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H. Dorn

Publications and source records attributed to H. Dorn.

18 recordsLinked to original sources
arXiv2004

Comments on the scalar propagator in AdS x S and the BMN plane wave

We discuss the scalar propagator on generic AdS_{d+1} x S^{d'+1} backgrounds. For the conformally flat situations and masses corresponding to Weyl invariant actions the propagator is powerlike in the sum of the chordal distances with respect to AdS_{d+1} and S^{d'+1}. In all other cases the propagator depends on both chordal distances separately. We discuss the KK mode summation to construct the propagator in brief. For AdS_5 x S^5 we relate our propagator to the expression in the BMN plane wave limit and find a geometric interpretation of the variables occurring in the known explicit construction on the plane wave.

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arXiv1999

Concavity of the $Q\bar Q$ potential in ${\cal N}=4$ super Yang-Mills gauge theory and AdS/CFT duality

We derive a generalised concavity condition for potentials between static sources obtained from Wilson loops coupling both to gauge bosons and a set of scalar fields. It involves the second derivatives with respect to the distance in ordinary space as well as with respect to the relative orientation in internal space. In addition we discuss the use of this field theoretical condition as a nontrivial consistency check of the AdS/CFT duality.

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arXiv1999

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

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.

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arXiv1998

$Q\bar Q$ potential from AdS-CFT relation at $T\geq 0$: Dependence on orientation in internal space and higher curvature corrections

Within the classical approximation we calculate the static $Q\bar Q$ 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 $Q\bar Q$-force. The overall vanishing of the force for antipodal orientation known from zero tempera ture 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.

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arXiv1998

The mass term in non-Abelian gauge field dynamics on matrix D-branes and T-duality in the $σ$-model approach

The formal extension of the T-duality rules for open strings from Abelian to non-Abelian gauge field background leads in a well known manner to the notion of matrix valued D-brane position. The application of this concept to the non-Abelian gauge field RG $β$-function of the corresponding $σ$-model yields a mass term in the gauge field dynamics on the matrix D-brane. The direct calculation in a corresponding D-brane model does $not$ yield such a mass term, if the Dirichlet boundary condition is implemented as a constraint on the integrand in the defining functional integral. However, the mass term arises in the direct calculation for a D-brane model with dynamically realized boundary condition.

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arXiv1997

Non-Abelian gauge field dynamics on matrix D-branes in curved space and two-dimensional $σ$-models

A survey is given of the formulation of a $σ$-model describing an open string moving in general target space background fields and coupling to both a matrix-valued D-brane position and a matrix-valued gauge field on the D-brane. The equations of motion for the D-brane and the gauge field are derived from the conformal invariance condition on the string world sheet in lowest order of $\ap$. The ordering problem of the involved matrices is solved. In addition to our previous work we discuss a conflict between the classical T-duality rules and renormalization. The calculation of the RG $β$-functions does not yield the mass term obtained by formal application of these rules in the case of target space separated D-brane copies.

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arXiv1997

Nonabelian 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 nonabelian gauge field living on the D-brane. The formalism is based on the use of an 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 $α'$ -expansion.

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arXiv1997

Remarks on T-duality for open strings

This contribution gives in sigma-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 beta-functions and the Born-Infeld action in the case of a string coupled to a D-brane.

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arXiv1996

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

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.

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arXiv1995

String-string duality for some black hole type solutions

We apply the duality transformation relating the heterotic to the IIA string in 6D to the class of exact string solutions described by the chiral null model and derive explicit formulas for all fields after reduction to 4D. If the model is restricted to asymptotically flat black hole type solutions with well defined mass and charges the purely electric solutions on the heterotic side are mapped to dyonic ones on the IIA side. The mass remains invariant. Before and after the duality transformation the solutions belong to short $N=4$ SUSY multiplets and saturate the corresponding Bogomol'nyi bounds.

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arXiv1995

Some conclusions for noncritical string theory drawn from two- and three-point functions in the Liouville sector

Starting from the known expression for the three-point correlation functions for Liouville exponentials with generic real coefficients at we can prove the Liouville equation of motion at the level of three-point functions. Based on the analytical structure of the correlation functions we discuss a possible mass shell condition for excitations of noncritical strings and make some observations concerning correlators of Liouville fields.

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arXiv1994

Two and three-point functions in Liouville theory

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.

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arXiv1993

Operator product expansion of the energy momentum tensor in 2D conformal field theories on manifolds with boundary

Starting from the well-known expression for the trace anomaly we derive the $T\cdot T$ operator product expansion of the energy-momentum tensor in 2D conformal theories defined in the upper halfplane $without$ making use of the additional condition of no energy-momentum flux across the boundary. The OPE turns out to be the same as in the absence of the boundary. For this result it is crucial that the trace anomaly is proportional to the Gauß-Bonnet density. Some relations to the $σ$ - model approach for open strings are discussed.

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arXiv1992

Remarks on the continuum formulation of noncritical strings

We discuss various aspects of the calculation of correlation functions in conformal theories coupled to quantized 2-dimensional gravity. The main emphasis lies on the construction of a continuation in the number of insertions of the cosmological constant operator for $arbitrary$ dimension of the target space. Following closely our paper \cite{DO2} we add a more extended introduction and discussion of the peculiarities in 1-dimensional target space as well as some further remarks about the 4-point function.

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arXiv1992

On Correlation Functions for Non-critical Strings with c<1 but d>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.

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arXiv1992

Analysis of All Dimensionful Parameters Relevant in Gravitational Dressing of Conformal Theories

Starting from a covariant and background independent definition of normal ordered vertex operators we give an alternative derivation of the KPZ relation between conformal dimensions and their gravitational dressed partners. With our method we are able to study for arbitrary genus the dependence of N-point functions on all dimensionful parameters. Implications for the interpretation of gravitational dressed dimensions are discussed.

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