TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.2.075
TI  - CFTs with $\mathbf{U(m)\times U(n)}$ global symmetry in 3D and the chiral phase transition of QCD
PY  - 2023/08/31
UR  - https://www.scipost.org/SciPostPhys.15.2.075
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 2
SP  - 075
A1  - Kousvos, Stefanos Robert
AU  - Stergiou, Andreas
AB  - Conformal field theories (CFTs) with $U(m)\times U(n)$ global symmetry in $d=3$ dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs are analyzed in $d=4-\varepsilon$ and $d=3$. This includes perturbative computations in the $\varepsilon$ and large-$n$ expansions as well as non-perturbative ones with the numerical conformal bootstrap. New perturbative results are presented and a variety of non-perturbative bootstrap bounds are obtained in $d=3$. Various features of the bounds obtained for large values of $n$ disappear for low values of $n$ (keeping $m<n$ fixed), a phenomenon which is attributed to a transition of the corresponding fixed points to the non-unitary regime. Numerous bootstrap bounds are found that are saturated by large-$n$ results, even in the absence of any features in the bounds. A double scaling limit is also observed, for $m$ and $n$ large with $m/n$ fixed, both in perturbation theory as well as in the numerical bootstrap. For the case of two-flavor massless QCD existing bootstrap evidence is reproduced that the chiral phase transition may be second order, albeit associated to a universality class unrelated to the one usually discussed in the $\varepsilon$ expansion. Similar evidence is found for the case of three-flavor massless QCD, where we observe a pronounced kink.
ER  -

@Article{10.21468/SciPostPhys.15.2.075,
	title={{CFTs with $\mathbf{U(m)\times U(n)}$ global symmetry in 3D and the chiral phase transition of QCD}},
	author={Stefanos R. Kousvos and Andreas Stergiou},
	journal={SciPost Phys.},
	volume={15},
	pages={075},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.2.075},
	url={https://scipost.org/10.21468/SciPostPhys.15.2.075},
}