Arkady A. Tseytlin

On non-abelian generalisation of the Born-Infeld action in string theory

Abstract We point out that the part of the tree-level open string effective action for the non-abelian vector field which depends on the field strength but not on its covariant derivatives is not defined unambiguously. We show that in one adopts the definition under which one drops all terms depending on all possible products (symmetrised or antisymmetrised) of covariant derivatives then this part of the action is given by the symmetrised trace of the direct non-abelian generalisation of the Born-Infeld action. We discuss some possible applications to D-branes dynamics.

WAVES, BOOSTED BRANES AND BPS STATES IN M-THEORY

Certain type II string non-threshold BPS bound states are shown to be related to non-static backgrounds in 11-dimensional theory. The 11 D counterpart of the bound state of NS-NS and R-R type IIB strings wound around a circle is a pure gravitational wave propagating along a generic cycle of a 2-torus. The extremal (q1, q2) string with non-vanishing momentum along the circle (or infinitely boosted black string) corresponds in D = 11 to a 2-brane wrapped around a 2-torus with momentum flow along the (q1, q2) cycle. Applying duality tranformations to the string-string solution we find the type IIA background representing the bound state of a 2-brane and a 0-brane. Its lift to 11 dimensions is simply a 2-brane finitely boosted in transverse direction. This 11D solution interpolates between a static 2-brane (zero boost) and a gravitational wave in 11th dimension (infinite boost). Similar interpretations are given for various bound states involving 5-branes. Relations between transversely boosted M-branes and 12 supersymmetric non-threshold bound states 2+0 and 5+0 complement those beteen M-branes with momentum in longitudinal direction and 14 supersymmetric threshold bound states 1+0 and 4+0. In the second part of the paper we establish the correspondence between BPS states of type IIB strings on a circle and oscillating states of a fundamental supermembrane wrapped around a 2-torus. We show that the (q1, q2) string spectrum is reproduced by the membrane BPS spectrum, determined using a certain limit. This supports the picture suggested by Schwarz.

Conformal Sigma Models Corresponding to Gauged Wess-Zumino-Witten Theories

Abstract We develop a field-theoretical approach to the 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, dilation 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 supersymmetric 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 dilation 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.

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 1k-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 models perturbed by integrably marginal operators (constructed from currents of the Cartan subalgebra Hc of G). The latter models can also be interpreted as (G × 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 Hc) into G × 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.

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 dilation), as well as the action of O(D,D) duality transformations on them, are exact, i.e. are not modified by α′-corrections. This makesa discussion of different space-time representations of the same string solution (related by the 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 dilation. We discuss several particular examples including the (2+D=4)-dimensional background that was recently interpreted in terms of a WZW model.

Heterotic string solutions and coset conformal field theories

Abstract 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 α′-independent, i.e. have “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 unknown SL(2, R )/U(1) bosonic of superstring solutions. This solution does not correspond to a ‘heterotic’ combination of the left superstring and right bosonic L0-operators at the conformal field theory level. Some duality properties of the heterotic string solutions are studied.

On field redefinitions and exact solutions in string theory

Abstract String backgrounds associated with gauged G/H WZNW models in general depend nontrivially on α′. We note, however that there exists a local covariant α′ -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 dquation for the tachyon (which, like other Weyl anomaly equations, has scheme-dependent form) still contains corrections of all orders in α′. As a result, the string “probes” still feel the α′ -corrected background. The field redefinitions we discuss contain the dilaton terms in the metric transformation law. We also comment on exact forms of the duality transformation in different “schemes”.

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 the scale-dependent dilaton π and modulus ϕ fields. We take into account perturbative (genus-one), moduli-dependent “threshold” corrections to the coupling function ƒ(π, ϕ) in the gauge field kinetic term ƒ(π, ϕ)Fμν2, as well as the non-perturbative scalar potential V(π, ϕ), e.g., induced by gaugino condensation in the hidden gauge sector. Stable, finite-energy, electric solutions (corresponding to an abelian subgroup of a non-abelian gauge group) have the small scale region as the weak coupling region (π → −∞) with the modulus ϕ 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 (π→∞) and the compactification region (ϕ → 0). The non-perturbative potential V plays a crucial role at large scales, where it fixes the asymptotic values of π and ϕ to be at the minimum of V.

The partition function of the sigma model of the string on a compact two-space

Abstract We develop a manifestly covariant procedure of computation of the partitionfunction Z of a general renormalizable 2D sigma model defined on a compact two-space. Special attention is paid to a proper separation of the path integral into the integrals over the constant and nonconstant parts of the coordinate. The important role of the path integral measure in establishing the covariance and renormalizability properties of Z is stressed. We explicitly check the validity of the representation of the closed string effective action as the partial derivative of Z over the logarithm of the cutoff. We also comment on the status of the “ c -theorem” and suggest a resolution of a problem in the renormalization of the closed string loop corrections corresponding to the disc topology.

Structure of composite black p-brane configurations and related black holes☆

Abstract We comment on the structure of intersecting black p-brane solutions in string theory explaining how known solutions can be obtained from Schwarzschild solution simply by sequences of boosts and dualities. This implies, in particular, that dimensional reduction in all internal world-volume directions including time leads to a metric (related by analytic continuation to a cosmological metric) which does not depend on p-brane charges, i.e. is the same as the metric following by reduction from a higher-dimensional ‘neutral’ Schwarzschild black hole.