Trace formulas for Annuli

TL;DR

This paper derives trace formulas for annulus coefficients in 2D conformal field theory, relating them to other coefficients and proposing an orientation-sensitive trace formula.

Contribution

It introduces new trace formulas for annulus coefficients and polynomial relations among various boundary and crosscap coefficients in conformal field theory.

Findings

Derived trace formulas for annulus coefficients.

Established polynomial relations among annulus, Moebius, and Klein bottle coefficients.

Proposed an orientation-sensitive annulus trace formula.

Abstract

Assuming the completeness condition for boundaries we derive trace formulas for the annulus coefficients in 2-dimensional conformal field theory. We also derive polynomial equations that relate the annulus, Moebius and Klein bottle coefficients, and conjecture an annulus trace formula that is sensitive to the orientation of the boundaries.