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

Explicit Construction of Spin 4 Casimir Operator in the Coset Model SO^(5)1×SO^(5)m/SO^(5)1+m \hat{SO} (5)_{1} \times \hat{SO} (5)_{m} / \hat{SO} (5)_{1+m}

We generalize the Goddard-Kent-Olive (GKO) coset construction to the dimension 5/2 operator for $\hat{so} (5)$ and compute the fourth order Casimir invariant in the coset model $\hat{SO} (5)_{1} \times \hat{SO} (5)_{m} / \hat{SO} (5)_{1+m}$ with the generic unitary minimal $c < 5/2$ series that can be viewed as perturbations of the $m \rightarrow \infty$ limit, which has been investigated previously in the realization of $c= 5/2$ free fermion model.Comment: 11 page

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

Geometrically Induced Phase Transitions at Large N

Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2's. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2's causes discrete jumps in the energetically preferred confining vacuum and can also obstruct direct brane/anti-brane annihilation processes. The branes must hop to nearby S^2's before annihilating, thus significantly increasing the lifetime of the corresponding non-supersymmetric vacua. We also speculate that misaligned metastable glueball phases may generate a repulsive inter-brane force which stabilizes the radial mode present in compact Calabi-Yau threefolds.Comment: 47 pages, 7 figure

Meta-Stable Brane Configurations by Adding an Orientifold-Plane to Giveon-Kutasov

In hep-th/0703135, they have found the type IIA intersecting brane configuration where there exist three NS5-branes, D4-branes and anti-D4-branes. By analyzing the gravitational interaction for the D4-branes in the background of the NS5-branes, the phase structures in different regions of the parameter space were studied in the context of classical string theory. In this paper, by adding the orientifold 4-plane and 6-plane to the above brane configuration, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of these gauge theories.Comment: 21 pp, 6 figures; reduced bytes of figures, DBI action analysis added and to appear in JHE

The Full Structure of Quantum N=2N=2 Super-W3(2)W_3^{(2)} Algebra

We present the complete structure of the nonlinear $N=2$ super extension of Polyakov-Bershadsky, $W_3^{(2)}$, algebra with the generic central charge, $c$, at the {\it quantum} level. It contains extra two pairs of fermionic currents with integer spins 1 and 2, besides the currents of $N=2$ superconformal and $W_3^{(2)}$ algebras. For $c\rightarrow \infty$ limit, the algebra reduces to the classical one, which has been studied previously. The 'hybrid' field realization of this algebra is also discussed.Comment: 8 pages, latex, no figure

Meta-Stable Brane Configurations with Seven NS5-Branes

We present the intersecting brane configurations consisting of NS-branes, D4-branes(and anti D4-branes) and O6-plane, of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua in four dimensional N=1 supersymmetric SU(N_c) x SU(N_c') x SU(N_c'') gauge theory with a symmetric tensor field, a conjugate symmetric tensor field and bifundamental fields. We also describe the intersecting brane configurations of type IIA string theory corresponding to the nonsupersymmetric meta-stable vacua in the above gauge theory with an antisymmetric tensor field, a conjugate symmetric tensor field, eight fundamental flavors and bifundamentals. These brane configurations consist of NS-branes, D4-branes(and anti D4-branes), D6-branes and O6-planes.Comment: 34pp, 9 figures; Improved the draft and added some footnotes; Figure 1, footnote 7 and captions of Figures 7,8,9 added or improved and to appear in CQ

Supersymmetry Breaking Vacua from M Theory Fivebranes

We consider intersecting brane configurations realizing N=2 supersymmetric gauge theories broken to N=1 by multitrace superpotentials, and softly to N=0. We analyze, in the framework of M5-brane wrapping a curve, the supersymmetric vacua and the analogs of spontaneous supersymmetry breaking and soft supersymmetry breaking in gauge theories. We show that the M5-brane does not exhibit the analog of metastable spontaneous supersymmetry breaking, and does not have non-holomorphic minimal volume curves with holomorphic boundary conditions. However, we find that any point in the N=2 moduli space can be rotated to a non-holomorphic minimal volume curve, whose boundary conditions break supersymmetry. We interpret these as the analogs of soft supersymmetry breaking vacua in the gauge theory.Comment: 32 pages, 8 figures, harvmac; v2: corrections in eq. 3.6 and in section 6, reference adde