On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation

Abstract

It is well known that five-point function in Liouville field theory provides a representation of solutions of the SL(2,R)_k Knizhnik-Zamolodchikov equation at the level of four-point function. Here, we make use of such representation to study some aspects of the spectral flow symmetry of sl(2)_k affine algebra and its action on the observables of the WZNW theory. To illustrate the usefulness of this method we rederive the three-point function that violates the winding number in SL(2,R) in a very succinct way. In addition, we prove several identities holding between exact solutions of the Knizhnik-Zamolodchikov equation.

10 pages, no figures. v2: Typos corrected, formula and references added. v3: typo corrected in equation (20)

References in corpus (1)

• H(3)+ correlators from Liouville theory

Cited by in corpus (15)

• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Free field world-sheet correlators for ${\mathrm{AdS}}_3$
• Spectral Flow in AdS(3)/CFT(2)
• String correlators on ${\text{AdS}}_3$: Three-point functions
• On AGT description of N=2 SCFT with N_f=4
• Stress-energy tensor correlators from the world-sheet
• One-loop amplitudes of winding strings in AdS${}_3$ and the Coulomb gas approach
• A note on the spectral flow operator
• Winding Strings in AdS_3
• String correlators in AdS${}_3$ from FZZ duality
• A Note on Z_2 Symmetries of the KZ Equation
• String correlators on ${\text{AdS}}_3$: Four-point functions
• The $Ad{S}_3\times S^1$ Chiral Ring
• Three-Point Function in Perturbed Liouville Gravity
• Notes on the SL(2,R) CFT