60 research outputs found
Non-critical string, Liouville theory and geometric bootstrap hypothesis
The applications of the existing Liouville theories for the description of
the longitudinal dynamics of non-critical Nambu-Goto string are analyzed. We
show that the recently developed DOZZ solution to the Liouville theory leads to
the cut singularities in tree string amplitudes. We propose a new version of
the Polyakov geometric approach to Liouville theory and formulate its basic
consistency condition - the geometric bootstrap equation. Also in this approach
the tree amplitudes develop cut singularieties.Comment: 16 pages; revised versio
Super-Liouville - Double Liouville correspondence
The AGT motivated relation between the tensor product of the N = 1
super-Liouville field theory with the imaginary free fermion (SL) and a certain
projected tensor product of the real and the imaginary Liouville field theories
(LL) is analyzed. Using conformal field theory techniques we give a complete
proof of the equivalence in the NS sector. It is shown that the SL-LL
correspondence is based on the equivalence of chiral objects including suitably
chosen chiral structure constants of all the three Liouville theories involved.Comment: The Introduction expanded, main points of the paper clarified.
Misprints corrected and references added. Published in JHE
Braiding properties of the N=1 super-conformal blocks (Ramond sector)
Using a super scalar field representation of the chiral vertex operators we
develop a general method of calculating braiding matrices for all types of N=1
super-conformal 4-point blocks involving Ramond external weights. We give
explicit analytic formulae in a number of cases.Comment: LaTeX, 42+1 pages, typo correcte
Elliptic recurrence representation of the N=1 superconformal blocks in the Ramond sector
The structure of the 4-point N=1 super-conformal blocks in the Ramond sector
is analyzed. The elliptic recursion relations for these blocks are derived.Comment: 21 pages, no figures. An error in the description of the R-NS block
of the Ramond field and all its consequences correcte
Joining-splitting interaction of non-critical string
The joining--splitting interaction of non-critical bosonic string is analyzed
in the light-cone formulation. The Mandelstam method of constructing tree
string amplitudes is extended to the bosonic massive string models of the
discrete series. The general properties of the Liouville longitudinal
excitations which are necessary and sufficient for the Lorentz covariance of
the light-cone amplitudes are derived. The results suggest that the covariant
and the light-cone approach are equivalent also in the non-critical dimensions.
Some aspects of unitarity of interacting non-critical massive string theory are
discussed.Comment: 38 pages, 4 embedded figures, discussion in the Introduction
clarified, Appendix D and some material from Section 5 remove
Singular vector structure of quantum curves
We show that quantum curves arise in infinite families and have the structure
of singular vectors of a relevant symmetry algebra. We analyze in detail the
case of the hermitian one-matrix model with the underlying Virasoro algebra,
and the super-eigenvalue model with the underlying super-Virasoro algebra. In
the Virasoro case we relate singular vector structure of quantum curves to the
topological recursion, and in the super-Virasoro case we introduce the notion
of super-quantum curves. We also discuss the double quantum structure of the
quantum curves and analyze specific examples of Gaussian and multi-Penner
models.Comment: 33 pages; proceedings of the 2016 AMS von Neumann Symposiu
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