Gaussian Effective Potential and the Coleman's normal-ordering Prescription : the Functional Integral Formalism

For a class of system, the potential of whose Bosonic Hamiltonian has a Fourier representation in the sense of tempered distributions, we calculate the Gaussian effective potential within the framework of functional integral formalism. We show that the Coleman's normal-ordering prescription can be formally generalized to the functional integral formalism.Comment: 6 pages, revtex; With derivation details and an example added. To appear in J. Phys.

Higher-spin Realisations of the Bosonic String

It has been shown that certain $W$ algebras can be linearised by the inclusion of a spin--1 current. This provides a way of obtaining new realisations of the $W$ algebras. Recently such new realisations of $W_3$ were used in order to embed the bosonic string in the critical and non-critical $W_3$ strings. In this paper, we consider similar embeddings in $W_{2,4}$ and $W_{2,6}$ strings. The linearisation of $W_{2,4}$ is already known, and can be achieved for all values of central charge. We use this to embed the bosonic string in critical and non-critical $W_{2,4}$ strings. We then derive the linearisation of $W_{2,6}$ using a spin--1 current, which turns out to be possible only at central charge $c=390$. We use this to embed the bosonic string in a non-critical $W_{2,6}$ string.Comment: 8 pages. CTP TAMU-10/95

Liouville and Toda Solitons in M-theory

We study the general form of the equations for isotropic single-scalar, multi-scalar and dyonic $p$-branes in superstring theory and M-theory, and show that they can be cast into the form of Liouville, Toda (or Toda-like) equations. The general solutions describe non-extremal isotropic $p$-branes, reducing to the previously-known extremal solutions in limiting cases. In the non-extremal case, the dilatonic scalar fields are finite at the outer event horizon.Comment: Latex, 10 pages. Minor corrections to text and titl