35 research outputs found
Solitons and Vertex Operators in Twisted Affine Toda Field Theories
Affine Toda field theories in two dimensions constitute families of
integrable, relativistically invariant field theories in correspondence with
the affine Kac-Moody algebras. The particles which are the quantum excitations
of the fields display interesting patterns in their masses and coupling and
which have recently been shown to extend to the classical soliton solutions
arising when the couplings are imaginary. Here these results are extended from
the untwisted to the twisted algebras. The new soliton solutions and their
masses are found by a folding procedure which can be applied to the affine
Kac-Moody algebras themselves to provide new insights into their structures.
The relevant foldings are related to inner automorphisms of the associated
finite dimensional Lie group which are calculated explicitly and related to
what is known as the twisted Coxeter element. The fact that the twisted affine
Kac-Moody algebras possess vertex operator constructions emerges naturally and
is relevant to the soliton solutions.Comment: 27 pages (harvmac) + 3 figures (LaTex) at the end of the file,
Swansea SWAT/93-94/1
A Class of String Backgrounds as a Semiclassical Limit of WZW Models
A class of string backgrounds associated with non semi-simple groups is
obtained as a special large level limit of ordinary WZW models. The models have
an integer Virasoro central charge and they include the background recently
studied by Nappi and Witten.Comment: 9 page
Supersymmetric integrable scattering theories with unstable particles
We propose scattering matrices for N=1 supersymmetric integrable quantum
field theories in 1+1 dimensions which involve unstable particles in their
spectra. By means of the thermodynamic Bethe ansatz we analyze the ultraviolet
behaviour of some of these theories and identify the effective Virasoro central
charge of the underlying conformal field theories.Comment: 15 pages Late
On the Erasure and Regeneration of the Primordial Baryon Asymmetry by Sphalerons
We show that a cosmological baryon asymmetry generated at the GUT scale,
which would be destroyed at lower temperatures by sphalerons and possible new
B- or L-violating effects, can naturally be preserved by an asymmetry in the
number of right-handed electrons. This results in a significant softening of
previously derived baryogenesis-based constraints on the strength of exotic B-
or L-violating interactions.Comment: 10 pp. LaTex (2 figures, included) UMN-TH-1201/9
PT Invariant Complex E (8) Root Spaces
We provide a construction procedure for complex root spaces invariant under antilinear transformations, which may be applied to any Coxeter group. The procedure is based on the factorisation of a chosen element of the Coxeter group into two factors. Each of the factors constitutes an involution and may therefore be deformed in an antilinear fashion. Having the importance of the E(8)-Coxeter group in mind, such as underlying a particular perturbation of the Ising model and the fact that for it no solution could be found previously, we exemplify the procedure for this particular case. As a concrete application of this construction we propose new generalisations of Calogero-Moser Sutherland models and affine Toda field theories based on the invariant complex root spaces and deformed complex simple roots, respectively
Yangians, Integrable Quantum Systems and Dorey's rule
We study tensor products of fundamental representations of Yangians and show
that the fundamental quotients of such tensor products are given by Dorey's
rule.Comment: We have made corrections to the results for the Yangians associated
to the non--simply laced algebra
q-Quaternions and q-deformed su(2) instantons
We construct (anti)instanton solutions of a would-be q-deformed su(2)
Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant
noncommutative space] by reinterpreting the function algebra on the latter as a
q-quaternion bialgebra. Since the (anti)selfduality equations are covariant
under the quantum group of deformed rotations, translations and scale change,
by applying the latter we can generate new solutions from the one centered at
the origin and with unit size. We also construct multi-instanton solutions. As
they depend on noncommuting parameters playing the roles of `sizes' and
`coordinates of the centers' of the instantons, this indicates that the moduli
space of a complete theory will be a noncommutative manifold. Similarly, gauge
transformations should be allowed to depend on additional noncommutative
parameters.Comment: Latex file, 39 pages. Final version appeared in JM
Conformal Affine Toda Soliton and Moduli of IIB Superstring on
In this paper we interpret the hidden symmetry of the moduli space of IIB
superstring on in terms of the chiral embedding in
, which turns to be the conformal affine Toda model.
We review how the position of poles in the Riemann-Hilbert formulation
of dressing transformation and how the value of loop parameters in the
vertex operator of affine algebra determines the moduli space of the soliton
solutions, which describes the moduli space of the Green-Schwarz superstring.
We show also how this affine SU(4) symmetry affinize the conformal symmetry in
the twistor space, and how a soliton string corresponds to a Robinson
congruence with twist and dilation spin coefficients of twistor.Comment: Final version, Misprints corrected, Note adde
Penrose limits of Lie Branes and a Nappi--Witten braneworld
Departing from the observation that the Penrose limit of AdS_3 x S^3 is a
group contraction in the sense of Inonu and Wigner, we explore the relation
between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a
six-dimensional symmetric plane wave analogous to the four-dimensional
Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant
lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy
classes. We determine the (twisted and untwisted) symmetric D-branes in the
plane wave background and we prove the existence of a space-filling D5-brane
and, separately, of a foliation by D3-branes with the geometry of the
Nappi--Witten spacetime which can be understood as the Penrose limit of the
AdS_2 x S^2 D3-brane in AdS_3 x S^3. Parenthetically we also derive a simple
criterion for a symmetric plane wave to be isometric to a lorentzian Lie group.
In particular we observe that the maximally supersymmetric plane wave in IIB
string theory is isometric to a lorentzian Lie group, whereas the one in
M-theory is not.Comment: 21 pages (v2: references added