We discuss the conditions under which Higgs and confining regimes in gauge theories with fundamental representation matter fields can be sharply distinguished. It is widely believed that these regimes are smoothly connected unless they are distinguished by the realization of global symmetries. However, we show that when a U(1) global symmetry is spontaneously broken in both the confining and Higgs regimes, the two phases can be separated by a phase boundary. The phase transition between the two regimes may be detected by a novel topological vortex order parameter. We first illustrate these ideas by explicit calculations in gauge theories in three spacetime dimensions. Then we show how our analysis generalizes to four dimensions, where it implies that nuclear matter and quark matter are sharply distinct phases of QCD with an approximate SU(3) flavor symmetry.
Bibliographical noteFunding Information:
We are especially grateful to Fiona Burnell for extensive discussions and collaboration at the initial stages of this project. We are also grateful to M. Alford, F. Benini, S. Benvenuti, K. S. Damle, L. Fidkowski, D. Harlow, Z. Komargodski, S. Minwalla, E. Poppitz, N. Seiberg, Y. Tanizaki, and M. Ünsal for helpful discussions and suggestions during the long gestation of this paper. A. C. acknowledges support from the University of Minnesota. T. J. is supported by a UMN CSE Fellowship. S. S. acknowledges the support of Iowa State University startup funds. L. Y. acknowledges support from the U.S. Department of Energy Grant No. DE-SC-0011637.
© 2020 authors. Published by the American Physical Society.