arXiv subjects

Walter Troost

Publications and source records attributed to Walter Troost.

18 recordsLinked to original sources

arXiv2001

The non-abelian Born-Infeld action at order F^6

To gain insight into the non-abelian Born-Infeld (NBI) action, we study coinciding D-branes wrapped on tori, and turn on magnetic fields on their worldvolume. We then compare predictions for the spectrum of open strings stretching between these D-branes, from perturbative string theory and from the effective NBI action. Under some plausible assumptions, we find corrections to the Str-prescription for the NBI action at order F^6. In the process we give a way to classify terms in the NBI action that can be written in terms of field strengths only, in terms of permutation group theory.

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arXiv1999

New solutions to an old equation

We present a brief historical overview of the classical theory of a radiating point charge, described by the Lorentz-Dirac equation. A recent development is the discovery of tunnelling of a charge through a potential barrier, in a completely classical context. Also, a concrete example is discussed of the existence of several physically acceptable solutions for a range of initial data. We end by pointing out some open problems in connection with D-brane and monopole physics.

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arXiv1998

The rigid limit in Special Kahler geometry; From K3-fibrations to Special Riemann surfaces: a detailed case study

The limiting procedure of special Kahler manifolds to their rigid limit is studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of certain singularities. In two examples we consider all the periods in and around the rigid limit, identifying the nontrivial ones in the limit as periods of a meromorphic form on the relevant Riemann surfaces. We show how the Kahler potential of the special Kahler manifold reduces to that of a rigid special Kahler manifold. We extensively make use of the structure of these Calabi-Yau manifolds as K3 fibrations, which is useful to obtain the periods even before the K3 degenerates to an ALE manifold in the limit. We study various methods to calculate the periods and their properties. The development of these methods is an important step to obtain exact results from supergravity on Calabi-Yau manifolds.

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arXiv1998

Special geometry of Calabi-Yau compactifications near a rigid limit

We discuss, in the framework of special Kahler geometry, some aspects of the "rigid limit" of type IIB string theory compactified on a Calabi-Yau threefold. We outline the general idea and demonstrate by direct analysis of a specific example how this limit is obtained. The decoupling of gravity and the reduction of special Kahler geometry from local to rigid is demonstrated explicitly, without first going to a noncompact approximation of the Calabi-Yau. In doing so, we obtain the Seiberg-Witten Riemann surfaces corresponding to different rigid limits as degenerating branches of a higher genus Riemann surface, defined for all values of the moduli. Apart from giving a nice geometrical picture, this allows one to calculate easily some gravitational corrections to e.g. the Seiberg-Witten central charge formula. We make some connections to the 2/5-brane picture, also away from the rigid limit, though only at the formal level.

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arXiv1998

A detailed case study of the rigid limit in Special Kähler geometry using K3

This is a résumé of an extensive investigation of some examples in which one obtains the rigid limit of N=2 supergravity by means of an expansion around singular points in the moduli space of a Calabi-Yau 3-fold. We make extensive use of the K3 fibration of the Calabi-Yau manifolds which are considered. At the end the fibration parameter becomes the coordinate of the Riemann surface whose moduli space realises rigid N=2 supersymmetry.

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arXiv1996

Higher Loop Anomalies and their Consistency Conditions in Nonlocal Regularization

An algebraic program of computation and characterization of higher loop BRST anomalies is presented. We propose a procedure for disentangling a genuine{\it local} higher loop anomaly from the quantum dressings of lower loop anomalies. For such higher loop anomalies we derive a local consistency condition, which is the generalisation of the Wess-Zumino condition for the one-loop anomaly. The development is presented in the framework of the field-antifield formalism, making use of a nonlocal regularization method. The theoretical construction is exemplified by explicitly computing the two-loop anomaly of chiral $W_3$ gravity. We also give, for the first time, an explicit check of the local two--loop consistency condition that is associated with this anomaly.

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arXiv1996

The BPHZ renormalised BV master equation and Two-loop Anomalies in Chiral Gravities

Anomalies and BRST invariance are governed, in the context of Lagrangian Batalin-Vilkovisky quantization, by the master equation, whose classical limit is $(S, S)=0$. Using Zimmerman's normal products and the BPHZ renormalisation method, we obtain a corresponding local quantum operator equation, which is valid to all orders in perturbation theory. The formulation implies a calculational method for anomalies to all orders that is useful also outside the BV context and that remains completely within regularised perturbation theory. It makes no difference in principle whether the anomaly appears at one loop or at higher loops. The method is illustrated by computing the one- and two-loop anomalies in chiral $W_3$ gravity.

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arXiv1996

The Definitions of Special Geometry

The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry', related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of special geometry, which we want to clear up, for rigid as well as for local N=2.

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arXiv1996

Classical Tunneling from the Lorentz-Dirac Equation

The classical equation of motion of a charged point particle, including its radiation reaction, is described by the Lorentz-Dirac equation. We found a new class of solutions that describe tunneling (in a completely classical context!). For nonrelativistic electrons and a square barrier, the solution is elementary and explicit. We show the persistance of the solution for smoother potentials. For a large range of initial velocities, initial conditions may leave a (discrete) ambiguity on the resulting motion.

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arXiv1996

The BRST--antibracket cohomology of $2d$ gravity conformally coupled to scalar matter

We compute completely the BRST--antibracket cohomology on local functionals in two-dimensional Weyl invariant gravity for given classical field content (two dimensional metric and scalar matter fields) and gauge symmetries (two dimensional diffeomorphisms and local Weyl transformations). This covers the determination of all classical actions, of all their rigid symmetries, of all background charges and of all candidate gauge anomalies. In particular we show that the antifield dependence can be entirely removed from the anomalies and that, if the target space has isometries, the condition for the absence of matter field dependent Weyl anomalies is more general than the familiar `dilaton equations'.

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arXiv1996

Background charges and consistent continuous deformations of $2d$ gravity theories

We construct and discuss all background charges and continuous consistent deformations of standard $2d$ gravity theories with scalar matter fields. It turns out that the background charges and those deformations which change nontrivially both the form of the action and of its gauge symmetries are closely linked and exist only if the target space has at least one special (`covariantly constant') Killing vector which must be a null vector in the case of the deformations. The deformed actions provide interesting novel $2d$ gravity models. We argue that some of them lead to non-critical string theories.

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arXiv1994

On the Lagrangian Realization of Non-Critical ${\cal W}$-Strings

A large class of non-critical string theories with extended worldsheet gauge symmetry are described by two coupled, gauged Wess-Zumino-Witten Models. We give a detailed analysis of the gauge invariant action and in particular the gauge fixing procedure and the resulting BRST symmetries. The results are applied to the example of ${\cal W}_3$ strings.

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arXiv1994

Regularisation, the BV method, and the antibracket cohomology

We review the Lagrangian Batalin--Vilkovisky method for gauge theories. This includes gauge fixing, quantisation and regularisation. We emphasize the role of cohomology of the antibracket operation. Our main example is $d=2$ gravity, for which we also discuss the solutions for the cohomology in the space of local integrals. This leads to the most general form for the action, for anomalies and for background charges.

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arXiv1994

BRST-Antibracket Cohomology in 2D Conformal Gravity

We present results of a computation of the BRST-antibracket cohomology in the space of local functionals of the fields and antifields for a class of 2d gravitational theories which are conformally invariant at the classical level. In particular all classical local action functionals, all candidate anomalies and all BRST--invariant functionals depending nontrivially on antifields are given and discussed for these models.

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arXiv1993

Chiral Quantization on a Group Manifold

The phase space of a particle on a group manifold can be split in left and right sectors, in close analogy with the chiral sectors in Wess Zumino Witten models. We perform a classical analysis of the sectors, and the geometric quantization in the case of $SU(2)$. The quadratic relation, classically identifying $SU(2)$ as the sphere $S^3$, is replaced quantum mechanically by a similar condition on non-commutative operators ('quantum sphere'). The resulting quantum exchange algebra of the chiral group variables is quartic, not quadratic. The fusion of the sectors leads to a Hilbert space that is subtly different from the one obtained by a more direct (un--split) quantization.

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arXiv1993

Regularization and the BV Formalism

We summarize the application of the field--antifield formalism to the quantization of gauge field theories. After the gauge fixing, the main issues are the regularization and anomalies. We illustrate this for chiral $W_3$ gravity. We discuss also gauge theories with a non-local action, induced by a matter system with an anomaly. As an illustration we use induced WZW models, including a discussion of non--local regularization, the importance of the measure and regularization of multiple loops. In these theories antifields become propagating --- one of many roles assigned to them in the BV formalism.

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arXiv1993

The Relation between Linear and Non-Linear $N=3,4$ Supergravity Theories

The effective actions for $d=2$, $N=3,4$ chiral supergravities with a linear and a non-linear gauge algebra are related to each other by a quantum reduction, the latter is obtained from the former by putting quantum currents equal to zero. This implies that the renormalisation factors for the quantum actions are identical.

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arXiv1993

Induced and Effective Gravity Theories in D=2

As a preparation for the study of {\it arbitrary} extensions of $d=2$ gravity we present a detailed investigation of $SO(N)$ supergravity. By gauging a chiral, nilpotent subgroup of the $OSp(N|2)$ Wess-Zumino-Witten model we obtain an all order expression for the effective action. Reality of the coupling constant imposes the usual restrictions on $c$ for $N=0$ and 1. No such restrictions appear for $N\geq 2$. For $N=2$, 3 and 4, no renormalizations of the coupling constant beyond one loop occur. These results are related to non-renormalization theorems for theories with extended supersymmetries. Arbitrary (super)extensions of $d=2$ gravity are then analyzed. The induced theory is represented by a WZW model for which a chiral, solvable group is gauged. From this, we obtain the effective action. All order expressions for both the coupling constant renormalization and the wavefunction renormalization are given. From this we classify all extensions of $d=2$ gravity for which the coupling constant gets at most a one loop renormalization. As an application of the general strategy, $N=4$ theories based on $D(2,1,\a)$ and $SU(1,1|2)$, all $WA$ gravities and the $N=2$ $W_n$ models are treated in some detail.

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