Sinh-Gordon Boundary TBA and Boundary Liouville Reflection Amplitude
Z.Bajnok, Chaiho Rim, Al. Zamolodchikov
TL;DR
This paper investigates the ground state energy of the sinh-Gordon model on a strip using boundary thermodynamic Bethe ansatz and compares it with boundary Liouville reflection amplitude, confirming their agreement and exploring the ultraviolet behavior.
Contribution
It provides a detailed comparison between boundary TBA and Liouville reflection amplitude for the sinh-Gordon model, validating their consistency in the ultraviolet limit.
Findings
Perfect agreement between TBA and Liouville amplitude in certain parameter ranges
Ultraviolet limit of the effective central charge can exceed one
Bound states can form from the Liouville zero mode
Abstract
The ground state energy of the sinh-Gordon model defined on the strip is studied using the boundary thermodynamic Bethe ansatz equation. Its ultraviolet (small width of the strip) behavior is compared with the one obtained from the boundary Liouville reflection amplitude. The results are in perfect agreement in the allowable range of the parameters and provide convincing support for both approaches. We also describe how the ultraviolet limit of the effective central charge can exceed one in the parameter range when the Liouville zero mode forms a bound state.
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