On field redefinitions and exact solutions in string theory

String backgrounds associated with gauged $G/H$ WZNW models in general depend non-trivially on $\alpha'$. We note, however, that there exists a local covariant \a'-dependent field redefinition that relates the exact metric-dilaton background corresponding to the $SL(2,R)/U(1)$ model to its leading-order form ($D=2$ black hole). As a consequence, there exists a `scheme' in which the string effective equations have the latter as an exact solution. However, the corresponding equation for the tachyon (which, like other Weyl anomaly coefficients, has scheme-dependent form) still contains corrections of all orders in $\alpha'$. As a result, the `probes' (the tachyons) still feel the $\alpha'$-corrected background. The field redefinitions we discuss contain the dilaton terms in the metric transformation law. We comment on exact forms of the duality transformation in different `schemes'.Comment: 11 pages, harvmac, CERN-TH.6970/93 [ A new section on tachyonic equation is added: while there exists a scheme where the exact D=2 `black hole' metric-dilaton background has semiclassical form, the equation for the tachyon still contains \alpha'-corrections, i.e. the tachyon still feels the \alpha'-corrected background

A class of finite two - dimensional sigma models and string vacua

We consider a two - dimensional Minkowski signature sigma model with a $2+N$ - dimensional target space metric having a null Killing vector. It is shown that the model is finite to all orders of the loop expansion if the dependence of the ``transverse" part of the metric \ggij (u,x) on the light cone coordinate $u$ is subject to the standard renormalization group equation of the $N$ - dimensional sigma model, {d\ggij\over du} = \gb_{ij} =R_{ij} + ... . In particular, we discuss the `one - coupling' case when \ggij(u,x) is a metric of an $N$ - dimensional symmetric space \gij(x) multiplied by a function $f(u)$. The theory is finite if $f(u)$ is equal to the ``running" coupling of the symmetric space sigma model (with $u$ playing the role of the RG ``time"). For example, the geometry of space - time with \gij being the metric of the $N$ - sphere is determined by the form of the \gb - function of the $O(N+1)$ model. The ``asymptotic freedom" limit of large $u$ corresponds to the weak coupling limit of small $2+N$ - dimensional curvature. We prove that there exists a dilaton field which together with the $2+N$ - dimensional metric solves the sigma model Weyl invariance conditions. The resulting backgrounds thus represent new tree level string vacua. We also remark on possible connections with some $2d$ quantum gravity models.Comment: 15 pages [Complete revision. The main statement of the previous version is generalised to the case of an arbitrary ``transverse" metric satisfying sigma model renormalization group equation.

Higher Order Conformal Invariance of String Backgrounds Obtained by O(d,d) Transformations

Proposals that $O(d,d)$ boosts of trivial backgrounds lead to non-trivial conformally invariant backgrounds are checked to two loop order. We find that conformal invariance can be achieved by adding simple higher order corrections to the metric and dilaton.Comment: 8 page

Heterotic p-branes from Massive Sigma Models

We explicitly construct massive (0,4) supersymmetric ADHM sigma models which have heterotic p-brane solitons as their conformal fixed points. These yield the familiar gauge 5-brane and a new 1-brane solution which preserve 1/2 and 1/4 of the spacetime supersymmetry respectively. We also discuss an analogous construction for the type II NS-NS p-branes using (4,4) supersymmetric models.Comment: 23 pages Phyzzx. Extended discussion of self-duality of a gauge field in eight dimensions. To appear in Nucl. Phys.

Chiral invariant renormalization of the pion--nucleon interaction

The leading divergences of the generating functional for Green functions of quark currents between one--nucleon states are calculated with heat kernel techniques. The results allow for a chiral invariant renormalization of all two--nucleon Green functions of the pion--nucleon system to $O(p^3)$ in the low--energy expansion.Comment: 13 pages, LaTex, 2 figures in appended postscript file, Univ. Wien preprint UWThPh-1994-

Quantum Field Theories on Manifolds with Curved Boundaries: Scalar Fields

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed Dirichlet and Neumann boundary conditions. The method is applied to a general renormalisable scalar field theory in four dimensions using dimensional regularisation to two loops and expanding about arbitrary background fields. Detailed results are also specialised to an $O(n)$ symmetric model with a single coupling constant. Extra boundary terms are introduced into the action which give rise to either Dirichlet or generalised Neumann boundary conditions for the quantum fields. For plane boundaries the resulting renormalisation group functions are in accord with earlier results but here the additional terms depending on the extrinsic curvature of the boundary are found. Various consistency relations are also checked and the implications of conformal invariance at the critical point where the $\beta$ function vanishes are also derived. The local Scr\"odinger equation for the wave functional defined by the functional integral under deformations of the boundary is also verified to two loops. Its consistency with the renormalisation group to all orders in perturbation theory is discussed.Comment: 50 pages, DAMTP/92-3

Exact Bosonic and Supersymmetric String Black Hole Solutions

We show that Witten's two-dimensional string black hole metric is exactly conformally invariant in the supersymmetric case. We also demonstrate that this metric, together with a recently proposed exact metric for the bosonic case, are respectively consistent with the supersymmetric and bosonic $\sigma$-model conformal invariance conditions up to four-loop order.Comment: 14

DILATONIC GRAVITY NEAR TWO DIMENSIONS AND ASYMPTOTIC FREEDOM OF THE GRAVITATIONAL COUPLING CONSTANT

Two models of dilatonic gravity are investigated: (i) dilaton-Yang-Mills gravity and (ii) higher-derivative dilatonic gravity. Both are renormalizable in $2+\epsilon$ dimensions and have a smooth limit for $\epsilon \rightarrow 0$. The corresponding one-loop effective actions and beta-functions are found. Both theories are shown to possess a non-trivial ultraviolet fixed point ---for all dilatonic couplings--- in which the gravitational constant is asymptotically free. It is shown that in the regime of asymptotic freedom the matter central charge can be significantly increased by two different mechanisms ---as compared with pure dilatonic gravity, where $n < 24$.Comment: LaTeX, 10 pages, no figure

Scale without Conformal Invariance: An Example

We give an explicit example of a model in D=4-epsilon space-time dimensions that is scale but not conformally invariant, is unitary, and has finite correlators. The invariance is associated with a limit cycle renormalization group (RG) trajectory. We also prove, to second order in the loop expansion, in D=4-epsilon, that scale implies conformal invariance for models of any number of real scalars. For models with one real scalar and any number of Weyl spinors we show that scale implies conformal invariance to all orders in perturbation theory.Comment: 13 pages, 2 figures, Erratum adde

Conformal Invariance and Renormalization Group in Quantum Gravity Near Two Dimensions

We study quantum gravity in $2+\epsilon$ dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for matter central charge $0<c<25$. We show that the spacetime singularity at the big bang is resolved by the renormalization effect and universes are found to bounce back from the big crunch. Our formulation may be viewed as a Ginzburg-Landau theory which can describe both the broken and the unbroken phase of quantum gravity and the phase transition between them.Comment: 32 pages, TIT-HEP-256, KEK-TH-395, YITP/U-94-1