Abstract
We consider BRST quantized 2D gravity coupled to conformal matter with arbitrary central change c{sup M} = c(p,q) < 1 in the conformal gauge. We apply a Lian-Zuckerman SO(2,C) ((p,q) - dependent) rotation to Witten`s c{sup M} = 1 chiral ground ring. We show that the ring structure generated by the (relative BRST cohomology) discrete states in the (matter x Liouville x ghosts) Fock module may be obtained by this rotation. We give also explicit formulae for the discrete states. For some of them we use new formulae for c<1 Fock modules singular vectors which we present in terms of Schur polynomials generalizing the c = 1 expressions of Goldstone, while the rest of the discrete states we obtain by finding the proper SO(2,C) rotation. Our formulae give the extra physical states (arising from the relative BRST cohomology) on the boundaries of the p x q rectangles of the conformal lattice and thus all such states in (1,q) or (p,1) models. (author). 24 refs.
Citation Formats
Chair, N, Dobrev, V K, and Kanno, H.
SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter.
IAEA: N. p.,
1992.
Web.
Chair, N, Dobrev, V K, & Kanno, H.
SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter.
IAEA.
Chair, N, Dobrev, V K, and Kanno, H.
1992.
"SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter."
IAEA.
@misc{etde_10157368,
title = {SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter}
author = {Chair, N, Dobrev, V K, and Kanno, H}
abstractNote = {We consider BRST quantized 2D gravity coupled to conformal matter with arbitrary central change c{sup M} = c(p,q) < 1 in the conformal gauge. We apply a Lian-Zuckerman SO(2,C) ((p,q) - dependent) rotation to Witten`s c{sup M} = 1 chiral ground ring. We show that the ring structure generated by the (relative BRST cohomology) discrete states in the (matter x Liouville x ghosts) Fock module may be obtained by this rotation. We give also explicit formulae for the discrete states. For some of them we use new formulae for c<1 Fock modules singular vectors which we present in terms of Schur polynomials generalizing the c = 1 expressions of Goldstone, while the rest of the discrete states we obtain by finding the proper SO(2,C) rotation. Our formulae give the extra physical states (arising from the relative BRST cohomology) on the boundaries of the p x q rectangles of the conformal lattice and thus all such states in (1,q) or (p,1) models. (author). 24 refs.}
place = {IAEA}
year = {1992}
month = {Jan}
}
title = {SO(2,C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter}
author = {Chair, N, Dobrev, V K, and Kanno, H}
abstractNote = {We consider BRST quantized 2D gravity coupled to conformal matter with arbitrary central change c{sup M} = c(p,q) < 1 in the conformal gauge. We apply a Lian-Zuckerman SO(2,C) ((p,q) - dependent) rotation to Witten`s c{sup M} = 1 chiral ground ring. We show that the ring structure generated by the (relative BRST cohomology) discrete states in the (matter x Liouville x ghosts) Fock module may be obtained by this rotation. We give also explicit formulae for the discrete states. For some of them we use new formulae for c<1 Fock modules singular vectors which we present in terms of Schur polynomials generalizing the c = 1 expressions of Goldstone, while the rest of the discrete states we obtain by finding the proper SO(2,C) rotation. Our formulae give the extra physical states (arising from the relative BRST cohomology) on the boundaries of the p x q rectangles of the conformal lattice and thus all such states in (1,q) or (p,1) models. (author). 24 refs.}
place = {IAEA}
year = {1992}
month = {Jan}
}