Refined regularity of SLE

We prove refined (variation and H-type) regularity statements for the SLE trace. Previous works by Viklund, Lawler (2011) and Friz, Tran (2017) have identified and proved the optimal p-variation and H exponents of SLE_κ (under capacity parametrisation). We refine their results and show that the trace has finite ψ-variation for ψ(x) = xᵖ(log 1/x)-p-ε and H-type modulus φ(x) = x^α(log 1/x)1+ε. For the regularity of SLE₈ (which is φ(x) = (log 1/x)-1/4+ε), we simplify a step in the proof by Kavvadias, Miller, and Schoug (2021).