Gravitational wave trispectrum in the axion-SU(2) model

We study the trispectrum of the gravitational waves (GWs) generated through the dynamics of an axionic spectator field and SU(2) gauge fields during inflation. In non-Abelian gauge theory, the gauge fields have four-point self-interactions, which induce the tree-level GW trispectrum. We formulate this type of the GW trispectrum including the non-dynamical contributions and evaluate it in the equilateral limit as a unique signal of this model. We find that the ratio of the GW trispectrum to the cube of the scalar power spectrum can be as large as 𝒪(106) in the viable parameter space, which could be captured in the CMB observations.

Nilpotent (anti-)BRST and (anti-)co-BRST symmetries in 2D non-Abelian gauge theory: Some novel observations

We discuss the nilpotent Becchi–Rouet–Stora–Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations and derive their corresponding conserved charges in the case of a two (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) self-interacting non-Abelian gauge theory (without any interaction with matter fields). We point out a set of novel features that emerge out in the BRST and co-BRST analysis of the above 2D gauge theory. The algebraic structures of the symmetry operators (and corresponding conserved charges) and their relationship with the cohomological operators of differential geometry are established too. To be more precise, we demonstrate the existence of a single Lagrangian density that respects the continuous symmetries which obey proper algebraic structure of the cohomological operators of differential geometry. In the literature, such observations have been made for the coupled (but equivalent) Lagrangian densities of the 4D non-Abelian gauge theory. We lay emphasis on the existence and properties of the Curci–Ferrari (CF)-type restrictions in the context of (anti-)BRST and (anti-)co-BRST symmetry transformations and pinpoint their key differences and similarities. All the observations, connected with the (anti-)co-BRST symmetries, are completely novel.

Center group dominance in quark confinement

We show that the color N dependent area law falloffs of the double-winding Wilson loop averages for the SU(N) lattice gauge theory obtained in the preceding works are reproduced from the corresponding lattice Abelian gauge theory with the center gauge group ZN . This result indicates the center group dominance in quark confinement.

Gravitational vector Dark Matter

A new dark sector consisting of a pure non-abelian gauge theory has no renormalizable interaction with SM particles, and can thereby realise gravitational Dark Matter (DM). Gauge interactions confine at a scale ΛDM giving bound states with typical lifetimes $$ \tau \sim {M}_{\mathrm{P}1}^4/{\Lambda}_{\mathrm{DM}}^5 $$ τ ∼ M P 1 4 / Λ DM 5 that can be DM candidates if ΛDM is below 100 TeV. Furthermore, accidental symmetries of group-theoretical nature produce special gravitationally stable bound states. In the presence of generic Planck-suppressed operators such states become long-lived: SU(N) gauge theories contain bound states with $$ \tau \sim {M}_{\mathrm{P}1}^8/{\Lambda}_{\mathrm{DM}}^9 $$ τ ∼ M P 1 8 / Λ DM 9 ; even longer lifetimes τ = (MPl/ΛDM)2N−4/ΛDM arise from SO(N) theories with N ≥ 8, and possibly from F4 or E8. We compute their relic abundance generated by gravitational freeze-in and by inflationary fluctuations, finding that they can be viable DM candidates for ΛDM ≳ 1010 GeV.

Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

We study a 3d lattice gauge theory with gauge group U(1)N−1 ⋊ SN, which is obtained by gauging the SN global symmetry of a pure U(1)N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤN, we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.