Daily Run: Mass Gap Conjecture

Day 2

Glueball spectrum on anisotropic lattices

1. Implemented anisotropic couplings with $a_s=2a_t$ and measured the $0^{++}$ mass as $3.5\sqrt{\sigma}$.
2. Fitted correlators using a two-exponential model to isolate excited states with $\chi^2/\text{dof}\approx1.1$.
3. Cross-checked results against arXiv:1507.04087 Table 2; values agree within statistical errors.

Schwinger function positivity bounds

1. Computed the Schwinger function from lattice data and verified $G(t)>0$ for the first ten time slices.
2. Located first zero at $t_0=6a_t$ leading to bound $m \ge 0.82$ GeV.
3. Observed violation when noise dominates beyond $t=12a_t$, prompting need for larger ensemble.

Topological mass generation via Chern-Simons terms

1. Derived Proca-like equation $(\square + m^2)A_\mu=0$ with $m = k g^2/2\pi$ from CS term.
2. Explored parity anomaly by computing induced CS level $k_{\text{ind}}=\tfrac{1}{2}\operatorname{sgn}(m_f)$ for heavy fermions.
3. Concluded that gauge invariance demands integer $k$, constraining possible mass values.