Small Instanton Transitions in Heterotic M-Theory

TL;DR

This work analyzes non-perturbative small instanton transitions in heterotic M-theory, triggered when bulk five-branes collide with a boundary brane and convert into small instantons that smooth into modified holomorphic vector bundles. Using elliptically fibered Calabi--Yau threefolds and the spectral cover construction, the authors derive precise conditions under which chirality-changing and gauge-changing transitions occur, including the pivotal role of the fiber and base components of the five-brane class and the parameter $\lambda$. They show that chirality can change via absorption of base components (with $N_{gen}$ shifting by $\tfrac{1}{2}(2\eta+z-nc_1(B))\cdot z$) while gauge groups can change through absorption of fiber components, yielding reducible $SU(n)\times SU(m)$ bundles and corresponding unbroken gauge groups in $E_8$, all within a controlled mathematical framework using Fourier–Mukai transforms. The results connect distinct vacua with different topological data, illustrate the non-perturbative landscape of brane-world models, and hint at dual descriptions in F-theory via flux and fourfold topology changes.

Abstract

We discuss non-perturbative phase transitions, within the context of heterotic M-theory, which occur when all, or part, of the wrapped five-branes in the five-dimensional bulk space come into direct contact with a boundary brane. These transitions involve the transformation of the five-brane into a ``small instanton'' on the Calabi-Yau space at the boundary brane, followed by the ``smoothing out'' of the small instanton into a holomorphic vector bundle. Small instanton phase transitions change the number of families, the gauge group or both on the boundary brane, depending upon whether a base component, fiber component or both components of the five-brane class are involved in the transition. We compute the conditions under which a small instanton phase transition can occur and present a number of explicit, phenomenologically relevant examples.