Matter in transition

TL;DR

This paper investigates novel matter content transitions in 6D and 4D quantum field theories, where matter representations change without altering the gauge group, realized via superconformal points and dual string theory descriptions.

Contribution

It introduces and analyzes matter transitions involving different representations in gauge theories, including explicit models and dual descriptions in F-theory and heterotic frameworks.

Findings

Matter transitions occur at superconformal points in certain gauge theories.

Explicit Weierstrass models for non-standard representations are constructed.

Analogous transitions are identified for groups like Sp(3), SO(12), and SU(3).

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.