On the persistence of symmetry

Current Work

My present interests sit at the intersection of non-perturbative effects in quantum field theory and the algebraic structures that survive their renormalization. The motivating question is straightforward and unsolved: when a symmetry of the classical action is broken by quantum corrections — an anomaly — what remains of it?

Concretely, I am thinking about the chiral-anomaly equation

$${\partial }_{\mu }{J}_5^{\mu }=\frac{1}{16{\pi }^2}{\epsilon }^{\mu \nu \rho \sigma }\mathrm{tr}\left(F_{\mu \nu }{F}_{\rho \sigma }\right)$$

and the way the right-hand side, far from a defect, encodes the topology of the gauge bundle through characteristic classes. The same mathematics — index theorems, secondary cohomology — animates a quieter parallel I keep returning to: the geometry of perspective in Sung-dynasty landscape painting, where the mountains and rivers of Du Fu's wreckage become a problem in projective invariants. The Calabi–Yau condition,

$$R_{\mu \bar{\nu }}=0,$$

and the Sung painter's recession of ink washes both, I suspect, belong to a single discipline: how to draw something that respects its own consistency conditions. The notes below pull at this thread from different sides.

Selected Notes

• Notes from the Stack 2026.04.15 · Typography
• On Setting Valéry in Mincho 2026.03.29 · Typography
• A Walk Through Hongō 2026.03.08 · Field Notes

Talks & Teaching

By invitation. Surviving slides and lecture fragments are circulated privately; ask.

Contact

Letters, errata, and counterexamples welcome at scholar [at] sanga.moe. The seam between physics and the Chinese line is wider than either party assumes; correspondence improves both halves.