The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

Journal of High Energy Physics

Harish Murali¹  Martin Kruczenski² 

[1] Department of Physics and Astronomy, Purdue Quantum Science and Engineering Institute (PQSEI), Purdue University, W. Lafayette, IN, USA;Department of Physics and Astronomy, Purdue Quantum Science and Engineering Institute (PQSEI), Purdue University, W. Lafayette, IN, USA;Purdue Quantum Science and Engineering Institute (PQSEI), Purdue University, W. Lafayette, IN, USA;

关键词: Boundary Quantum Field Theory;    Field Theories in Lower Dimensions;    Integrable Field Theories;    Nonperturbative Effects;   

DOI  :  10.1007/JHEP04(2021)097

来源: Springer

【 摘 要 】

The S-matrix bootstrap is extended to a 1+1d theory with O(N) symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.

【 授权许可】

CC BY