H.J. Otto

Two and three point functions in Liouville theory

Abstract Based on our generalization of the Goulian-Li continuation in the power of the 2D cosmological term we construct the two- and three-point correlation functions for Liouville exponentials with generic real coefficients. As a strong argument in favour of the procedure we prove the Liouville equation of motion on the level of three-point functions. The analytical structure of the correlation functions as well as some of its consequences for string theory are discussed. This includes a conjecture on the mass shell condition for excitations of noncritical strings. We also make a comment concerning the correlation functions of the Liouville field itself.

On T-duality for open strings in general abelian and nonabelian gauge field backgrounds

Abstract We discuss T-duality for open strings in general background fields both in the functional integral formulation as well as in the language of canonical transformations. The Dirichlet boundary condition in the dual theory has to be treated as a constraint on the functional integration. Furthermore, we give meaning to the notion of matrix valued string end point position in the presence of nonabelian gauge field background.

On correlation functions for noncritical strings with c = 1

We construct a Goulian-Li-type continuation in the number of insertions of the cosmological constant operator which is no longer restricted to one dimensional target space. The method is applied to the calculation of the three-point and a special four-point correlation function. Various aspects of the emerging analytical structure are discussed.

Q anti-Q potential from AdS - CFT relation at T greater than or equal to 0: Dependence on orientation in internal space and higher curvature corrections

Within the classical approximation we calculate the static Q potential via the AdS/CFT relation for nonzero temperature and arbitrary internal orientation of the quarks. We use a higher order curvature corrected target space background. For timelike Wilson loops there arises a critical line in the orientation-distance plane which is shifted to larger distances relative to the calculation with uncorrected background. Beyond that line there is no Q-force. The overall vanishing of the force for antipodal orientation known from zero temperature remains valid. The spacelike Wilson loops yield a string tension for a (2+1)-dimensional gauge theory, independent of the relative internal orientation, but sensitive to the background correction.

Open Bosonic Strings in General Background Fields

We discuss the renormalization properties of the 2 dim. field theory describing an open bosonic string in the background fields corresponding to its massless excitations. The relevant β-functions are calculated for gravitational, antisymmetric tensor and Yang-Mills background on 1-loop level, for pure Yang-Mills background an 2-loop level and in the Abelian case up to 3 loops. We find a renormalization scheme dependence starting at 2 loop order. Putting β to zero yields the equation of motion for the non-linear electrodynamics of Fradkin and Tseytlin.

Remarks on T-duality for open strings

Abstract This contribution gives in σ-model language a short review of recent work on T-duality for open strings in the presence of abelian or non-abelian gauge fields. Furthermore, it adds a critical discussion of the relation between RG β-functions and the Born-Infeld action in the case of a string coupled to a D-brane.

On scaling dimensions of vertex operators in conformally gauged 2D quantum gravity

Abstract We give an alternative derivation of the KPZ relation for the scaling dimensions of a comformal theory coupled to 2D quantum gravity in conformal gauge. The analysis is based on a covariant and background independent definition of normal-ordered vertex operators and carefully taking into account all the parameters carrying mass dimension. The method allows for an extension to nonzero conformal spin.

On the energy-momentum tensor in non-linear σ-models with torsion

Abstract We study the renormalization properties of the energy-momentum tensor in a σ-model with torsion. Our normal product version contains besides the classical expression and the trace anomaly an off-diagonal term proportional to the squared torsion. Specialized to a group manifold, this term is crucial to reproduce the correct perturbative expansion of the energy-momentum tensor in Sugawara form.

On Wilson loops and Q\bar Q-potentials from the AdS/CFT relation at T≥0

We give a short introduction to and a partial review of the work on the calculation of Wilson loops and Q \(\bar Q\)-potentials via the conjectured AdS/CFT duality. Included is a discussion of the relative weight of the stringy correction to the target space background versus the correction by the quantum fluctuations of the string world sheet.

Weyl and Möbius invariance in the path integral derivation of reggeon vertices

Abstract We discuss some issues concerning Weyl and Mobius invariance in the functional integral derivation of the N -reggeon vertex both for matter fields and bosonized ghost. The usual recipe of conformal transport of the metric scale is avoided by the introduction of conformally transformed normal ordered exponentials describing reggeon emission.