Modern Physics Letters A

Quantum theory of dilaton gravity coupled to a nonlinear sigma model with a maximally symmetric target space is studied in 2+ε dimensions. The uv stable fixed point for the curvature of the nonlinear sigma model demands a new fixed point theory for the dilaton coupling function. The fixed point of the dilaton coupling is a saddle point similarly to the previous case of the flat target space.

We classify the moduli spaces of the four-dimensional topological half-flat gravity models by using the canonical bundle. For a K3-surface or T⁴, they describe an equivalent class of a trio of the Einstein-Kähler forms (the hyperkähler forms). We calculate the dimensions of these moduli spaces by using the Atiyah-Singer Index theorem. We mention the partition function and the possibility of the observables in the Witten-type topological half-flat gravity model case.

Expressions for SO(4) invariant Euclidean QCD generating functionals are introduced which should produce nonvanishing gluon condensates. We consider first the loop expansion of the corresponding effectíve action searching for a description differing from the usual perturbation theory. At this level, we consider special free propagators which have off-diagonal long range order. The calculation of the polarization tensor leads to a gluon mass term which is proportional to the squared root of the finite value for <G²>. The summation of all the one-loop contributions to the energy having only mass insertions, indicates the spontaneous generation of the condensate from the perturbative ground state in a way resembling the similar effect in the case of chromomagnetic field models.

We consider perturbations of the nonunitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of nonintegrable singularities in the resulting theories leads to constraints on the dimension of the perturbing operator. We give some general solutions of these constraints, illustrating with examples of specific models. We also examine the effect of such perturbations on the Hopf equation and derive the interesting result that the latter is invariant under a certain class of perturbations, to first-order in perturbation theory, examples of which are given in specific cases.

We present a manifestly N=2 supersymmetric formulation of N=2 super- algebra (its classical version) in terms of the spin-one unconstrained supercurrent generating an N=2 superconformal subalgebra and the spins-1/2, two bosonic and spins-1/2, two fermionic constrained supercurrents. We consider a superfield reduction of N=2 super- to N=2 super-W₃ and construct a family of evolution equations for which N=2 super- provides the second Hamiltonian structure.

A new extension of the standard Virasoro algebra as well as its W-generalizations containing the Antoniadis et al. and Frappat et al. symmetries (Refs. 8 and 9 as special cases), are obtained. The fundamentals of the quantum field theory representation of the Frappat et al. symmetry are given. Other remarkable properties are also discussed.

We reopen the discussion on the two-photon production of the intermediate mass Higgs-boson in peripheral ultrarelativistic heavy-ion collisions at LHC. Due to larger expected luminosity, larger collision energy and higher photon energies, the Higgs production rate is enlarged by more than a factor of 10 in Ca+Ca collisions compared to Pb+Pb collisions. Besides the background of direct -production via two-photon fusion, we also discuss photon-gluon fusion into .

We study quantum strings in strong gravitational fields. The relevant small parameter is where R_c is the curvature of the spacetime and T₀ is the string tension. Within our systematic expansion we obtain to zeroth-order the null string (string with zero tension), while the first-order correction incorporates the string dynamics. We apply our formalism to quantum null strings in de Sitter spacetime. After a reparametrization of the worldsheet coordinates, the equations of motion are simplified. The quantum algebra generated by the constraints is considered, ordering the momentum operators to the right of the coordinate operators. No critical dimension appears. It is anticipated, however, that the conformal anomaly will appear when the first-order corrections proportional to T₀, are introduced.