Abstract
We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity ( Liouville field theory). In the Liouville sector, we show that four-point correlation functions of ‘tachyons’ exhibit logarithmic singularities, and that the theory turns out to be logarithmic. The relation with Zamolodchikov's logarithmic degenerate fields is also discussed. Our result holds for generic values of (p,q).
Highlights
Minimal string theories are interesting string laboratories whose target space is two dimensions
The total central charge is 26 for bosonic cases, and their worldsheet description can be realised by twodimensional gravity (Liouville field theory) coupled to (p, q) minimal conformal field theories [3, 4]
We find that quite many four-point functions of tachyons have logarithmic singularities for generic (p, q), and that minimal string theory is logarithmic
Summary
Minimal string theories are interesting string laboratories whose target space is two dimensions (see [1, 2] and the references therein). Zamolodchikov has recently shown an operator-valued relation of logarithmic degenerate fields with a particular type of primaries [15] Such primaries naturally emerge in two-dimensional gravity coupled to minimal matter. In the rest of this paper, we calculate Liouville four-point correlation functions of the gravitational sector of tachyons in two-dimensional gravity coupled to (p, q) minimal conformal field theories without applying the differentiation method [5, 17]. In [15], Liouville primaries with the following condition appear in our notation in an operator-valued relation of logarithmic degenerate fields: βm,n m) n). This condition coincides with the on-shell condition, i.e. eq (2.4). Since (ri, ti) ∈ Gp,q, this leads to the combinations in (3.2) and the inequalities (3.1)
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