Non-Perturbative Heterotic D=6,4 Orbifold Vacua

TL;DR

The paper demonstrates that a broad class of non-perturbative heterotic orbifolds in $D=6$, $N=1$ can be made consistent despite violating standard modular invariance, by incorporating non-perturbative five-brane effects and antisymmetric $B$-field flux shifts $E_B$. It develops a framework linking perturbative spectra (with $E_B$-induced shifts) to non-perturbative sectors through small-instanton physics and index-theorem counts on $Z_M$ ALE spaces, and shows that some models are heterotic duals of Type IIB orientifolds, including through several $Z_M^A$ constructions for even $M$. The work further extends these ideas toward $D=4$, $N=1$ and demonstrates chirality-changing transitions in certain $Z_N imes Z_M$ orbifolds, revealing non-perturbative connections between vacua with different numbers of chiral generations. Collectively, the results provide a tractable, largely perturbative-by-construction method to realize and analyze a diverse set of non-perturbative heterotic vacua, anchored by well-understood small-instanton dynamics and Coulomb-phase tensor multiplets, with concrete duals in Type IIB orientifolds and potential extensions to phenomenologically relevant four-dimensional theories.

Abstract

We consider D=6, N=1, Z_M orbifold compactifications of heterotic strings in which the usual modular invariance constraints are violated. It is argued that in the presence of non-perturbative effects many of these vacua are nevertheless consistent. The perturbative massless sector can be computed explicitly from the perturbative mass formula subject to an extra shift in the vacuum energy. This shift is associated to a non-trivial antisymmetric B-field flux at the orbifold fixed points. The non-perturbative piece is given by five-branes either moving in the bulk or stuck at the fixed points, giving rise to Coulomb phases with tensor multiplets. The heterotic duals of some Type IIB orientifolds belong to this class of orbifold models. We also discuss how to carry out this type of construction to the D=4, N=1 case and specific $Z_M\times Z_M$ examples are presented in which non-perturbative transitions changing the number of chiral generations do occur.