More on Meta-Stable Brane Configuration

We describe the intersecting brane configuration of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua in four dimensional N=1 supersymmetric SU(N_c) gauge theory with an antisymmetric flavor, a conjugate symmetric flavor, eight fundamental flavors, m_f fundamental flavors and m_f antifundamental flavors. This is done by analyzing the N=1 supersymmetric SU(2m_f-N_c+4) magnetic gauge theory with dual matters and the corresponding dual superpotential.Comment: 20 pp, 3 figures; Pages 11,12, and 14 improved; to appear in CQ

Meta-Stable Brane Configuration and Gauged Flavor Symmetry

Starting from an N=1 supersymmetric electric gauge theory with the gauge group Sp(N_c) x SO(2N_c') with fundamentals for the first gauge group factor and a bifundamental, we apply Seiberg dual to the symplectic gauge group only and arrive at the N=1 supersymmetric dual magnetic gauge theory with dual matters including the gauge singlets and superpotential. By analyzing the F-term equations of the dual magnetic superpotential, we describe the intersecting brane configuration of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory.Comment: 16 pp, 3 figures; stability analysis in page 7 and 8 added and the presentation improved; reduced bytes of figures and to appear in MPL

Stable configuration of a molecule as spontaneous symmetry breaking

In a molecule subjected to no external fields, motion of nuclei is governed by a function V of nuclear coordinates. This function (potential energy) is a sum of two terms: Coulomb repulsion between nuclei and the electronic effective potential E which results from the Born-Oppenheimer approximation. In this paper we have presented a group of coordinate transformations which are the symmetries of functions E and V. We showed that the formula for dynamical representation, which has fundamental importance in the symmetry analysis of normal modes of a molecule, follows from these symmetries. In addition, we proved that every molecule has at least one normal mode belonging to the totally symmetric (and therefore Raman-active) irreducible representation of the point group of that molecule. Next, we used symmetries of V and E to analyze possible shapes of some molecule types. We applied both Abud-Sartori-Michel theorem and symmetry adapted expansion of the electronic effective potential around united atom. Finally, we derived an approximate relation which predicts order of magnitude of the vibration frequency from the bond length in a diatomic molecule.Comment: 17 pages, Accidentally omitted superscript T (for transpose) on the matrix appearing at page 5, line 4 from above, added. One sentence in the abstract slightly changed for clarity. Few sentences slightly changed. 4 references added. The formula 54 corrected for the factor 1.41. Results unchange

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

Reverse Bisimulations on Stable Configuration Structures

The relationships between various equivalences on configuration structures, including interleaving bisimulation (IB), step bisimulation (SB) and hereditary history-preserving (HH) bisimulation, have been investigated by van Glabbeek and Goltz (and later Fecher). Since HH bisimulation may be characterised by the use of reverse as well as forward transitions, it is of interest to investigate forms of IB and SB where both forward and reverse transitions are allowed. We give various characterisations of reverse SB, showing that forward steps do not add extra power. We strengthen Bednarczyk's result that, in the absence of auto-concurrency, reverse IB is as strong as HH bisimulation, by showing that we need only exclude auto-concurrent events at the same depth in the configuration