Yuya Tanizaki

We discuss the $SU(3)/[U(1)\ifmmode\times\else\texttimes\fi{}U(1)]$ nonlinear sigma model in 1+1D and, more broadly, its linearized counterparts. Such theories can be expressed as $U(1)\ifmmode\times\else\texttimes\fi{}U(1)$ gauge theories and therefore allow for two topological $\ensuremath{\theta}$ angles. These models provide a field theoretic description of the $SU(3)$ chains. We show that, for particular values of $\ensuremath{\theta}$ angles, a global symmetry group of such systems has a '

We elucidate that the phase diagram of massless $N$-flavor QCD under a ${\mathbb{Z}}_{N}$ flavor-twisted boundary condition (massless ${\mathbb{Z}}_{N}$-QCD) is constrained by a 't Hooft anomaly involving two-form gauge fields. As a consequence, massless ${\mathbb{Z}}_{N}$-QCD turns out to realize persistent order at any temperature and quark chemical potential; namely, the symmetric and gapped phase is strictly forbidden. This is the first result on the finite-$(T,\ensuremath{\mu})$ phase diagr

A bstract We consider the SU( N ) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p . We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2 π -periodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only ℤ N 1-form symmet

We discuss possible vacuum structures of SU(n) × SU(n) gauge theories with bifundamental matters at finite θ angles. In order to give a precise constraint, a mixed ’t Hooft anomaly is studied in detail by gauging the center ℤ n one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the con-straints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement.

The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model

Zero-dimensional $O(n)$-symmetric sigma models are studied using the Picard-Lefschetz integration method in the presence of small symmetry-breaking perturbations. Because of approximate symmetry, downward flows turn out to show significant structures: They slowly travel along the set of pseudoclassical points, and branch into other directions so as to span middle-dimensional integration cycles. We propose an efficient way to find such slow motions for computing Lefschetz thimbles. In the limit o

Abstract We construct an anomaly-preserving compactification of 4D gauge theories, including SU(N) Yang–Mills theory, $\mathcal {N}=1$ supersymmetric Yang–Mills theory, and quantum chromodynamics (QCD), down to 2D by turning on the ’t Hooft flux through T2. This provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and the multi-branch structure of vacua. We give a semiclassical description of these phenomena based on the cen

We consider multi-flavor massless (1 + 1)-dimensional QED with chemical potentials at finite spatial length and the zero-temperature limit. Its sign problem is solved using the mean-field calculation with complex saddle points.

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. Here, we study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.

A bstract We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small ℝ 2 × T 2 with a suitable magnetic flux. We first discuss the ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The T 2 compactification with the magnetic flux preserves the ’t Hooft anomaly, and the 2d effective theory is constrained by the same anomaly of 4d QCD(

We study new symmetries of the Cardy-Rabinovici model and their dynamical applications. The Cardy-Rabinovici model is a 4d U (1) gauge theory with electric and magnetic matters, which is a good playground for studying the dynamics of the Yang-Mills theory with θ angle. In this model, the electromagnetic S L (2, ℤ) self-duality is not realized in a naive way. Still, the S L (2, ℤ) transformations become legitimate duality operations by appropriately gauging the ℤ N 1-form symmetry. We construct n

A bstract We extend the definition of Lüscher’s lattice topological charge to the case of 4d SU( N ) gauge fields coupled with ℤ N 2-form gauge fields. This result is achieved while maintaining the locality, the SU( N ) gauge invariance, and ℤ N 1-form gauge invariance, and we find that the manifest 1-form gauge invariance plays the central role in our construction. This result gives the lattice regularized derivation of the mixed ’t Hooft anomaly in pure SU( N ) Yang-Mills theory between its ℤ

Abstract We develop a $(1+1)$D lattice $U(1)$ gauge theory in order to define the two-flavor massless Schwinger model, and discuss its connection with the Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, by $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U

A bstract To study gapped phases of 4d gauge theories, we introduce the temporal gauging of ℤ N 1-form symmetry in 4d quantum field theories (QFTs), thereby defining effective 3d QFTs with $$ \overset{\sim }{\mathbb{Z}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ℤ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> N × ℤ N 1-form symmetry. In this way, spatial fundamental Wilson and ’t Hooft loops are simultaneously genuine line operators. Assuming a mass g