119 research outputs found
On field redefinitions and exact solutions in string theory
String backgrounds associated with gauged WZNW models in general depend
non-trivially on . We note, however, that there exists a local
covariant \a'-dependent field redefinition that relates the exact
metric-dilaton background corresponding to the model to its
leading-order form ( 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 . As a result, the `probes' (the
tachyons) still feel the -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
- 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 is subject to the standard renormalization group equation of the
- 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 - dimensional symmetric space \gij(x) multiplied by a
function . The theory is finite if is equal to the ``running"
coupling of the symmetric space sigma model (with playing the role of the
RG ``time"). For example, the geometry of space - time with \gij being the
metric of the - sphere is determined by the form of the \gb - function of
the model. The ``asymptotic freedom" limit of large corresponds to
the weak coupling limit of small - dimensional curvature. We prove that
there exists a dilaton field which together with the - 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 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 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 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
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
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 -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 dimensions and have a smooth limit for . 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 .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 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 . 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
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