113 research outputs found

### Anomaly matching in QCD thermal phase transition

We study an 't Hooft anomaly of massless QCD at finite temperature. With the
imaginary baryon chemical potential at the Roberge-Weiss point, there is a
$\mathbb{Z}_2$ symmetry which can be used to define confinement. We show the
existence of a mixed anomaly between the $\mathbb{Z}_2$ symmetry and the chiral
symmetry, which gives a strong relation between confinement and chiral symmetry
breaking. The anomaly is a parity anomaly in the QCD Lagrangian reduced to
three dimensions. It is reproduced in the chiral Lagrangian by a topological
term related to Skyrmion charge, matching the anomaly before and after QCD
phase transition. The effect of the imaginary chemical potential is suppresssed
in the large $N$ expansion, and we discuss implications of the 't~Hooft anomaly
matching for the nature of QCD phase transition with and without the imaginary
chemical potential. Arguments based on universality alone are disfavored, and a
first order phase transition may be the simplest possibility if the large $N$
expansion is qualitatively good.Comment: 41 pages, 5 figures. V2: references adde

### Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories

We consider general 5d $SU(N)$ quiver gauge theories whose nodes form an ADE
Dynkin diagram of type $G$. Each node has $SU(N_i)$ gauge group of general
rank, Chern-Simons level $\kappa_i$ and additional $w_i$ fundamentals. When the
total flavor number at each node is less than or equal to $2N_i-2|\kappa_i|$,
we give general rules under which the symmetries associated to instanton
currents are enhanced to $G \times G$ or a subgroup of it in the UV 5d
superconformal theory. When the total flavor number violates that condition at
some of the nodes, further enhancement of flavor symmetries occurs. In
particular we find a large class of gauge theories interpreted as $S^1$
compactification of 6d superconformal theories which are waiting for
string/F-theory realization. We also consider hypermultiplets in
(anti-)symmetric representation.Comment: 22 pages; v2: references adde

### From 4d Yang-Mills to 2d $\mathbb{CP}^{N-1}$ model: IR problem and confinement at weak coupling

We study four-dimensional $\mathrm{SU}(N)$ Yang-Mills theory on $\mathbb{R}
\times \mathbb{T}^3=\mathbb{R} \times S^1_A \times S^1_B \times S^1_C$, with a
twisted boundary condition by a $\mathbb{Z}_N$ center symmetry imposed on
$S^1_B \times S^1_C$. This setup has no IR zero modes and hence is free from IR
divergences which could spoil trans-series expansion for physical observables.
Moreover, we show that the center symmetry is preserved at weak coupling
regime. This is shown by first reducing the theory on $\mathbb{T}^2=S_A \times
S_B$, to connect the model to the two-dimensional $\mathbb{CP}^{N-1}$-model.
Then, we prove that the twisted boundary condition by the center symmetry for
the Yang-Mills is reduced to the twisted boundary condition by the
$\mathbb{Z}_N$ global symmetry of $\mathbb{CP}^{N-1}$. There are $N$ classical
vacua, and fractional instantons connecting those $N$ vacua dynamically restore
the center symmetry. We also point out the presence of singularities on the
Borel plane which depend on the shape of the compactification manifold, and
comment on its implications.Comment: 37 pages, 5 figures; v2:references adde

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