c M < 1 String Theory as a Constrained Topological Sigma Model

  • Pablo M. Llatas
  • Published 1994

Abstract

It has been argued by Ishikawa and Kato that by making use of a specific bosonization, cM = 1 string theory can be regarded as a constrained topological sigma model. We generalize their construction for any (p, q) minimal model coupled to two dimensional (2d) gravity and show that the energy–momentum tensor and the topological charge of a constrained topological sigma model can be mapped to the energy–momentum tensor and the BRST charge of cM < 1 string theory at zero cosmological constant. We systematically study the physical state spectrum of this topological sigma model and recover the spectrum in the absolute cohomology of cM < 1 string theory. This procedure provides us a manifestly topological representation of the continuum Liouville formulation of cM < 1 string theory. E-mail address: llatas@th.rug.nl Address after April 1, 1995: Department of Physics, University of California at Santa Barbara, CA 93106, USA. E-mail address: roy@th.rug.nl Address after January 15, 1995: Departamento de Fisica de Particulas, Universidade de Santiago, E-15706, Santiago de Compostela, Spain. It has been shown recently from various points of view that cM = 1 string theory has manifestly topological field theoretic descriptions. It was first pointed out in ref.[1] that a special Kazama-Suzuki coset model is equivalent to cM = 1 matter coupled to 2d gravity. Further arguments in favor of the topological nature of cM = 1 string theory were given by identifying it with a topological sigma model [2], a topological G/G model [3] as well as a topological Landau-Ginzburg model [4,5] with a particular superpotential. The latter identification also clarified the origin of the long suspected integrability structure [5,6] in cM = 1 string theory. It should be pointed out here that in these works the equivalence was established by comparing the cohomology structure as well as by computing some correlation functions which agree with the matrix–model results. A more direct approach, clarifying the reason why the observables can be obtained from a topological model, was taken by Ishikawa and Kato in ref.[7]. They have shown that by making use of a specific bosonization one can identify cM = 1 string theory with a topological sigma model at the level of Lagrangians rather than at the level of amplitudes. The topological nature of the Liouville approach to cM < 1 string theory is not as clear as in cM = 1 case. It has long been known that certain topological matter coupled to 2d topological gravity reproduce [8,9] the matrix–model results of cM < 1 string theory. The Landau-Ginzburg formulation and the integrability structure in this case are also fairly well-understood [10]. After a considerable amount of effort a family of twisted N = 2 superconformal structures have been revealed [11,12,13] in the continuum Liouville approach to cM < 1 string theory indicating a close relationship with some topological field theories. Using this information it became clear why (1, q) models coupled to gravity are topological [12]. But still a manifestly topological representation of the Liouville formulation of cM < 1 string theory remained illusive. An attempt in this direction was made in ref.[14]. By using a bosonization (which reduced to the topological gravity formulation of Distler [15] as a special case), we found that there is a topological gravity structure in any (p, q) model coupled to 2d gravity. It was noted also that the total BRST charge of the topological gravity is different from the string BRST charge and hence it was not clear how to obtain the full spectrum of cM < 1 string theory in the topological gravity representation. In this paper, we look at a different bosonization similar to the one found in ref.[7] for cM = 1 string theory. We generalize the construction for any (p, q) minimal model coupled to 2d gravity and show in analogy that cM < 1 string theory can also be regarded

Cite this paper

@inproceedings{Llatas1994cM, title={c M < 1 String Theory as a Constrained Topological Sigma Model}, author={Pablo M. Llatas}, year={1994} }