Talk page
Title:
Numerical solution of systolic minimal-area problems
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Abstract:
Zwiebach’s covariant closed string field theory requires knowledge of the minimal-area metric with unit systole on a given punctured Riemann surface (the systole being the length of the shortest non-contractible loop). Exact solutions are known only in genus 0 with any number of punctures, and genus 1 with zero punctures. I’ll explain how, using calibrations, the systolic condition can be imposed as a local constraint, allowing the minimal-area problem to be formulated as a convex program that is amenable to numerical solution. This program admits a dual program that is also numerically solvable, and that reveals interesting qualitative features of the solutions. I will exhibit some solutions obtained by this method, and comment on applications and generalizations of the method. (Based on arXiv:1806.00449 and arXiv:1806.00450 with B. Zwiebach.)
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