On SO(32) heterotic — type I superstring duality in ten dimensions

Abstract

We provide some additional evidence in favour of the strong -weak coupling duality between the SO(32) heterotic and type I superstring theories by comparing terms quartic in the gauge field strength in their low-energy effective actions. We argue that these terms should not receive higher-loop string corrections so that duality should relate the leadingorder perturbative coefficients in the two theories. In particular, we demonstrate that the coefficient of the F 4 -term in the one-loop (torus) part of the SO(32) heterotic string action is exactly the same as the coefficient of the F 4 -term in the tree-level (disc) part of the type I action.October 1995 ⋆ e-mail address: tseytlin@ic.ac.uk † On leave from Lebedev Physics Institute, Moscow.

Heterotic — type I superstring duality and low-energy effective actions

“…Thus the absence of the trF 2 trF 2 term in the torus correction in SO(32) heterotic string is crucial for the consistency of the duality: in type I theory such double-trace term could not originate from the disc diagram which has only one boundary. As was pointed out in [18], the coefficient of the disc t 8 trF 4 term in type I theory [10,11] is indeed the same as the 1-loop coefficient of this term (see (3.8),(3.7)) the heterotic string [21,22].…”

“…2 There are, indeed, examples of terms in the string effective actions which are either not renormalised by string higher-loop corrections (like second-derivative terms and 'anomalycancelling' terms, see, e.g., [12,13,14,15]) or receive contributions only from specific orders of string perturbative expansion (see [16,17]). In [18] we considered a term quartic in the gauge field strength trF 4 which, in heterotic string theory, is absent at the tree level [19,20] but appears at the one-loop level [21,22,23]. We have argued that it does not receive corrections from higher loops since D = 10 supersymmetry relates [24,25] it to the 'anomaly-cancelling' term BtrF 4 [26] which is not renormalised at higher orders [27,15] (see also below).…”

“…Here we shall try to elucidate further the interplay between duality, supersymmetry and the structure of loop expansion in heterotic and type I theories by extending the discussion in [18] to the curvature-dependent R 4 -terms. We shall see that the relation between the R 4 corrections is more complicated than between the F 4 terms, reflecting the existence of several super-invariants containing R 4 contractions [30,24,25].…”

Two-loop superstrings VI Nonrenormalization theorems and the 4-point function

“…A second is from the duality [36] between the Heterotic E 8 × E 8 theory and M-theory [37], [38]. A third is from the interplay between space-time supersymmetry and space-time anomalies [33]. A discussion of such non-renormalization effects order by order in the string coupling was given in [34,35].…”

“…In particular, the Heterotic Spin(32)/Z 2 -Type I duality [30,31,32] has been used to argue that nonvanishing two-loop corrections to R 4 should arise on the Heterotic side [33].…”