Heterotic-type IIA duality and degenerations of K3 surfaces

Abstract

Abstract:We study the duality between four-dimensional N = 2 compactifications of heterotic and type IIA string theories. Via adiabatic fibration of the duality in six dimensions, type IIA string theory compactified on a K3-fibred Calabi-Yau threefold has a potential heterotic dual compactification. This adiabatic picture fails whenever the K3 fibre degenerates into multiple components over points in the base of the fibration. Guided by monodromy, we identify such degenerate K3 fibres as solitons generalizing the NS5-brane in heterotic string theory. The theory of degenerations of K3 surfaces can then be used to find which solitons can be present on the heterotic side. Similar to small instanton transitions, these solitons escort singular transitions between different Calabi-Yau threefolds. Starting from well-known examples of heterotic-type IIA duality, such transitions can take us to type IIA compactifications with unknown heterotic duals.

Tensionless strings and the weak gravity conjecture

“…More generally, however, the K3-surface K of the dual heterotic compactification space K × T 2 is not elliptically fibered globally. Type IIA -heterotic duality under such more general conditions has been revisited in the recent work [47]. More specifically, degenerations of the K3 fiber in the fibration (2.24) of Y 3 can lead to heterotic 5-brane defects in the dual theory.…”

“…Upon S 1 -reduction, which takes us to the dual IIA string on Y 3 , the M5-brane turns into an NS5-brane wrapped on the K3 surface C 0 . As an NS5-brane on K3 is known to be dual to the heterotic string in 6d [46], adiabatically fibering it over the base of the K3 fibration again identifies the string in question with the heterotic one, albeit compactified in a less standard way (see the recent work [47] for an account of that more general Type IIA/heterotic duality).The appearance of a potentially weakly coupled, critical heterotic string from a D3-brane wrapped on a shrinking curve C 0 allows us to determine the charge and mass spectrum in some detail, at least near that limit. However, even for configurations where the heterotic string is non-perturbative and not necessarily weakly coupled, estimates for the spectrum can be made by considering its elliptic genus.…”

“…Upon S 1 -reduction, which takes us to the dual IIA string on Y 3 , the M5-brane turns into an NS5-brane wrapped on the K3 surface C 0 . As an NS5-brane on K3 is known to be dual to the heterotic string in 6d [46], adiabatically fibering it over the base of the K3 fibration again identifies the string in question with the heterotic one, albeit compactified in a less standard way (see the recent work [47] for an account of that more general Type IIA/heterotic duality).…”

Towards generalized mirror symmetry for twisted connected sum G2 manifolds

“…degenerations of K3 fibres [72,73] together with a generalization to fibre components of multiplicity > 1, see also [74,75]. For any pair of the examples of building blocks tabulated above, we may find hyper Kähler rotations for the elliptic K3 fibres such that…”

Modular forms as classification invariants of 4D $$ \mathcal{N} $$ = 2 Heterotic-IIA dual vacua

“…A Heterotic string compactification to 3+1-dimensions has an unbroken N = 2 supersymmetry (8 supersymmetry charges), if and only if the right-mover of the internal worldsheet CFT contains an N = 4 superconformal algebra (SCA) with central chargec = 6 and an N = 2 free SCA withc = 3 corresponding to a flat space of one complex dimension [14][15][16]. We restrict our attention in this article only to compactifications without an NS5-brane or its generalizations discussed in section 5 of [17].…”