Abstract
D-instanton world-volume theory has open string zero modes describing collective coordinates of the instanton. The usual perturbative amplitudes in the D-instanton background suffer from infra-red divergences due to the presence of these zero modes, and the usual approach of analytic continuation in momenta does not work since all open string states on a D-instanton carry strictly zero momentum. String field theory is well-suited for tackling these issues. However we find a new subtlety due to the existence of additional zero modes in the ghost sector. This causes a breakdown of the Siegel gauge, but a different gauge fixing consistent with the BV formalism renders the perturbation theory finite and unambiguous. At each order, this produces extra contribution to the amplitude besides what is obtained from integration over the moduli space of Riemann surfaces.
Highlights
JHEP08(2020)075 theory was eventually resolved using string field theory, leading to results in agreement with those in the dual matrix model [8]
The usual perturbative amplitudes in the D-instanton background suffer from infra-red divergences due to the presence of these zero modes, and the usual approach of analytic continuation in momenta does not work since all open string states on a D-instanton carry strictly zero momentum
While the conventional world-sheet approach does not give us a systematic procedure for dealing with these divergences, the treatment of these collective modes in string field theory is the same as in ordinary quantum field theory. Instead of treating these modes perturbatively, we leave them unintegrated at the beginning, evaluate the Feynman diagrams using the propagators of the other modes, and after summing over all the Feynman diagrams we integrate over the collective modes
Summary
Let us consider a quantum field theory with instanton solutions. In order to identify the instanton contribution to the Green’s function of a collection of operators, which we shall denote by O, we shall divide the path integral over the fields Φ into different sectors labelled by their instanton number. DΦp exp[Sp] O gives the amplitudes containing world-sheets that do not have any boundary ending on the D-instanton, but we must allow world-sheets with multiple disconnected components, including vacuum bubbles which do not have any external vertex operator insertion. For D-instantons this means that we must remove all diagrams in which all the external state vertex operators end on world-sheets without any boundary ending on the D-instanton, even if they are multiplied by vacuum bubbles containing boundaries that do end on the D-instanton. At least one of the disconnected components must have both, a boundary ending on the D-instanton and a closed string vertex operator insertion Each such contribution will be multiplied by a single factor of N e−1/gs, irrespective of the number of disconnected components it has
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