Second quantised string theory

Abstract

An attempt is made to construct a non-perturbative, second quantised framework for string theory by describing worldsheets implicitly as the solution surfaces of D — 2 functions on D-dimensional space time. The formalism in fact generalises to extended objects of arbitrary dimension. The worldsheets are not parameterised and hence modular invariance and duality should be incorporated at a fundamental level, thus avoiding the overcounting of vacuum graphs encountered with string field theory. Couplings to background fields are introduced which reduce to the usual Polyakov couplings on choosing a parameterisation of the worldsheet. The formalism has a natural GL{D — 2,R) gauge invariance which is awkward to fix owing to the existence of a delta function in the action. BRST ghosts can be introduced however it is not clear how to remove all the gauge invariance while the delta function remains in the action. Replacing the delta function with a more general function of the D — 2 implicit functions yields gauge fixed equations of motion however it is no longer clear how to introduce ghosts. A Hamiltonian quantisation is presented however ambiguities arise for cases of greater complexity than the particle in two dimensions. The formalism appears to furnish a topological field theory for vanishing metric and may prove useful in investigating the conjectured unbroken phase of general relativity.

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Identifiers

ORCID for Timothy Morris: orcid.org/0000-0001-6256-9962

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