Abstract
We explore a novel type of transition in certain 6D and 4D quantum field theories, in which the matter content of the theory changes while the gauge group and other parts of the spectrum remain invariant. Such transitions can occur, for example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation. These matter transitions are realized by passing through superconformal theories at the transition point. We explore these transitions in dual F-theory and heterotic descriptions, where a number of novel features arise. For example, in the heterotic description the relevant 6D SU(7) theories are described by bundles on K3 surfaces where the geometry of the K3 is constrained in addition to the bundle structure. On the F-theory side, non-standard representations such as the three-index antisymmetric representation of SU(N) require Weierstrass models that cannot be realized from the standard SU(N) Tate form. We also briefly describe some other situations, with groups such as Sp(3), SO(12), and SU(3), where analogous matter transitions can occur between different representations. For SU(3), in particular, we find a matter transition between adjoint matter and matter in the symmetric representation, giving an explicit Weierstrass model for the F-theory description of the symmetric representation that complements another recent analogous construction.
Highlights
A variety of different types of transitions can occur in physical theories in which the massless or light spectrum of the theory changes
For example, for SU(6) and SU(7) gauge groups, where matter fields in a three-index antisymmetric representation and the fundamental representation are exchanged in the transition for matter in the two-index antisymmetric representation
In both cases the transition can be described by moving along a one-parameter family of theories that passes through a strongly coupled superconformal fixed point, but does not move onto the tensor branch. In both the heterotic bundle and the resolved F-theory geometry these transitions are realizable as geometric transitions. Our description of these transitions in both F-theory and the heterotic theory is for the most part quite general, but for comparison of these perspectives we focus in particular on cases where the F-theory geometry is compactified on a K3 fibration over a base B and the heterotic geometry describes an elliptic fibration over the same base B
Summary
A variety of different types of transitions can occur in physical theories in which the massless or light spectrum of the theory changes. On the heterotic side these transitions arise when an instanton is shrunk and moved into a separate component of the bundle structure group in the same E8 component In both cases the transition can be described by moving along a one-parameter family of theories that passes through a strongly coupled superconformal fixed point, but does not move onto the tensor branch. In both the heterotic bundle and the resolved F-theory geometry these transitions are realizable as geometric transitions (i.e. topology changing transitions). A variety of useful technical results are provided in the appendices
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