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

Light-cone formulation and spin spectrum of non-critical fermionic string

A free fermionic string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<d<10$. It is shown that after the GSO projection this model is equivalent to the fermionic massive string and to the non-critical Rammond-Neveu-Schwarz string. The spin spectrum of the model is analysed. For $d=4$ the character generating functions is obtained and the particle content of first few levels is numerically calculated.Comment: 13 page

From CFT to Ramond super-quantum curves

As we have shown in the previous work, using the formalism of matrix and eigenvalue models, to a given classical algebraic curve one can associate an infinite family of quantum curves, which are in one-to-one correspondence with singular vectors of a certain (e.g. Virasoro or super-Virasoro) underlying algebra. In this paper we reformulate this problem in the language of conformal field theory. Such a reformulation has several advantages: it leads to the identification of quantum curves more efficiently, it proves in full generality that they indeed have the structure of singular vectors, it enables identification of corresponding eigenvalue models. Moreover, this approach can be easily generalized to other underlying algebras. To illustrate these statements we apply the conformal field theory formalism to the case of the Ramond version of the super-Virasoro algebra. We derive two classes of corresponding Ramond super-eigenvalue models, construct Ramond super-quantum curves that have the structure of relevant singular vectors, and identify underlying Ramond super-spectral curves. We also analyze Ramond multi-Penner models and show that they lead to supersymmetric generalizations of BPZ equations.Comment: 72 page

Non-Critical Light-Cone String

The free non-critical string quantum model is constructed directly in the light-cone variables in the range of dimensions $1<D<25$. The longitudinal degrees of freedom are described by an abstract Verma module. The central charge of this module is restricted by the requirement of the closure of the nonlinear realization of the Poincare algebra. The spin content of the model is analysed. In particular for D=4 the explicit formulae for the character generating functions of the open and closed massive strings are given and the spin spectrum of first 12 excited levels is calculated. It is shown that for the space-time dimension in the range $1<D<25$ the non-critical light-cone string is equivalent to the critical massive string and to the non-critical Nambu-Goto string.Comment: 20 pages, Late

Conformal blocks related to the R-R states in the \hat c =1 SCFT

We derive an explicit form of a family of four-point Neveu-Schwarz blocks with $\hat c =1,$ external weights $\Delta_i = 1/8$ and arbitrary intermediate weight. The derivation is based on a set of identities obeyed in the free superscalar theory by correlation functions of fields satisfying Ramond condition with respect to the bosonic (dimension 1) and the fermionic (dimension 1/2) currents.Comment: 15 pages, no figure

Whittaker pairs for the Virasoro algebra and the Gaiotto - BMT states

In this paper we analyze Whittaker modules for two families of Wittaker pairs related to the subalgebras of the Virasoro algebra generated by L_r,..., L_{2r} and L_1,L_n. The structure theorems for the corresponding universal Whittaker modules are proved and some of their consequences are derived. All the Gaiotto {arXiv:0908.0307} and the Bonelli-Maruyoshi-Tanzini {arXiv:1112.1691} states in an arbitrary Virasoro algebra Verma module are explicitly constructed.Comment: 19 pages, Revision of Section 3 (Theorems 3.5, 3.6 and Corollary 3.7 of Section 3 of the first published version are valid only in the case of $n=3$), correction of Lemma 2.7, one reference adde

Liouville theory and uniformization of four-punctured sphere

Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.Comment: 17 pages, no figure

Static Quark Potential from the Polyakov Sum over Surfaces

Using the Polyakov string ansatz for the rectangular Wilson loop we calculate the static potential in the semiclassical approximation. Our results lead to a well defined sum over surfaces in the range $1<d<25$.Comment: 17 pages, (with a TeX error on the title page corrected - nothing else changed

Classical and quantum massive string

The classical and the quantum massive string model based on a modified BDHP action is analyzed in the range of dimensions $1<d<25$. The discussion concerning classical theory includes a formulation of the geometrical variational principle, a phase-space description of the two-dimensional dynamics, and a detailed analysis of the target space geometry of classical solutions. The model is quantized using "old" covariant method. In particular an appropriate construction of DDF operators is given and the no-ghost theorem is proved. For a critical value of one of free parameters of the model the quantum theory acquires an extra symmetry not present on the classical level. In this case the quantum model is equivalent to the noncritical Polyakov string and to the old Fairlie-Chodos-Thorn massive string.Comment: 29 pages, 2 figures, LaTeX + eps