Fractional supersymmetric Liouville theory and the multi-cut matrix models

Abstract

We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p, q) minimal fractional superstring theories appear in the Z k -symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators. * Every odd k-cut model (i.e. k is odd) has the same contour integral as even 2k-cut models have. They are, however, physically different systems because their Liouville directions e −bφ = Re (ζ bos ) = Re (ζ k ) are different. 5 Only when k ≤ 2, the two-matrix models can include the one-matrix models as the special case of the system because the Gaussian potential V (y) = y 2 which is necessary for the reduction into one-matrix model is forbidden in the higher Z k symmetric case. 6 We cannot use this measure when the number of the matrices in the model is odd, which includes one-matrix models and matrix quantum mechanics. 7 This kind of matrix contour integral is also observed in the supermatrix description of the type 0 superstrings [57].

Central charges of para-Liouville and Toda theories from M5-branes

“…Generalization of NSR superstrings using these algebras were explored e.g. in [16,17]. The m-th para-W ( G) algebra is the symmetry of the m-th para-Toda model of type G, which has the following action [18] …”

Stokes phenomena and quantum integrability in non-critical string/M theory

“…In particular, these critical points are controlled by multi-component KP hierarchy [39] and this fact makes possible various quantitative analysis of the matrix models [43,44,72]. What is more, the two-cut {θ I } I (1) critical points were found to describe minimal type 0 superstring theory [81][82][83], and, as an extension of this, a special kind of the multi-cut critical points (which is also shown in Section 2.2.1) were proposed to describe minimal fractional superstring theory (or minimal parafermionic string theory) [73]. An interesting new feature found by quantitative analyses of these critical points is the fact that these multi-cut systems generally include a number of perturbative vacua in its string-theory landscape [43] and also include various perturbative string-theory sectors in its wavefunctions [44].…”

“…This kind of study has been investigated from various viewpoints [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. In this paper, succeeding the previous study of the authors [72], we investigate this issue in the framework of the multi-cut two-matrix models [39,73] [43,44,72].…”

“…In this paper, on the other hand, we extend this boundary condition to wider classes of the multi-cut critical points (general number of cuts, k, and general Poincaré index, r), especially the critical points which correspond to minimal fractional superstring (or parafermionic string) theory [73]. A major difference from the critical points of the previous study is lack of the Z k -symmetry which is intrinsic in the multi-cut two-matrix models.…”

Analytic study for the string theory landscapes via matrix models

“…The corresponding conditions for the Stokes matrices are known as the multi-cut boundary condition [23]. In particular, in the case of (p, q) minimal string theory, the constraint is the same as p-cut critical points of the multi-cut matrix models [31][32][33][34].…”