra

We investigate the explicit construction of the $WB_{2}$ algebra, which is closed and associative for all values of the central charge $c$, using the Jacobi identity and show the agreement with the results studied previously. Then we illustrate a realization of $c=\frac{5}{2}$ free fermion model, which is $m \rightarrow \infty$ limit of unitary minimal series, $c ( WB_{2} )=\frac{5}{2} (1-\frac{12}{ (m+3)(m+4) })$ based on the cosets $( \hat{B_{2}} \oplus \hat{B_{2}}, \hat{B_{2} })$ at level $(1,m).$ We confirm by explicit computations that the bosonic currents in the $WB_{2}$ algebra are indeed given by the Casimir operators of $\hat{B_{2}}$ .Comment: 16 page