## Topological Landau-Ginzburg formulation and integrable structure of two-dimensional string theory

We construct a topological Landau-Ginzburg formulation of the two-dimensional string at the self-dual radius. The model is an analytic continuation of the Ak+1 minimal model to k = -3. We compute the superpotential and calculate tachyon correlators in the Landau-Ginzburg framework. The results are in complete agreement with matrix model calculations. We identify the momentum one tachyon as the puncture operator, non-negative momentum tachyons as primary fields, and negative momentum ones as descendants. The model thus has an infinite number of primary fields, and the topological metric vanishes on the small phase space when restricted to these. We find a parity invariant multi-contact algebra with irreducible contact terms of arbitrarily large number of fields. The formulation of this Landau-Ginzburg description in terms of period integrals coincides with the genus zero W1+∞ identities of two-dimensional string theory. We study the underlying Toda lattice integrable hierarchy in the Lax formulation and find that the Landau-Ginzburg superpotential coincides with a derivative of the Baker-Akhiezer wave function in the dispersionless limit. This establishes a connection between the topological and integrable structures. Guided by this connection we derive relations formally analogous to the string equation. © 1994.

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## Related Subject Headings

- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics

### Citation

*Nuclear Physics, Section B*,

*425*(1–2), 150–172. https://doi.org/10.1016/0550-3213(94)90176-7

*Nuclear Physics, Section B*425, no. 1–2 (August 22, 1994): 150–72. https://doi.org/10.1016/0550-3213(94)90176-7.

*Nuclear Physics, Section B*, vol. 425, no. 1–2, Aug. 1994, pp. 150–72.

*Scopus*, doi:10.1016/0550-3213(94)90176-7.

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Nuclear & Particles Physics
- 5107 Particle and high energy physics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
- 0105 Mathematical Physics