Masahito Yamazaki

Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and construction of gapped phases with noninvertible symmetry can be mapped to those involving conventional group symmetries. We demonstrate this approach by classifying symmetry-protected-topological phases with a broad class of noninvertible symmetries in arbitrary spacetime dimensions. Our results reveal new classifications that extend beyond those based on group symmetries. Additionally, we construct lattice models in (1+1)D and (2+1)D that realize these new phases and explore their anomalous interfaces.

Non-invertible dualities/symmetries have become an important tool in the study of quantum field theories and quantum lattice models in recent years. One of the most studied examples is non-invertible dualities obtained by gauging a discrete group. When the physical system has more global symmetries than the gauged symmetry, it has not been thoroughly investigated how those global symmetries transform under non-invertible duality. In this paper, we study the change of global symmetries under non-invertible duality of gauging a discrete group G G in the context of (1+1)-dimensional quantum lattice models. We obtain the global symmetries of the dual model by focusing on different Hilbert space sectors determined by the \mathrm{Rep}(G) R e p ( G ) symmetry. We provide general conjectures of global symmetries of the dual model forming an algebraic ring of the double cosets. We present concrete examples of the XXZ models and the duals, providing strong evidence for the conjectures.

One of the simplest standard model extensions leading to a domain wall network is a real scalar S with a Z 2 symmetry spontaneously broken during universe evolution. Motivated by the swampland program, we explore the possibility that quantum gravity effects are responsible for violation of the discrete symmetry, triggering the annihilation of the domain wall network. We explore the resulting cosmological implications in terms of dark radiation, dark matter, gravitational waves, primordial black holes, and wormholes connected to baby universes.

While general quantum field theories (QFTs) have yet to be rigorously defined in mathematics, they have generated new mathematics and have served as a unifying principle connecting different branches of the subject. In 1989, Witten made a profound impact on the mathematical community by systematically constructing knot invariants via the three-dimensional Chern-Simons theory. One of the historical roots of knot invariants was integrable models, whose explanation in terms of QFT remained unsolved for decades. Recently, this problem was solved by a perturbative analysis of the four-dimensional Chern-Simons theory, which provides a novel framework for understanding and unifying many different aspects of integrable models. In this article, we summarize the basic aspects of these developments for non-experts in both physics and mathematics.

We construct statistical mechanical models of crystal melting describing the flavoured Witten indices of \mathcal{N}≥ 2 ???? ≥ 2 supersymmetric quiver gauge theories. Our results can be derived from the Jeffrey-Kirwan (JK) residue formulas, and generalize the previous results for quivers corresponding to toric Calabi-Yau threefolds and fourfolds to a large class of quivers satisfying the no-overlap condition, including those corresponding to some non-toric Calabi-Yau manifolds. We construct new quiver algebras which we call the double quiver Yangians/algebras, as well as their representations in terms of the aforementioned crystals. For theories with four supercharges, we compare the double quiver algebras with the existing quiver Yangians/BPS algebras, which we show can also be constructed from the JK residues. For theories with two supercharges, the double quiver algebras provide an algebraic description of the BPS states, including the information of the fixed points and their relative coefficients in the full partition functions.

We present an exploratory study to determine the confinement-deconfinement transition temperature at finite θ, T _c (θ), for the 4d SU(2) pure Yang-Mills theory. Lattice numerical simulations are performed on three spatial sizes N _S = 24, 32, 48 with a fixed temporal size N _T = 8. We introduce a non-zero θ-angle by the sub-volume method to mitigate the sign problem. By taking advantage of the universality in the second order phase transition and the Binder cumulant of the order parameter, the θ-dependence of T _c is determined to be T _c (θ)/T _c (0) = 1 − 0.16(2) (θ/π)² − 0.03(4) (θ/π)⁴ up to θ ∼ 0.9 π. The reliability of the extrapolations in the sub-volume method is extensively checked. We also point out that the temperature dependence of the topological susceptibility should exhibit a singularity with the exponent for the specific heat.