Abstract
We show how to make a topological string theory starting from an N = 4 superconformal theory. The critical dimension for this theory is c Ì = 2 (c = 6) . It is shown that superstrings (in both the RNS and GS formulations) and critical N = 2 strings are special cases of this topological theory. Applications for this new topological theory include: (1) Proving the vanishing to all orders of all scattering amplitudes for the self-dual N = 2 string with flat background, with the exception of the three-point function and the closed-string partition function; (2) Showing that the topological partition function of the N = 2 string on the K3 background may be interpreted as computing the superpotential in harmonic superspace generated upon compactification of type II superstrings from 10 to 6 dimensions; and (3) Providing a new prescription for calculating s uperstring amplitudes which appears to be free of total-derivative ambiguities.
Highlights
Topological quantum field theories in two dimensions have become increasingly important over the past few years
In a previous paper [5], we used topological theories in a reverse way to show the equivalence of various strings: Roughly speaking, we untwisted the supersymmetry of the critical bosonic string and found that it has a superconformal symmetry with central charge corresponding to the critical dimension of N = 1 superstrings
We have formulated a new topological string theory based on N = 4 superconformal symmetry which has critical dimension c = 2
Summary
Topological quantum field theories in two dimensions have become increasingly important over the past few years. In a previous paper [5] , we used topological theories in a reverse way to show the equivalence of various strings: Roughly speaking, we untwisted the supersymmetry of the critical bosonic string and found that it has a superconformal symmetry with central charge corresponding to the critical dimension of N = 1 superstrings. We coupled it to N = 1 supergravity and found that the theory is equivalent to the original bosonic string.
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