arXiv subjects
Publications and source records attributed to Peter West.
We derive new actions for the bosonic p-brane, super p-brane and the p-brane moving in AdS(dS) space-times using the theory of non-linear realisation without requiring the adoption of any constraints or using superfields. The Goldstone boson associated with the breaking of Lorentz transformations becomes a dynamical field whose equation of motion relates it algebraically to the remaining Goldstone fields.
We will show how the theory of non-linear realisations can be used to naturally incorporate world line diffeomorphisms and kappa transformations for the point particle and superpoint particle respectively. Similar results also hold for a general p-brane and super p-brane, however, we must in these cases include an additional Lorentz transformation.
After dimensional reduction to three dimensions, the lowest order effective actions for pure gravity, M-theory and the Bosonic string admit an enhanced symmetry group. In this paper we initiate study of how this enhancement is affected by the inclusion of higher derivative terms. In particular we show that the coefficients of the scalar fields associated to the Cartan subalgebra are given by weights of the enhanced symmetry group.
We calculate, using the group theoretic approach to string theory, the tree and one loop scattering of four open and closed arbitrary bosonic string states. In the limit of high energy, but fixed angle, the multi-string vertex at tree and one loop levels that we find takes a very simple form. We propose, and present arguments for, a form for the high energy multi-string vertex at all loops; in particular we give a path integral derivation of this vertex. Our results agree with those of Gross and Mende for tachyon scattering amplitudes, but those for any other string scattering are substantially different from that discussed in reference [5]. We also develop some of the technology used in the group theoretic method to compute loop corrections.
We consider a theory in which supersymmetry is partially spontaneously broken and show that the dynamical fields in the same supersymmetric multiplet as the Goldstino are Goldstone bosons whose corresponding generators are central charges in the underlying supersymmetry algebra. We illustrate how this works for four dimensional Born-Infeld theory and five brane of M theory. We conjecture, with supporting arguments, that the dynamics of the branes of M theory can be extended so as to possess an E_{11} symmetry.
A description of the bosonic sector of ten-dimensional N=1 supergravity as a non-linear realisation is given. We show that if a suitable extension of this theory were invariant under a Kac-Moody algebra, then this algebra would have to contain a rank eleven Kac-Moody algebra, that can be identified to be a particular real form of very-extended D_8. We also describe the extension of N=1 supergravity coupled to an abelian vector gauge field as a non-linear realisation, and find the Kac-Moody algebra governing the symmetries of this theory to be very-extended B_8. Finally, we discuss the related points for the N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields.
We analyse the very-extended Kac-Moody algebras as representations in terms of certain A_d subalgebras and find the generators at low levels. Our results for low levels agree precisely with the bosonic field content of the theories containing gravity, forms and scalars which upon reduction to three dimensions can be described by a non-linear realisation. We explain how the Dynkin diagrams of the very-extended algebras encode information about the field content and generalised T-duality transformations.
We consider theories containing gravity, at most one dilaton and form field strengths. We show that the existence of particular BPS solutions of intersecting extremal closed branes select the theories, which upon dimensional reduction to three dimensions possess a simple simply laced Lie group symmetry G. Furthermore these theories can be fully reconstructed from the dynamics of such branes and of their openings. Amongst such theories are the effective actions of the bosonic sector of M-theory and of the bosonic string. The BPS intersecting brane solutions form representations of a subgroup of the group of Weyl reflections and outer automorphisms of the triple Kac-Moody extension G+++ of the G algebra, which cannot be embedded in the overextended Kac-Moody subalgebra G++ characterising the cosmological Kasner solutions.
A description of the bosonic sector of massive IIA supergravity as a non-linear realisation is given. An essential feature of this construction is that the momentum generators have non-trivial commutation relations with the generators associated with the gauge fields.
We formulate the bosonic sector of IIB supergravity as a non-linear realisation. We show that this non-linear realisation contains the Borel subalgebras of SL(11) and $E_7$ and argue that it can be enlarged so as to be based on the rank eleven Kac-Moody algebra $E_{11}$
We describe a generalization of Yang--Mills topological field theory for Abelian two-forms in six dimensions. The connection of this theory by a twist to Poincaré supersymmetric theories is given. We also briefly consider interactions and the case of self-dual three-forms in eight dimensions.
We calculate the Kahlerian and the lowest order non-Kahlerian contributions to the one loop effective superpotential using super-Feynman graphs in the massless Wess-Zumino Model, the massive Wess-Zumino Model and N=1, U(1) gauge theory. We also calculate the Kahlerian term in Yang-Mills Theory for a general gauge group. Using this latter result we find the one loop Kahlerian contribution for N=2 Yang-Mills Theory in terms of N=1 superfields and we show that it can only come from non-holomorphic contributions to the N=2 effective potential.
We show how to relate the parafermions that occur in the $W_3$ string to the standard construction of parafermions. This result is then used to show that one of the screening charges that occurs in parafermionic theories is precisely the non-trivial part of the $W_3$ string BRST charge. A way of generalizing this pattern for a $W_N$ string is explained. This enables us to construct the full BRST charge for a $W_{2,N}$ string and to prove the relation of such a string to the algebra $W_{N-1}$ for arbitrary $N$, We also show how to calculate part of the BRST charge for a $W_N$ string, and we explain how our method might be extended to obtain the full BRST charge for such a string.
It has recently been shown that the ordinary bosonic string can be represented by a special background of N=1 or N=2 strings. In this paper, it will be shown that the bosonic string can also be represented by a special background of $W$-strings.
Recent progress on the physical states and scattering amplitudes of the $W_3$ string is reviewed with particular emphasis on the relation between this string theory and the Ising model.
A general formalism for covariant $W_3$ string scattering is given. It is found necessary to use screening charges that are constructed from the $W_3$ fields including ghosts. The scattering amplitudes so constructed contain within them Ising model correlation functions and agree with those found previously by the authors. Using the screening charge and a picture changing operator, an infinite number of states in the cohomology of Q are generated from only three states. We conjecture that, apart from discrete states, these are all the states in the cohomology of Q.
A spectrum generating algebra is constructed and used to find all the physical states of the $W_3$ string with standard ghost number. These states are shown to have positive norm and their partition function is found to involve the Ising model characters corresponding to the weights 0 and 1/16. The theory is found to be modular invariant if , in addition, one includes states that correspond to the Ising character of weight 1/2. It is shown that these additional states are indeed contained in the cohomology of $Q$.