Higher Derivative F-terms in N=2 Strings

TL;DR

This work investigates higher-derivative F-terms in N=2 string vacua, focusing on the generalized couplings $F_{g,n} W^{2g} (\Pi f)^n$ and their realization in heterotic compactifications on $K3\\times T^2$ with Type II dual descriptions. It derives holomorphic anomaly equations for both the standard $F_g$ terms and their $F_{g,n}$ extensions in the $O(2,n)$ moduli sector, and shows that the leading singularities near conifold-like loci reproduce the free energy of the $c=1$ string at a radius $R$, establishing a deep link between these higher-derivative couplings and non-perturbative string dynamics. The heterotic analysis yields recursion relations in the generating functions $G_g$ and $G_{g,n}$, while a D-brane realization of the conifold demonstrates that a suitable vector field can reproduce the leading singular structure, supporting the proposed dual picture. Overall, the results provide evidence for a deeper heterotic–Type II duality at the level of higher-derivative interactions and reveal a compelling connection to $c=1$ string theory, though the complete mapping away from leading singularities remains to be clarified.

Abstract

We study a special class of higher derivative F-terms of the form $F_{g,n}W^{2g}(Πf)^{n}$ where W is the N=2 gravitational superfield and $Π$ is the chiral projector applied to a non-holomorphic function $f$ of the heterotic dilaton vector superfield. We analyze these couplings in the heterotic theory on $K3\times T^2$ , where it is found they satisfy an anomaly equation as the well studied $F_{g,0}$ terms. We recognize that, near a point of SU(2) enhancement, a given generating function of the leading singularity of the $F_{g,n}$ reproduces the free energy of a c=1 string at an arbitrary radius R. According to the N=2 heterotic-type II duality in 4d, we then study these couplings near a conifold singularity, using its local description in terms of intersecting D-5-branes. In this context, it turns out that there exists, among the other states involved, a vector gauge field reproducing the heterotic leading singularity structure.