Topological Landau-Ginzburg model of two-dimensional string theory

Abstract

We study a topological Landau-Ginzburg model with superpotential W (X) = X −1 . This is argued to be equivalent to c = 1 string theory compactified at the self-dual radius.We compute the tree-level correlation function of N tachyons in this theory and show their agreement with matrix-model results. We also discuss the nature of contact terms, the perturbed superpotential and the flow of operators in the small phase space. The role of gravitational descendants in this theory is examined, and the tachyon two-point function in genus 1 is obtained using a conjectured modification of the gravitational recursion relations.

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry

“…It would be interesting to see if the methods of this paper can be extended to other models, for example, the K-th N = 2 unitary minimal model which can be realized as the SU(2) K / U(1) Kazama-Suzuki model or as the IR limit of the Landau-Ginzburg model with the superpotential W = X K+2 . In fact, the equivalence of the two models motivated the observation of [10,11] that certain correlation functions of the SL(2, R) 1+2 / U(1) Kazama-Suzuki model and the W = X −1 Landau-Ginzburg model agree. (As pointed out in the first reference of [30], for certain purposes SL(2, R) K / U(1) can be regarded as an analytic continuation of SU(2) K / U(1) to negative K.) More generally, it was proposed in [12] that there is a relation between the SL(2, R) k+2 / U(1) Kazama-Suzuki model and (W = X −k )/Z k Landau-Ginzburg orbifold (for integer k).…”

“…Instead of a 2d Black Hole we consider a fermionic 2d Black Hole, defined as the level k SL(2, R)/ U(1) Kazama-Suzuki supercoset model [7], and instead of sine-Lioville theory we consider N = 2 supersymmetric Liouville theory [8]. This duality was conjectured in [9] from the space-time point of view; closely related ideas were discussed earlier in [10,11,12], and the duality was studied more recently in [13]. The supercoset model can be viewed as an N = 1 supersymmetric sigmamodel with target-space metric (1.1).…”

Topological strings with scaling violation and Toda lattice hierarchy

“…It is originally defined as a non-critical string theory and has physical scattering process among tachyons. Therefore, it is an astonishing fact that the c = 1 string theory is topological [6] [7] [8] [9] and integrable [10] [11]. Another example is the topological CP 1 model [12] [13] [14].…”

Notes on the S-matrix of bosonic and topological non-critical strings

“…Strong evidence in favor of this equivalence has been presented on the level of BRST cohomologies and correlation functions in [17,18]. It has been further argued that there is another equivalence between the topologically twisted coset SL(2, IR) 1 /U (1) and the topological Landau-Ginzburg (LG) model with superpotential W (X) = X −1 [19]. This suggests an additional connection between the topologically twisted coset CFT and the topological string theory on the conifold [20,21].…”