arXiv subjects

A. A. Tseytlin

Publications and source records attributed to A. A. Tseytlin.

At least 235 records · Page 13Linked to original sources

arXiv1994

On string cosmology and the RG flow in 2d field theory

Time-dependent solutions of bosonic string theory resemble renormalisation group trajectories in the space of 2d field theories: they often interpolate between repulsive and attractive static solutions. It is shown that the attractive static solutions are those whose spatial sections are minima of |\bar c-25|, where \bar c is the `c-function'. The size of the domain of attraction of such a solution may be a measure of the probability of the corresponding string vacuum. Our discussion has also an implication for the RG flow in theories coupled to dynamical 2d gravity: the flow from models with c>25 to models with c<25 is forbidden.

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arXiv1994

On `rolling moduli' solutions in string cosmology

Given a static string solution with some free constant parameters (`moduli') it may be possible to construct a time-dependent solution by just replacing the moduli by some functions of time. We present several examples when such `rolling moduli' ansatz is consistent. In particular, the anisotropic D=4 cosmological solution of Nappi and Witten can be reinterpreted as a time-dependent generalisation of the (analytic continuation of) D=3 `charged black string' background with the `charge' changing with time. We find some new D=4 cosmological solutions which are `two rolling moduli' generalisations of the previously known ones. We also comment on interplay between duality transformations and the replacement of moduli by functions of time.

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arXiv1994

Exact four dimensional string solutions and Toda-like sigma models from `null-gauged' WZNW theories

We construct a new class of exact string solutions with a four dimensional target space metric of signature ($-,+,+,+$) by gauging the independent left and right nilpotent subgroups with `null' generators of WZNW models for rank 2 non-compact groups $G$. The `null' property of the generators (${\rm Tr }(N_n N_m)=0$) implies the consistency of the gauging and the absence of $\a'$-corrections to the semiclassical backgrounds obtained from the gauged WZNW models. In the case of the maximally non-compact groups ($G= SL(3), SO(2,2), SO(2,3), G_2$) the construction corresponds to gauging some of the subgroups generated by the nilpotent `step' operators in the Gauss decomposition. The rank 2 case is a particular example of a general construction leading to conformal backgrounds with one time-like direction. The conformal theories obtained by integrating out the gauge field can be considered as sigma model analogs of Toda models (their classical equations of motion are equivalent to Toda model equations). The procedure of `null gauging' applies also to other non-compact groups.

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arXiv1994

Four Dimensional Plane Wave String Solutions with Coset CFT Description

We present a number of D=4 bosonic and heterotic string solutions with a covariantly constant null Killing vector which, like the solution of Nappi and Witten (NW), correspond to (gauged) WZW models and thus have a direct conformal field theory interpretation. A class of exact plane wave solutions (which includes the NW solution) is constructed by `boosting' the twisted products of two D=2 `cosmological' or `black-hole' cosets of SL(2,R) and SU(2). We describe a general limiting procedure by which one can construct new solutions with a covariantly constant null Killing vector starting with known string backgrounds. By applying a non-abelian duality transformation to the NW model we find a D=4 solution which has a covariantly constant null Killing vector but is not a plane wave. Higher dimensional bosonic backgrounds with isometries can be interpreted as lower dimensional backgrounds with extra gauge fields. Some of them are at the same time solutions of the heterotic string theory. In particular, the NW model represents also a D=3 `gravi-electromagnetic' heterotic string plane wave. In addition to the (1,1) supersymmetric embeddings of bosonic solutions we construct a number of non-trivial (1,0) supersymmetric exact D=4 heterotic string plane wave solutions some of which are related (by a boost and analytic continuation) to limiting cases of D=4 heterotic black hole solutions.

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arXiv1994

String solutions with non-constant scalar fields

We discuss charged string solutions of the effective equations of D=4 heterotic string theory with non-constant dilaton and modulus fields. The effective action contains a generic moduli-dependent coupling function in the gauge field kinetic term and a non-perturbative scalar potential. This is a review of hep-th/9307123 by M. Cvetic and the author. To be published in the Proceedings of 27-th International Symposium on Theory of Elementary Particles, Wendisch - Rietz, September 1993.

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arXiv1993

Antisymmetric tensor coupling and conformal invariance in sigma models corresponding to gauged WZNW theories

String backgrounds associated with gauged $G/H$ WZNW models generically depend on $α'$ or $1/k$. The exact expressions for the corresponding metric $G_{\m\n}$, antisymmetric tensor $B_{\m\n}$, and dilaton $ϕ$ can be obtained by eliminating the $2d$ gauge field from the local part of the effective action of the gauged WZNW model. We show that there exists a manifestly gauge-invariant prescription for the derivation of the antisymmetric tensor coupling. When the subgroup $H$ is one-dimensional and $G$ is simple the antisymmetric tensor is given by the semiclassical ($α'$-independent) expression. We consider in detail the simplest non-trivial example with non-trivial $B_{\m\n}$ -- the D=3 sigma model corresponding to the $[SL(2,R) x R]/R$ gauged WZNW theory (`charged black string') and show that the exact expressions for $G_{\m\n}$, $B_{\m\n}$ and $ϕ$ solve the Weyl invariance conditions in the two-loop approximation. Similar conclusion is reached for the closely related $SL(2,R)/R$ chiral gauged WZNW model. We find that there exists a scheme in which the semiclassical background is also a solution of the two-loop conformal invariance equations (but the tachyon equation takes a non-canonical form). We discuss in detail the role of field redefinitions (scheme dependence) in establishing a correspondence between the sigma model and conformal field theory results.

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arXiv1993

On a `universal' class of WZW-type conformal models

We consider a class of sigma models that appears from a generalisation of the gauged WZW model parametrised by a constant matrix $Q$. Particular values of $Q$ correspond to the standard gauged WZW models, chiral gauged WZW models and a bosonised version of the non-abelian Thirring model. The condition of conformal invariance of the models (to one loop or $1/k$-order but exactly in $Q$) is derived and is represented as an algebraic equation on $Q$. Solving this equation we demonstrate explicitly the conformal invariance of the sigma models associated with arbitrary $G/H$ gauged and chiral gauged WZW theories as well as of the models that can be represented as WZW model perturbed by integrably marginal operators (constructed from currents of the Cartan subalgebra $H_c$ of $G$). The latter models can be also interpreted as $G x H/H$ gauged WZW models and have the corresponding target space couplings (metric, antisymmetric tensor and dilaton) depending on an arbitrary constant matrix which parametrises an embedding of the abelian subgroup $H$ (isomorphic to $H_c$) into $G x H$. We discuss the relation of our conformal invariance equation to the large $k$ form of the master equation of the affine-Virasoro construction. Our equation describes `reducible' versions of some `irreducible' solutions (cosets) of the master equation. We suggest a classically non-Lorentz-invariant sigma model that may correspond to other solutions of the master equation.

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arXiv1993

Charged string solutions with dilaton and modulus fields

We find charged, abelian, spherically symmetric solutions (in flat space-time) corresponding to the effective action of $D=4$ heterotic string theory with scale-dependent dilaton $\p$ and modulus $\vp$ fields. We take into account perturbative (genus-one), moduli-dependent `threshold' corrections to the coupling function $f(\p,\vp)$ in the gauge field kinetic term $f(\p,\vp) F^2_{\m\n}$, as well as non-perturbative scalar potential $V(\p, \vp)$, e.g. induced by gaugino condensation in the hidden gauge sector. Stable, finite energy, electric solutions (corresponding to on abelian subgroup of a non-abelian gauge group) have the small scale region as the weak coupling region ($ϕ\ra -\infty$) with the modulus $\vp$ slowly varying towards smaller values. Stable, finite energy, abelian magnetic solutions exist only for a specific range of threshold correction parameters. At small scales they correspond to the strong coupling region ($\p\ra \infty$) and the compactification region ($\vp\ra 0$). The non-perturbative potential $V$ plays a crucial role at large scales, where it fixes the asymptotic values of $ϕ$ and $\vp$ to be at the minimum of $V$.

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arXiv1993

Duality invariant class of exact string backgrounds

We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.

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arXiv1993

On field redefinitions and exact solutions in string theory

String backgrounds associated with gauged $G/H$ WZNW models in general depend non-trivially on $α'$. 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 $α'$. As a result, the `probes' (the tachyons) still feel the $α'$-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'.

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arXiv1993

Chiral gauged WZNW models and heterotic string backgrounds

We construct new heterotic string backgrounds which are analogous to superstring solutions corresponding to coset models but are not simply the `embeddings'of the latter. They are described by the (1,0) supersymmetric extension of the $G/H$ chiral gauged WZNW models. The `chiral gauged' WZNW action differs from the standard gauged WZNW action by the absence of the $A\bar A$-term (and thus is not gauge invariant in the usual sense) but can still be expressed as a combination of WZNW actions and is conformal invariant. We explain a close relation between gauged and chiral gauged WZNW models and prove that in the case of the abelian $H$ the $G/H$ chiral gauged theory is equivalent to a particular $(G\times H)/H$ gauged WZNW theory. In contrast to the gauged WZNW model, the chiral gauged one admits a (1,0) supersymmetric extension which is consistent at the quantum level. Integrating out the $2d$ gauge field we determine the exact (in $α'$) form of the couplings of the corresponding heterotic sigma model. While in the bosonic (superstring) cases all the fields depend (do not depend) non-trivially on $α'$ here the metric receives only one $O(α')$ correction while the antisymmetric tensor and the dilaton remain semiclassical. As a simplest example, we discuss the basic $D=3$ solution which is the heterotic string counterpart of the `black string' $SL(2,R) \times R/ R $ background.

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arXiv1993

Heterotic string solutions and coset conformal field theories

We discuss solutions of the heterotic string theory which are analogous to bosonic and superstring backgrounds related to coset conformal field theories. A class of exact `left-right symmetric' solutions is obtained by supplementing the metric, antisymmetric tensor and dilaton of the superstring solutions by the gauge field background equal to the generalised Lorentz connection with torsion. As in the superstring case, these backgrounds are $\a'$-independent, i.e. have a `semiclassical' form. The corresponding heterotic string sigma model is obtained from the combination of the (1,0) supersymmetric gauged WZNW action with the action of internal fermions coupled to the target space gauge field. The pure (1,0) supersymmetric gauged WZNW theory is anomalous and does not describe a consistent heterotic string solution. We also find (to the order $α'^3$) a two-dimensional perturbative heterotic string solution with the trivial gauge field background. To the leading order in $α'$ it coincides with the known $SL(2,R)/U(1)$ bosonic or superstring solutions. This solution does not correspond to a `heterotic' combination of the left superstring and right bosonic $L_0$-operators at the conformal field theory level. Some duality properties of the heterotic string solutions are studied.

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arXiv1993

Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories

We develop a field-theoretical approach to determination of the background target space fields corresponding to general $G/H$ coset conformal theories described by gauged WZW models. The basic idea is to identify the effective action of a gauged WZW theory with the effective action of a sigma model. The derivation of the quantum effective action in the gauged WZW theory is presented in detail, both in the bosonic and in the supersymmetric cases. We explain why and how one can truncate the effective action by omitting most of the non-local terms (thus providing a justification for some previous suggestions). The resulting metric, dilaton and the antisymmetric tensor are non-trivial functions of $1/k$ (or $α'$) and represent a large class of conformal sigma models. The exact expressions for the fields in the sypersymmetric case are equal to the leading order (`semiclassical') bosonic expressions (with no shift of $k$). An explicit form in which we find the sigma model couplings makes it possible to prove that the metric and the dilaton are equivalent to the fields which are obtained in the operator approach, i.e. by identifying the $L_0$-operator of the conformal theory with a Klein-Gordon operator in a background. The metric can be considered as a `deformation' of an invariant metric on the coset space $G/H$ and the dilaton can be in general represented in terms of the logarithm of the ratio of the determinants of the `deformed' and `round' metrics.

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arXiv1993

Two-dimensional conformal sigma models and exact string solutions

We discuss two classes of exact (in $\a'$) string solutions described by conformal sigma models. They can be viewed as two possibilities of constructing a conformal model out of the non-conformal one based on the metric of a $D$-dimensional homogeneous $G/H$ space. The first possibility is to introduce two extra dimensions (one space-like and one time-like) and to impose the null Killing symmetry condition on the resulting $2+D$ dimensional metric. In the case when the ``transverse" model is $n=2$ supersymmetric and the $G/H$ space is Kähler-Einstein the resulting metric-dilaton background can be found explicitly. The second possibility - which is realised in the sigma models corresponding to $G/H$ conformal theories - is to deform the metric, introducing at the same time a non-trivial dilaton and antisymmetric tensor backgrounds. The expressions for the metric and dilaton in this case are derived using the operator approach in which one identifies the equations for marginal operators of conformal theory with the linearised (near a background) expressions for the `$\b$-functions'. Equivalent results are then reproduced in the direct field-theoretical approach based on computing first the effective action of the $G/H$ gauged WZW model and then solving for the $2d$ gauge field. Both the bosonic and the supersymmetric cases are discussed. ( To be published in the Proceedings of the 26 Workshop ``From Superstrings to Supergravity", Erice, 5-12 December,1992.)

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arXiv1993

Effective action of gauged WZW model and exact string solutions

We suggest how to derive the exact (all order in $\a'$) expressions for the background fields for string solutions corresponding to gauged WZW models directly at the $2d$ field theory level. One is first to replace the classical gauged WZW action by the quantum effective one and then to integrate out the gauge field. We find the explicit expression for the gauge invariant non-local effective action of the gauged WZW model. The two terms (corresponding to the group and subgroup) which appear with the same coefficients in the classical action get different $k$-dependent coefficients in the effective one. The procedure of integrating out the gauge field is considered in detail for the $SL(2,R)/U(1)$ model and the exact expressions for the $D=2$ metric and the dilaton (originally found in the conformal field theory approach) are reproduced.

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arXiv1992

Finite sigma models and exact string solutions with Minkowski signature metric

We consider $2d$ sigma models with a $D=2+N$ - dimensional Minkowski signature target space metric having a covariantly constant null Killing vector. These models are UV finite. The $2+N$-dimensional target space metric can be explicitly determined for a class of supersymmetric sigma models with $N$-dimensional `transverse' part of the target space being homogeneous Kähler. The corresponding `transverse' sub-theory is an $n=2$ supersymmetric sigma model with the exact $\gb$-function coinciding with its one-loop expression. For example, the finite $D=4$ model has $O(3)$ supersymmetric sigma model as its `transverse' part. Moreover, there exists a non-trivial dilaton field such that the Weyl invariance conditions are also satisfied, i.e. the resulting models correspond to string vacua. Generic solutions are represented in terms of the RG flow in `transverse' theory. We suggest a possible application of the constructed Weyl invariant sigma models to quantisation of $2d$ gravity. They may be interpreted as `effective actions' of the quantum $2d$ dilaton gravity coupled to a (non-conformal) $N$-dimensional `matter' theory. The conformal factor of the $2d$ metric and $2d$ `dilaton' are identified with the light cone coordinates of the $2+N$ - dimensional sigma model.

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arXiv1992

Dilaton shift under duality and torsion of elliptic complex

We observe that the ratio of determinants of $2d$ Laplacians which appear in the duality transformation relating two sigma models with abelian isometries can be represented as a torsion of an elliptic (DeRham) complex. As a result, this ratio can be computed exactly and is given by the exponential of a local functional of $2d$ metric and target space metric. In this way the well known dilaton shift under duality is reproduced. We also present the exact computation of the determinant which appears in the duality transformation in the path integral.

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arXiv1992

String vacuum backgrounds with covariantly constant null Killing vector and 2d quantum gravity

We consider a $2d$ sigma model with a $2+N$ - dimensional Minkowski signature target space metric having a covariantly constant null Killing vector. We study solutions of the conformal invariance conditions in $2+N$ dimensions and find that generic solutions can be represented in terms of the RG flow in $N$ - dimensional ``transverse space'' theory. The resulting conformal invariant sigma model is interpreted as a quantum action of the $2d$ scalar (``dilaton") quantum gravity model coupled to a (non-conformal) `transverse' sigma model. The conformal factor of the $2d$ metric is identified with a light cone coordinate of the $2+N$ - dimensional sigma model. We also discuss the case when the transverse theory is conformal (with or without the antisymmetric tensor background) and reproduce in a systematic way the solutions with flat transverse space known before.

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