arXiv subjects

M. de Roo

Publications and source records attributed to M. de Roo.

26 records · Page 2Linked to original sources

arXiv1995

Duality symmetry in four-dimensional string actions

We reduce the dual version of $D=10$, $N=1$ supergravity coupled to $n$ vector fields to four dimensions, and derive the $SL(2,R)\times O(6,6+n)$ transformations which leave the equations of motion invariant. For $n=0$ $SL(2,R)$ is also a symmetry of the action, but for $n>0$ only those $SL(2,R)$ transformations which act linearly on all fields leave the action invariant. The resulting four-dimensional theory is related to the bosonic part of the usual formulation of $N=4$ supergravity coupled to matter by a duality transformation.

hep-th↗

arXiv1994

On realizing the bosonic string as a noncritical $W_3$-string

We discuss a realization of the bosonic string as a noncritical $W_3$-string. The relevant noncritical $W_3$-string is characterized by a Liouville sector which is restricted to a (non-unitary) $(3,2)$ $W_3$ minimal model with central charge contribution $c_l = - 2$. Furthermore, the matter sector of this $W_3$-string contains $26$ free scalars which realize a critical bosonic string. The BRST operator for this $W_3$-string can be written as the sum of two, mutually anticommuting, nilpotent BRST operators: $Q = Q_0 + Q_1$ in such a way that the scalars which realize the bosonic string appear only in $Q_0$ while the central charge contribution of the fields present in $Q_1$ equals zero. We argue that, in the simplest case that the Liouville sector is given by the identity operator only, the $Q_1$-cohomology is given by a particular (non-unitary) $(3,2)$ Virasoro minimal model at $c=0$.

hep-th↗

arXiv1993

On the Cohomology of the Noncritical $W$-string

We investigate the cohomology structure of a general noncritical $W_N$-string. We do this by introducing a new basis in the Hilbert space in which the BRST operator splits into a ``nested'' sum of nilpotent BRST operators. We give explicit details for the case $N=3$. In that case the BRST operator $Q$ can be written as the sum of two, mutually anticommuting, nilpotent BRST operators: $Q=Q_0+Q_1$. We argue that if one chooses for the Liouville sector a $(p,q)$ $W_3$ minimal model then the cohomology of the $Q_1$ operator is closely related to a $(p,q)$ Virasoro minimal model. In particular, the special case of a (4,3) unitary $W_3$ minimal model with central charge $c=0$ leads to a $c=1/2$ Ising model in the $Q_1$ cohomology. Despite all this, noncritical $W_3$ strings are not identical to noncritical Virasoro strings.

hep-th↗

arXiv1993

A BRST Analysis of $W$-symmetries

We perform a classical BRST analysis of the symmetries corresponding to a generic $w_N$-algebra. An essential feature of our method is that we write the $w_N$-algebra in a special basis such that the algebra manifestly has a ``nested'' set of subalgebras $v_N^N \subset v_N^{N-1} \subset \dots \subset v_N^2 \equiv w_N$ where the subalgebra $v_N^i\ (i=2, \dots ,N)$ consists of generators of spin $s=\{i,i+1,\dots ,N\}$, respectively. In the new basis the BRST charge can be written as a ``nested'' sum of $N-1$ nilpotent BRST charges. In view of potential applications to (critical and/or non-critical) $W$-string theories we discuss the quantum extension of our results. In particular, we present the quantum BRST-operator for the $W_4$-algebra in the new basis. For both critical and non-critical $W$-strings we apply our results to discuss the relation with minimal models.

hep-th↗

arXiv1993

On the BRST Operator of $W$-Strings

We discuss the conditions under which the BRST operator of a $W$-string can be written as the sum of two operators that are separately nilpotent and anticommute with each other. We illustrate our results with the example of the non-critical $W_3$-string. Furthermore, we apply our results to make a conjecture about a relationship between the spectrum of a non-critical $W_n$-string and a $W_{n-1}$-string.

hep-th↗

arXiv1992

The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions

We construct the supersymmetric completion of quartic $R+R^4$-actions in the ten-dimensional effective action of the heterotic string. Two invariants, of which the bosonic parts are known from one-loop string amplitude calculations, are obtained. One of these invariants can be generalized to an $R+F^2+F^4$-invariant for supersymmetric Yang-Mills theory coupled to supergravity. Supersymmetry requires the presence of $B\wedge R\wedge R\wedge R\wedge R$-terms, ($B\wedge F\wedge F\wedge F\wedge F$ for Yang-Mills) which correspond to counterterms in the Green-Schwarz anomaly cancellation. Within the context of our calculation the $ζ(3)R^4$-term from the tree-level string effective action does not allow supersymmetrization.

hep-th↗

arXiv1992

Realisations of $W_3$ Symmetry

We perform a systematic investigation of free-scalar realisations of the Za\-mo\-lod\-chi\-kov $W_3$ algebra in which the operator product of two spin-three generators contains a non-zero operator of spin four which has vanishing norm. This generalises earlier work where such an operator was required to be absent. By allowing this spin-four null operator we obtain several realisations of the $W_3$ algebra both in terms of two scalars as well as in terms of an arbitrary number $n$ of free scalars. Our analysis is complete for the case of two-scalar realisations.

hep-th↗

arXiv1991

N=2\ $W$-supergravity

We quantise the classical gauge theory of $N=2\ w_\infty$-supergravity and show how the underlying $N=2$ super-$w_\infty$ algebra gets deformed into an $N=2$ super-$W_\infty$ algebra. Both algebras contain the $N=2$ super-Virasoro algebra as a subalgebra. We discuss how one can extract from these results information about quantum $N=2\ W_N$-supergravity theories containing a finite number of higher-spin symmetries with superspin $s\le N$. As an example we discuss the case of quantum $N=2\ W_3$-supergravity.

hep-th↗