Quantum conserved currents in affine Toda theories

Delius, G.W.; Grisaru, Marcus T.; Zanon, D.

doi:10.1016/0550-3213(92)90103-I

Quantum conserved currents in affine Toda theories

G.W. Delius
(
- CERN
)
,
Marcus T. Grisaru
(
- CERN
)
,
D. Zanon
(
- Milan U. and
- INFN, Milan
)

Dec, 1991

22 pages

Published in:

Nucl.Phys.B 385 (1992) 307-328

Published: 1992

e-Print:

hep-th/9202069 [hep-th]

DOI:

10.1016/0550-3213(92)90103-I

Report number:

CERN-TH-6336-91,
IFUM-412-FT

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Abstract:

We study the renormalization and conservation at the quantum level of higher-spin currents in affine Toda theories with particular emphasis on the nonsimply-laced cases. For specific examples, namely the spin-3 current for the

a_3~{(2)}

and

c_2~{(1)}

theories, we prove conservation to all-loop order, thus establishing the existence of factorized S-matrices. For these theories, as well as the simply-laced

a_2~{(1)}

theory, we compute one-loop corrections to the corresponding higher-spin charges and study charge conservation for the three-particle vertex function. For the

a_3~{(2)}

theory we show that although the current is conserved, anomalous threshold singularities spoil the conservation of the corresponding charge for the on-shell vertex function, implying a breakdown of some of the bootstrap procedures commonly used in determining the exact S-matrix.

field theory: Toda
field theory: affine
dimension: 2
current: conservation law
spin: high
high: spin
S-matrix: factorization
perturbation theory: higher-order
renormalization
bootstrap

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