Yui Hayashi

A bstract We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters, and it enjoys the SL(2 , ℤ) self-duality at low-energies. SL(2 , ℤ) self-duality does not realize in a naive way, but we notice that the ST p duality transformation becomes the legitimate duality operation by performing the gauging of ℤ N 1-form symmetry with including the level- p discrete topological term. Due to such c

We derive general relationships between the number of complex poles of a propagator and the sign of the spectral function originating from the branch cut in the Minkowski region under some assumptions on the asymptotic behaviors of the propagator. We apply this relation to the mass-deformed Yang-Mills model with one-loop quantum corrections, which is identified with a low-energy effective theory of the Yang-Mills theory, to show that the gluon propagator in this model has a pair of complex conju

Complex singularities have been suggested in propagators of confined particles, e.g., the Landau-gauge gluon propagator. We rigorously reconstruct Minkowski propagators from Euclidean propagators with complex singularities. As a result, the analytically continued Wightman function is holomorphic in the tube, and the Lorentz symmetry and locality are kept intact, whereas the reconstructed Wightman function violates the temperedness and the positivity condition. Moreover, we argue that complex sin

In view of the expectation that the existence of complex poles is a signal of confinement, we investigate the analytic structure of the gluon, quark, and ghost propagators in the Landau gauge QCD and QCD-like theories by employing an effective model with a gluon mass term of the Yang-Mills theory, which we call the massive Yang-Mills model. In this model, we particularly investigate the number of complex poles in the parameter space of the model consisting of gauge coupling constant, gluon mass,

Propagators of confined particles, especially the Landau-gauge gluon propagator, may have complex singularities as suggested by recent numerical works as well as several theoretical models, e.g., motivated by the Gribov problem. In this paper, we study formal aspects of propagators with complex singularities in reconstructing Minkowski propagators starting from Euclidean propagators by the analytic continuation. We derive the following properties rigorously for propagators with arbitrary complex

Magnetic excitations play a crucial role in understanding the color confinement of 4D Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups of 4D Yang-Mills theory, we can achieve different weakly coupled descriptions of confinement phenomena: The monopole mechanism takes place on R^{3}×S^{1} with the double-trace deformation, and the center-vortex mechanism is effective on R^{2}×T^{2} with the 't Ho

A bstract We study QCD vacuum structure with the topological θ angle using a recently proposed semiclassical approach on ℝ 2 × T 2 with the ’t Hooft and baryon magnetic fluxes. Under the assumption of adiabatic continuity in this setup, the confining vacuum can be described by the dilute gas of center vortices. With this semiclassical approach, we derive the 2d effective description at small T 2 and successfully explain the reasonable theta dependence of the QCD vacuum: in the one-flavor QCD at

A bstract We study the phase structure of bifundamental quantum chromodynamics (QCD(BF)), which is the 4-dimensional SU( N ) × SU( N ) gauge theory coupled with the bifundamental fermion. Firstly, we refine constraints on its phase diagram from ’t Hooft anomalies and global inconsistencies, and we find more severe constraints than those in previous literature about QCD(BF). Secondly, we employ the recently-proposed semiclassical approach for confining vacua to investigate this model concretely,

Some gauge theories with a spontaneously broken U(1) symmetry exhibit fractional Aharonov-Bohm (AB) phases around vortices in the Higgs regime. We discuss continuity between confining and Higgs regimes in such gauge theories with fundamental matter fields, focusing on the AB phases. By explicit calculations in relevant lattice models, we demonstrate that the AB phase is smoothly connected between the confining and Higgs regimes, supporting the Higgs-confinement continuity. This result provides n

A bstract We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different ranks, which is the 4d SU( N 1 ) × SU( N 2 ) gauge theory coupled with a bifundamental Dirac fermion. After discussing the anomaly constraints on possible vacuum structures, we apply a novel semiclassical approach on ℝ 2 × T 2 with the baryon-’t Hooft flux to obtain the concrete dynamics. The 2d effective theory is derived by the dilute gas approximation of center vortices, and it serves as the basis for determ

A bstract We study $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 SU( N ) super Yang-Mills (SYM) theory on ℝ 2 × ( S 1 ) 3 × ( S 1 ) 4 with the ’t Hooft twist. The theory becomes weakly coupled if the length L 4 of ( S 1 ) 4 is sufficiently small, NL 4 Λ ≪ 1. We explore the nonperturbative dynamics at the weak-coupling regime by changing the size of L 3 and uncover how 3d monopole/bion-based effective theory for L 3 ≫ L 4 is related

It has been suggested that the Landau-gauge gluon propagator has complex singularities, which invalidates the Källén-Lehmann spectral representation. Since such singularities are beyond the standard formalism of quantum field theory, the reconstruction of Minkowski propagators from Euclidean propagators has to be carefully examined for their interpretation. In this talk, we present rigorous results on this reconstruction in the presence of complex singularities. As a result, the analytically con

We study the finite-temperature phase structure of the four-dimensional ${\rm SU(2)}$ adjoint Higgs model, focusing on a possible deconfinement-Higgs continuity: the conjecture that the high-temperature deconfined phase of Yang-Mills theory and the finite-temperature Higgs phase form a single thermodynamic phase. We combine three approaches: (i) global symmetry analysis, showing that Higgs and deconfined regimes are expected to share the same symmetry pattern distinct from the confined phase; (i

Magnetic excitations play a crucial role in understanding the color confinement of $4$d Yang-Mills theory, and we have the monopole and the center vortex as plausible candidates to explain its mechanism. Under suitable compactified setups of $4$d Yang-Mills theory, we can achieve different weakly-coupled descriptions of confinement phenomena: The monopole mechanism takes place on $\mathbb{R}^3\times S^1$ with the double-trace deformation, and the center-vortex mechanism is effective on $\mathbb{