Purdue University Graduate School
The_Rmatrix_Bootstrap_v6.pdf (7.2 MB)

The R-matrix bootstrap

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posted on 2021-04-30, 01:39 authored by Harish MuraliHarish Murali
In this thesis, we extend the numerical S-matrix bootstrap program to 1+1d theories with a boundary, where we bootstrap the 1-to-1 reflection matrix (R-matrix). We review the constraints that a physical R-matrix must obey, namely unitarity, analyticiy and crossing symmetry. We then carve out the allowed space of 2d R-matrices with the O(N) nonlinear sigma model and the periodic Yang Baxter solution in the bulk. We find a variety of integrable R-matrices along the boundary of the allowed space both with and without free parameters. The integrable models without a free parameter appear at vertices of the allowed space, while those with a free parameter occupy the whole boundary. We also introduce the extended analyticity constraint where we increase the domain of analyticity beyond the physical region. In some cases, the allowed space of R-matrices shrinks drastically and we observe new vertices which correspond to integrable theories. We also find a new integrable R-matrix through our numerics, which we later obtained by solving the boundary Yang--Baxter equation. Finally, we derive the dual to the extended analyticity problem and find that the formalism allows for R-matrices which do not saturate unitarity to lie on the boundary of the allowed region.


An Experimental and Theoretical High Energy Physics Program

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Quantum Information in a strongly interacting quantum simulator: from gauge/string theory duality to analogue black holes

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QuantiSED Fermilab consortium

Keck Foundation


Degree Type

  • Master of Science


  • Physics and Astronomy

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Martin Kruczenski

Additional Committee Member 2

Nima Lashkari

Additional Committee Member 3

Sergei Khlebnikov

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