Gas detection with hollow-core photonic bandgap fibre (HC-PBF) and pulsed photothermal (PT) interferometry spectroscopy are studied theoretically and experimentally. A theoretical model is developed and used to compute the gas-absorption-induced temperature and phase modulation in a HC-PBF filled with low-concentration of C2H2 in nitrogen. The PT phase modulation dynamics for different pulse duration, peak power and energy of pump beam are numerically modelled, which are supported by the experimental results obtained around the P(9) absorption line of C2H2 at 1530.371 nm. Thermal conduction is identified as the main process responsible for the phase modulation dynamics. For a constant peak pump power level, the phase modulation is found to increase with pulse duration up to ~1.2 μs, while it increases with decreasing pulse duration for a constant pulse energy. It is theoretically possible to achieve ppb level detection of C2H2 with ~1 m length HC-PBF and a pump beam with ~10 ns pulse duration and ~100 nJ pulse energy.