Harald Dorn

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.

Partition functions and double-trace deformations in AdS/CFT

We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFTd at large N and its dual picture in AdSd+1. Three complementary previous results are brought into full agreement with each other: bulk [1] and boundary [2] computations, as well as their formal identity [3]. We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuation determinants involved. A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection. All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary.

On the renormalization and short-distance properties of hadronic operators in QCD

Abstract We discuss the renormalization of the contour-dependent gauge-invariant composite bilocal or string operator q (2) exp |g ∫ 1 2 A d z|q(1) in QCD, which one would naturally associated with the hadronic bound states. We then discuss the short-distance expansion of this operator as the end points merge. We argue that some functional average overall possible paths between x 1 and x 2 may be the appropriate operator to describe the mesonic modes in QCD and that the short-distance expansion may provide a valuable insight into the nature of this functional average. Most of our considerations are for smooth contours; however, we propose a simple way of treating on the same footing the additional divergences pointed out by Polyakov due to sharp bends in the contour. This latter confirms the conclusions reached for smooth contours.

Diagrams of noncommutative Φ3 theory from string theory

Abstract Starting from tree and one-loop tachyon amplitudes of open string theory in the presence of a constant B -field, we explore two problems. First we show that in the noncommutative field theory limit the amplitudes reduce to tree and one-loop diagrams of the noncommutative Φ 3 theory. Next, we check factorization of the one-loop amplitudes in the long cylinder limit.

Comments on the energy–momentum tensor in non-commutative field theories

Abstract In a non-commutative field theory, the energy–momentum tensor obtained from the Noether method needs not be symmetric; in a massless theory, it needs not be traceless either. In a non-commutative scalar field theory, the method yields a locally conserved yet non-symmetric energy–momentum tensor whose trace does not vanish for massless fields. A non-symmetric tensor also governs the response of the action to a general coordinate transformation. In non-commutative gauge theory, if translations are suitably combined with gauge transformations, the method yields a covariantly constant tensor which is symmetric but only gauge covariant. Using suitable Wilson functionals, this can be improved to yield a locally conserved and gauge invariant, albeit non-symmetric, energy–momentum tensor.

NON-ABELIAN GAUGE FIELD DYNAMICS ON MATRIX D-BRANES

We construct a calculational scheme for handling the matrix ordering problems connected with the appearance of D-brane positions taking values in the same Lie algebra as the non-abelian gauge field living on the D-brane. The formalism is based on the use of a one-dimensional auxiliary field living on the boundary of the string world-sheet and taking care of the order of the matrix-valued fields. The resulting system of equations of motion for both the gauge field and the D-brane position is derived in lowest order of the α1 expansion.

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.

On open string σ-model and noncommutative gauge fields

Abstract We consider the ordinary and noncommutative Dirac-Born-Infeld theories within the open string σ -model. First, we propose a renormalization scheme, hybrid point splitting regularization, that leads directly to the Seiberg-Witten description including the two-form Φ . We also show how such a form appears within the standard renormalization scheme just by some freedom in changing variables. Second, we propose a Wilson factor which has the noncommutative gauge invariance on the classical level and then compute the σ -model partition function within one of the known renormalization scheme that preserves the noncommutative gauge invariance. As a result, we find the noncommutative Yang-Mills action.

On spacelike and timelike minimal surfaces in AdS(n)

We discuss timelike and spacelike minimal surfaces in AdSn using a Pohlmeyer type reduction. The differential equations for the reduced system are derived in a parallel treatment of both type of surfaces, with emphasis on their characteristic differences. In the timelike case we find a formulation corresponding to a complete gauge fixing of the torsion. In the spacelike case we derive three sets of equations, related to different parameterizations enforced by the Lorentzian signature of the metric in normal space. On the basis of these equations, we prove that there are no flat spacelike minimal surfaces in AdSn,n ≥ 4 beyond the four cusp surfaces used in the Alday-Maldacena conjecture. Furthermore, we give a parameterization of flat timelike minimal surfaces in AdS5 in terms of two chiral fields.