Abstract
The scattering amplitudes of gauge bosons in heterotic and open superstring theories are related by the single-valued projection which yields heterotic amplitudes by selecting a subset of multiple zeta value coefficients in the α′ (string tension parameter) expansion of open string amplitudes. In the present work, we argue that this relation holds also at the level of low-energy expansions (or individual Feynman diagrams) of the respective effective actions, by investigating the beta functions of two-dimensional sigma models describing world-sheets of open and heterotic strings. We analyze the sigma model Feynman diagrams generating identical effective action terms in both theories and show that the heterotic coefficients are given by the single-valued projection of the open ones. The single-valued projection appears as a result of summing over all radial orderings of heterotic vertices on the complex plane representing string world-sheet.
Highlights
In [2] two of the present authors demonstrated that the single trace part of the N –point tree–level heterotic superstring amplitudes AHNET is given by the single–valued projection of the corresponding type–I amplitude AIN : AHNET = sv(AIN )
We addressed the question how the relations between open and heterotic superstring scattering amplitudes discovered in Ref. [2] are reflected by the properties of the effective gauge field theory
According to Ref. [2], the amplitudes describing the scattering of gauge bosons in both theories, more precisely the amplitudes involving a given single trace gauge group factor, are related by the sv projection which maps open to heterotic amplitudes order by order in the α expansion
Summary
The purpose of this section is to establish notation and to recall some basic results of sigma-model computations in open superstring theory. The action describing the world-sheet Xμ(σ1, σ2) of open strings propagating in a general non-abelian gauge background Aμ(X) contains the bulk and boundary contributions [7, 8]:. In this theory, Φμ are the fermionic coordinates, with φμ = Φμ|∂Σ. The loop expansion leads to background-dependent ultraviolet divergences originating from the boundary couplings. Note that in the open string case, the solid line is incorporated in order to remind us that the vertices are located at the boundary, while in the heterotic case, a similar line will represent a propagating fermion. Corrections of order O(α 3) correspond to three–loop effects and are expected to be nonvanishing
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