Grand Unified Theories in Renormalisable, Classically Scale Invariant Gravity

大统一、小表示与大表示、强子对撞机及其他

Grand unification, small vs large representations, hadron colliders and all that

本文回顾基于SU(5)和SO(10)的大统一模型，指出小表示模型预言新轻粒子并修正W质量，而可重整化版本可能使右旋玻色子质量在LHC可达，且分裂超对称不必然导致轻态。

揭示大统一的标量扇区：现象学与影响

Unravelling the Scalar Sector of Grand Unification: Phenomenology & Implications

本文系统研究 GUT 标量场的双夸克、轻夸克耦合及其对核子衰变、中子振荡、味破坏和重子产生的约束，并展示扩展 $SU(5)$ 中重标量量子修正可解除费米子质量简并。

Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity

We discuss the nature of quantum field theories involving gravity that are classically scale-invariant. We show that gravitational radiative corrections are crucial in the determination of the nature of the vacuum state in such theories, which are renormalisable, technically natural, and can be asymptotically free in all dimensionless couplings. In the pure gravity case, we discuss the role of the Gauss-Bonnet term, and we find that Dimensional Transmutation (DT) à la Coleman-Weinberg leads to extrema of the effective action corresponding to nonzero values of the curvature, but such that these…

Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a θ-deformed nonlinear realisation of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix θ^{μν} the UV divergent part of its effective action in the background-field gauge, and, for N>=2, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full…

可积sigma模型在4d Chern-Simons理论中的1-loop可重整化性

1-loop renormalisability of integrable sigma-models from 4d Chern-Simons theory

本文证明了由4d Chern-Simons理论表面缺陷构造的一大类经典可积二维sigma模型在1-loop阶可重整化，推导了twist 1-form的流，适用于有理、三角和椭圆型模型。

大规模统一起源的增强标量耦合：连接辐射电弱对称破缺到SO(10)动态

Grand Unified Origin of Enhanced Scalar Couplings: Connecting Radiative Electroweak Symmetry Breaking to SO(10) Dynamics

本文探讨了通过SO(10)大统一理论自然产生辐射性电弱对称破缺所需的增强Higgs四阶耦合，揭示其与GUT尺度的关联。