Spontaneous breaking of baryon symmetry in strongly coupled three-dimensional theories
Antón F. Faedo, Carlos Hoyos, Javier G. Subils
TL;DR
This work shows that baryon-number symmetry $U(1)_{\mathcal B}$ is spontaneously broken in a class of ${\cal N}=1$ $2+1$-dimensional theories with a discrete spectrum by constructing and analyzing a Goldstone-mode vector fluctuation in a holographic dual. Through a consistent four-dimensional supergravity truncation containing a massless vector dual to the monopole current and a baryonic vector, the authors derive the full set of coupled vector equations and implement a Goldstone-mode ansatz. They solve the equations in both confining ($k=0$) and non-confining ($k\neq 0$) backgrounds, using analytic reductions and numerical shooting to demonstrate normalizable, regular solutions that correspond to the Goldstone mode, with the mode persisting even when a nonzero Chern–Simons level is present. The results reinforce the holographic picture of a baryonic sector akin to the Klebanov–Strassler cascade in lower dimensions and motivate further checks via baryon-operator vevs and potential moduli-space structure.
Abstract
We show that baryon number symmetry is spontaneously broken in a class of three-dimensional, ${\cal N}=1$ supersymmetric theories with a discrete mass spectrum. These models serve as lower-dimensional, less-supersymmetric analogs of the Klebanov-Strassler solution, sharing properties such as the presence of a cascade. The spontaneous symmetry breaking is evidenced by the appearance of a Goldstone mode, which corresponds to a vector fluctuation in the gravity dual.