New instanton effects in string theory

Abstract

We describe a new class of instanton effects in string compactifications that preserve only N = 1 supersymmetry in four dimensions. As is well-known, worldsheet or brane instantons in such a background can sometimes contribute to an effective superpotential for the moduli of the compactification. We generalize this phenomenon by showing that such instantons can also contribute to new multi-fermion and higher-derivative F -terms in the low-energy effective action. We consider in most detail the example of heterotic compactification on a Calabi-Yau threefold X with gauge bundle V , in which case we study worldsheet instanton effects that deform the complex structure of the moduli space associated to X and V . We also give new, slightly more economical derivations of some previous results about worldsheet instantons in Type IIA Calabi-Yau compactifications.

Perspectives on Pfaffians of heterotic world-sheet instantons

“…− which is a gauge-invariant quantity (here D + = D † − replaces the i∂ + above, leading to D replacing the D F above); this leads 6 …”

“…6 In 2, or more generally 8k + 2, dimensions the determinant line bundle of the complex chiral Dirac operator admits a canonical square root and √ det D is a section.…”

Derivative F-terms from heterotic M-theory five-brane instantons

“…The non-vanishing componets are G (2,1,1) , G (1,2,1) and G (2,2,0) . Here we are using notation from [17].…”

“…In [1] and [2] Beasley and Witten described a new class of instanton effects in N = 1 supersymmetric field theory and string theory. These effects are generating of derivative, or multi-fermion, F-terms.…”

“…In general, as was shown in [1], for N f ≥ N c instantons contribute to interactions of 2(N f − N c ) + 4 fermions. In the case of string theory, it was shown in [2] that derivative F-terms arise, in particular, from wrapping heterotic strings on non-isolated genus zero or higher genus curves. It is worth pointing out that, just like superpotential, derivative F-terms have a certain holomorphic signature.…”