International Journal of Modern Physics A

The structure of extended loop wave function is investigated in terms of the operator formalism. It is found that the extended loop wave function is characterized by the family number and classified by the partition of the family number. It is pointed out that the constraints to the extended loop function in quantum gravity exhibit a hierarchy structure.

We recently studied two large but disjoint classes of twisted open WZW strings: the open-string sectors of the WZW orientation orbifolds and the so-called basic class of twisted open WZW strings. In this paper, we discuss all T-dualizations of the basic class to construct the general twisted open WZW string — which includes the disjoint classes above as special cases. For the general case, we give the branes and twisted noncommutative geometry at the classical level and the twisted open-string KZ equations at the operator level. Many examples of the general construction are discussed, including in particular the simple case of twisted free-bosonic open strings. We also revisit the open-string sectors of the general WZW orientation orbifold in further detail. For completeness, we finally review the general twisted boundary state equation which provides a complementary description of the general twisted open WZW string.

We study the gravitational properties of a global monopole in (D=d+2)-dimensional space–time in the presence of electromagnetic field.

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold M with regular boundary Γ=∂M. The space ℳ of self-adjoint extensions of the covariant Laplacian on M is shown to have interesting geometrical and topological properties which are related to the different topological closures of M. In this sense, the change of topology of M is connected with the nontrivial structure of ℳ. The space ℳ itself can be identified with the unitary group of the Hilbert space of boundary data . This description, is shown to be equivalent to the classical von Neumann's description in terms of deficiency index subspaces, but it is more efficient and explicit because it is given only in terms of the boundary data, which are the natural external inputs of the system. A particularly interesting family of boundary conditions, identified as the set of unitary operators which are singular under the Cayley transform, (the Cayley manifold), turns out to play a relevant role in topology change phenomena. The singularity of the Cayley transform implies that some energy levels, usually associated with edge states, acquire an infinity energy when by an adiabatic change the boundary conditions reaches the Cayley submanifold 𝒞_. In this sense topological transitions require an infinite amount of quantum energy to occur, although the description of the topological transition in the space ℳ is smooth. This fact has relevant implications in string theory for possible scenarios with joint descriptions of open and closed strings. In the particular case of elliptic self-adjoint boundary conditions, the space 𝒞_ can be identified with a Lagrangian submanifold of the infinite dimensional Grassmannian. The corresponding Cayley manifold 𝒞_ is dual of the Maslov class of ℳ. The phenomena are illustrated with some simple low dimensional examples.

The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit calculations are given for those contributions to the conformal anomaly which emerge as a result of free scalar propagation as well as from scalar self-interactions up to second order in the scalar self-coupling. The renormalization-group behavior of the theory is, subsequently, exploited in order to advance the evaluation of the conformal anomaly to third order in the scalar self-coupling. As a direct consequence the effective action is evaluated to the same order. In effect, complete contributions to the theory's conformal anomaly and effective action are evaluated up to fourth-loop order.

The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on these higher order effects determined by the RG. Particular attention is paid to the relationship between bare and renormalized quantities. Application of the method of characteristics to the RG equation to determine higher order effects is discussed and used to examine the free energy in thermal field theory, the relationship between the bare and renormalized coupling, and the effective potential in massless scalar electrodynamics.

In this paper we study how the triviality bound on Higgs mass in the context of the Standard Model is modified by a light stabilized radion of the Goldberger–Wise variety. Our approach is inherently perturbative. Including the radion contribution to β(λ) and β(g_t) to one-loop we evolve the Higgs self coupling λ from the cutoff Λ(=<ϕ>) down to the electroweak scale μ₀=v. The triviality bound is obtained by requiring that which is the perturbative limit. We also study the effect of small changes in the UVBC on the triviality bound both in the presence and absence of a light radion.