Algebraic structures and eigenstates for integrable collective field theories

Avan, Jean; Jevicki, Antal

doi:10.1007/BF02096570

Algebraic structures and eigenstates for integrable collective field theories

Jean Avan
(
- Brown U.
)
,
Antal Jevicki
(
- Brown U.
)

Mar 10, 1992

27 pages

Published in:

Commun.Math.Phys. 150 (1992) 149-166

e-Print:

hep-th/9202065 [hep-th]

DOI:

10.1007/BF02096570

Report number:

BROWN-HEP-847

View in:

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Abstract:

Conditions for the construction of polynomial eigen--operators for the Hamiltonian of collective string field theories are explored. Such eigen--operators arise for only one monomial potential

v(x) = \mu x~2

in the collective field theory. They form a

w_{\infty}

--algebra isomorphic to the algebra of vertex operators in 2d gravity. Polynomial potentials of orders only strictly larger or smaller than 2 have no non--zero--energy polynomial eigen--operators. This analysis leads us to consider a particular potential

v(x)= \mu x~2 + g/x~2

. A Lie algebra of polynomial eigen--operators is then constructed for this potential. It is a symmetric 2--index Lie algebra, also represented as a sub--algebra of

U (s\ell (2)).

field theory: string
field theory: collective phenomena
Hamiltonian formalism
matrix model
potential
operator: algebra

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