Timelike T-duality in the string field Schrödinger functional

Timelike T-duality of string theory appears as a symmetry of time evolution in string field theory, exchanging evolution through times t and 1/t, and exchanging boundary states with backgrounds. This is demonstrated by constructing the string field Schrödinger functional, the generator of time evolution, based on Feynman diagram arguments and in analogy with quantum field theory. There the functional can be described using only properties of first quantised particles on a timelike orbifold. Using new sewing rules applicable to both open and closed strings we generalise this approach to bosonic string theory and express the string field Schrödinger functional in terms of strings on S/Z2.