International Journal of Modern Physics A

There has recently been a revival of interest in anti-de-Sitter space (AdS), brought about by the conjectured duality between physics in the bulk of AdS and a conformal field theory on the boundary. Since the whole subject of branes, singletons and superconformal field theories on the AdS boundary was an active area of research about ten years ago, we begin with a historical review, including the idea of the "membrane at the end of the universe." We then compare the old and new approaches and discuss some new results on AdS₅ × S⁵ and AdS₃ × S³.

We investigate D=4, N=1 F theory models realized by type IIB string compactification on toric threefolds. Massless spectra, gauge symmetries, phase transitions associated with divisor contractions and flops, and nonperturbative superpotentials are analyzed using elementary toric methods.

It is shown that R² and R³ terms dominate over the Einstein–Hilbert term in the gravitational action till the energy mass scale M ≥ 8.4 × 10⁸ GeV. In the presence of these higher derivative terms, the action for Riccions is obtained with quartic self-interaction potential. It is interesting to see that the instanton solution for Riccions gives rise to primordial inflation without any phase transition or symmetry breaking.

It is shown that the Schrödinger–Pauli (SP) equation is invariant with respect to the algebra gl(4,C) provided that the vector-potential of an external field has definite parities. This invariance algebra is used to reduce the SP equation to uncoupled subsystems and to search for extended and generalized supersymmetries.

The critical behavior of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behavior, the flow of the coarse grained free energy also describes the approach to scaling.

The Feynman path integral is used to quantize the symplectic leaves of the Poisson–Lie group SU(2)*. In this way we obtain the unitary representations of . This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. I also compare the results with the path integral quantization of spin.

We study two-body weak hadronic decays of ψ and ϒ employing the factorization scheme. Branching ratios for ψ → PP/PV and ϒ→ PP/PV decays in the Cabibbo-angle-enhanced and Cabibbo-angle-suppressed modes are predicted.

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from two-point to point–link–point interactions. We develop an associated graph theory with a generalized notion of connectivity and describe an algorithmic generation of the new multiple-line graphs. We indicate physical applications to spin glasses, partially annealed neural networks and SU(N) gauge Higgs systems. In particular the new expansion technique provides the possibility of avoiding the replica trick in spin glasses. We consider variational estimates for the SU(2) Higgs model of the electroweak phase transition. The results for the transition line, obtained by dynamical linked cluster expansions, agree quite well with corresponding high precision Monte Carlo results.