2021/06/23 by David Vegh, Vegh, David
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.2106.12597
6 pages, 9 figures
arxiv created 2021/06/23 · arxiv updated 2021/06/25
This paper is concerned with a class of approximate non-linear transformations that compress solutions of the (generalized) sinh-Gordon equation into parametrically small regions in two-dimensional spacetime. Given the sinh-Gordon field near a time-slice, a long Nambu-Goto string can be constructed in three-dimensional anti-de Sitter space. The string is then approximated to arbitrary accuracy by a slightly smoothed piecewise linear string of N segments. The corresponding sinh-Gordon field has a comb-like structure and its size is controlled by the amount of smoothing applied to the segmented string. In a (singular) large-N limit, the transformation commutes with time evolution. As an example, a static cosh-Gordon solution is discussed in detail. The corresponding smooth and segmented string solutions are obtained and the compressed cosh-Gordon potential is investigated.