arXiv subjects

H. Lu

Publications and source records attributed to H. Lu.

At least 451 records · Page 25Linked to original sources

arXiv1995

Embedding of the Bosonic String into the $W_3$ String

We investigate new realisations of the $W_3$ algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with $c=102$ and $c=100$ to build non-critical and critical $W_3$ BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string with $c=28-2$, together with a Kugo-Ojima topological term. Consequently, these new realisations provide embeddings of the Virasoro string into non-critical and critical $W_3$ strings.

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arXiv1994

A Superstring Theory in 2+2 Dimensions

In this paper we construct a $(2,2)$ dimensional string theory with manifest $N=1$ spacetime supersymmetry. We use Berkovits' approach of augmenting the spacetime supercoordinates by the conjugate momenta for the fermionic variables. The worldsheet symmetry algebra is a twisted and truncated ``small'' $N=4$ superconformal algebra. The physical spectrum of the open string contains an infinite number of massless states, including a supermultiplet of a self-dual Yang-Mills field and a right-handed spinor and a supermultiplet of an anti-self-dual Yang-Mills field and a left-handed spinor. The higher-spin multiplets are natural generalisations of these self-dual and anti-self-dual multiplets.

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arXiv1994

Quantising Higher-spin String Theories

In this paper, we examine the conditions under which a higher-spin string theory can be quantised. The quantisability is crucially dependent on the way in which the matter currents are realised at the classical level. In particular, we construct classical realisations for the $W_{2,s}$ algebra, which is generated by a primary spin-$s$ current in addition to the energy-momentum tensor, and discuss the quantisation for $s\le8$. From these examples we see that quantum BRST operators can exist even when there is no quantum generalisation of the classical $W_{2,s}$ algebra. Moreover, we find that there can be several inequivalent ways of quantising a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already-known $W$ strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalisations lead us to examine the whether classical BRST operators for $W_{2,{n\over 2}}$ ($n$ odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.

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arXiv1994

A note on W_{2,s} strings

BRST operators for two-dimensional theories with spin-2 and spin-$s$ currents, generalising the $W_3$ BRST operator of Thierry-Mieg, have previously been obtained. The construction was based on demanding nilpotence of the BRST operators, making no reference to whether or not an underlying $W$ algebra exists. In this paper, we analyse the known cases ($s=3$, 4, 5 and 6), showing that the two $s=4$ BRST operators are associated with the $W\!B_2$ algebra, and that two of the four $s=6$ BRST operators are associated with the $W\!G_2$ algebra. We discuss the cohomology of all the known higher-spin BRST operators, the Weyl symmetry of their physical states, and their relation with certain minimal models. We also obtain the BRST operator for the case $s=7$.

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arXiv1993

Critical and non-critical W_{2,4} strings

Nilpotent BRST operators for higher-spin $W_{2,s}$ strings, with currents of spins 2 and $s$, have recently been constructed for $s=4$, 5 and 6. In the case of $W_{2,4}$, this operator can be understood as being the BRST operator for the critical $W\!B_2$ string. In this paper, we construct a generalised BRST operator that can be associated with a non-critical $W_{2,4}$ string, in which $W\!B_2$ matter is coupled to the $W\!B_2$ gravity of the critical case. We also obtain the complete cohomology of the critical $W_{2,4}$ BRST operator, and investigate the physical spectra of the $s=5$ and $s=6$ string theories.

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arXiv1993

The Complete Cohomology of the W3 String

We present a simple procedure for constructing the complete cohomology of the BRST operator of the two-scalar and multi-scalar $W_3$ strings. The method consists of obtaining two level--15 physical operators in the two-scalar $W_3$ string that are invertible, and that can normal order with all other physical operators. They can be used to map all physical operators into non-trivial physical operators whose momenta lie in a fundamental unit cell. By carrying out an exhaustive analysis of physical operators in this cell, the entire cohomology problem is solved.

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arXiv1993

Higher-spin strings and W minimal models

We study the spectrum of physical states for higher-spin generalisations of string theory, based on two-dimensional theories with local spin-2 and spin-$s$ symmetries. We explore the relation of the resulting effective Virasoro string theories to certain $W$ minimal models. In particular, we show how the highest-weight states of the $W$ minimal models decompose into Virasoro primaries.

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arXiv1993

On Higher-spin Generalisations of String Theory

We construct BRST operators for certain higher-spin extensions of the Virasoro algebra, in which there is a spin-$s$ gauge field on the world sheet, as well as the spin-2 gauge field corrresponding to the two-dimensional metric. We use these BRST operators to study the physical states of the associated string theories, and show how they are related to certain minimal models.

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arXiv1993

On the Spectrum and Scattering of W_3 Strings

We present a detailed investigation of scattering processes in $W_3$ string theory. We discover further physical states with continuous momentum, which involve excitations of the ghosts as well as the matter, and use them to gain a better understanding of the interacting theory. The scattering amplitudes display factorisation properties, with states from the different sectors of the theory being exchanged in the various intermediate channels. We find strong evidence for the unitarity of the theory, despite the unusual ghost structure of some of the physical states. Finally, we show that by performing a transformation of the quantum fields that involves mixing the ghost fields with one of the matter fields, the structure of the physical states is dramatically simplified. The new formalism provides a concise framework within which to study the $W_3$ string.

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arXiv1993

The Interacting $W_3$ String

We present a procedure for computing gauge-invariant scattering amplitudes in the $W_3$ string, and use it to calculate three-point and four-point functions. We show that non-vanishing scattering amplitudes necessarily involve external physical states with excitations of ghosts as well as matter fields. The crossing properties of the four-point functions are studied, and it is shown that the duality of the Virasoro string amplitudes generalises in the $W_3$ string, with different sets of intermediate states being exchanged in different channels. We also exhibit a relation between the scattering amplitudes of the $W_3$ string and the fusion rules of the Ising model.

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arXiv1992

The Low-level Spectrum of the $W_3$ String

We investigate the spectrum of physical states in the $W_3$ string theory, up to level 2 for a multi-scalar string, and up to level 4 for the two-scalar string. The (open) $W_3$ string has a photon as its only massless state. By using screening charges to study the null physical states in the two-scalar $W_3$ string, we are able to learn about the gauge symmetries of the states in the multi-scalar $W_3$ string.

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arXiv1992

A Note on N=2 Superstrings

In this note we investigate the generalised critical $N=2$ superstrings in $(1,2p)$ spacetime signature. We calculate the four-point functions for the tachyon operators of these theories. In contrast to the usual $N=2$ superstring in $(2,2)$ spacetime, the four-point functions do not vanish. The exchanged particles of the four-point function are included in the physical spectrum of the corresponding theory and have vanishing fermion charge.

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arXiv1992

Aspects of N=2 Super-W_n Strings

We construct $N=2$ super-$W_{n+1}$ strings and obtain the complete physical spectrum, for arbitrary $n \ge 2$. We also derive more general realisations of the super-$W_{n+1}$ algebras in terms of $k$ commuting $N=2$ super energy-momentum tensors and $n-k$ pairs of complex superfields, with $0\le k \le [\ft{n+1}{2}]$.

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arXiv1992

On Realisations of W Algebras

It has been known for some time that $W$ algebras can be realised in terms of an energy-momentum tensor together with additional free scalar fields. Some recent results have shown that more general realisations are also possible. In this paper, we consider a wide class of realisations that may be obtained from the Miura transformation, related to the existence of canonical subalgebras of the Lie algebras on which the $W$ algebras are based. We give explicit formulae for all realisations of this kind, and discuss their applications in $W$-string theory.

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arXiv1992

New Realisations of W Algebras and W Strings

We discuss new realisations of $W$ algebras in which the currents are expressed in terms of two arbitrary commuting energy-momentum tensors together with a set of free scalar fields. This contrasts with the previously-known realisations, which involve only one energy-momentum tensor. Since realisations of non-linear algebras are not easy to come by, the fact that this new class exists is of intrinsic interest. We use these new realisations to build the corresponding $W$-string theories and show that they are effectively described by two independent ordinary Virasoro-like strings.

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arXiv1992

On Sibling and Exceptional W Strings

We discuss the physical spectrum for $W$ strings based on the algebras $B_n$, $D_n$, $E_6$, $E_7$ and $E_8$. For a simply-laced $W$ string, we find a connection with the $(h,h+1)$ unitary Virasoro minimal model, where $h$ is the dual Coxeter number of the underlying Lie algebra. For the $W$ string based on $B_n$, we find a connection with the $(2h,2h+2)$ unitary $N=1$ super-Virasoro minimal model.

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arXiv1992

The Complete Spectrum of the $W_N$ String

We obtain the complete physical spectrum of the $W_N$ string, for arbitrary $N$. The $W_N$ constraints freeze $N-2$ coordinates, while the remaining coordinates appear in the currents only {\it via} their energy-momentum tensor. The spectrum is then effectively described by a set of ordinary Virasoro-like string theories, but with a non-critical value for the central charge and a discrete set of non-standard values for the spin-2 intercepts. In particular, the physical spectrum of the $W_N$ string includes the usual massless states of the Virasoro string. By looking at the norms of low-lying states, we find strong indications that all the $W_N$ strings are unitary.

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arXiv1991

N=2 Superstrings with (1,2m) Spacetime Signature

We show that the $N=2$ superstring in $d=2D\ge6$ real dimensions, with criticality achieved by including background charges in the two real time directions, exhibits a ``coordinate-freezing'' phenomenon, whereby the momentum in one of the two time directions is constrained to take a specific value for each physical state. This effectively removes this time direction as a physical coordinate, leaving the theory with $(1,d-2)$ real spacetime signature. Norm calculations for low-lying physical states suggest that the theory is ghost free.

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