
One of the embarrassments of string field theory [1, 2] is that it has fewer symmetries than the first quantized approach. Reparameterization invariance is nowhere to be seen, which accounts for the fact that the midpoints and endpoints of strings become special points. Worse, the light cone theory seems to be totally incompatible with the midpoint theory. They seem to triangulate moduli space in entirely different ways. Each is totally different off-shell, each has a different set of interactions, yet they miraculously yield the same S matrix. For example, for closed strings, the nonpolynomial closed string field theory triangulates moduli space in a highly nontrivial fashion, while the light cone theory triangulates moduli space in an almost trivial fashion via strings that fission. Our goal is to postulate a geometric string field theory [3–7] in which reparameterization symmetry is built in from the start, that is, we wish to gauge the reparameterization group. In this way, one should be able to select as gauge choices either the endpoint or midpoint as special points along the string. Then, we should be able to view the various string field theories as gauge choices, that is, the “midpoint gauge” and “endpoint gauge”. This, in turn, would give us a unifying principle by which all self-consistent string field theories could be seen as gauge choices of a single theory.
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