General Spacetime Dimension Research Articles

Localization of matters on a string-like defect

After presenting string-like solutions with a warp factor to Einstein's equations, we study localization of various spin fields on a string-like defect in a general space–time dimension from the viewpoint of field theory. It is shown that spin 0 and 2 fields are localized on a defect with the exponentially decreasing warp factor. Spin 1 field can be also localized on a defect with the exponentially decreasing warp factor. On the other hand, spin one-half and three-half fields can be localized on a defect with the exponentially increasing warp factor, provided that additional interactions are not introduced. Thus, some mechanism of localization must be invoked for these fermionic fields. These results are very similar to those of a domain wall in five space–time dimensions except the case of spin 1 field.

Bosonic fields in the stringlike defect model

We study localization of bosonic bulk fields on a string-like defect with codimension 2 in a general space-time dimension in detail. We show that in cases of spin 0 scalar and spin 1 vector fields there are an infinite number of massless Kaluza-Klein (KK) states which are degenerate with respect to the radial quantum number, but only the massless zero mode state among them is coupled to fermion on the string-like defect. It is also commented on interesting extensions of the model at hand to various directions such as 'little' superstring theory, conformal field theory and a supersymmetric construction.

Higher-spin current multiplets in operator-product expansions

Irreducible currents with arbitrary spin are constructed in a general spacetime dimension, in the free-field limit and, at the bare level, in the presence of interactions. For the n-dimensional generalization of the (conformal) vector field, the (n/2-1)-form is used. Two-point functions and higher-spin central charges are evaluated at one-loop. As an application, the higher-spin hierarchies generated by the stress tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.

C function representation of the Local Potential Approximation

Within the Local Potential Approximation to Wilson's, or Polchinski's, exact renormalization group, and for general spacetime dimension, we construct a function, c, of the coupling constants; it has the property that (for unitary theories) it decreases monotonically along flows, and is stationary only at fixed points ---where it `counts degrees of freedom', i.e. is extensive, counting one for each Gaussian scalar. Furthermore, by choosing restrictions to some sub-manifold of coupling constant space, we arrive at a very promising variational approximation method.

Useful gauges for studying dynamical fermion mass generation in arbitrary space-time dimension.

We extend to general space-time dimensions ({ital d}{ge}2) a method of finding gauges where the chiral-symmetry-conserving piece of the fermion self-energy, {ital Z}({ital p}), equals one to single-loop order. These gauges can aid analysis of the gap equation for the fermion self-energy in several ways. As examples, we discuss non-Abelian gauge theories and also three-dimensional QED in the 1/{ital N} expansion.