科研之友
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摘要
We develop superstring bit models, in which the lightcone transverse coordinates in D spacetime dimensions are replaced with d = D -2 double-valued "flavor" indices x (k) -> f (k) = 1, 2; k = 2,..., d + 1. In such models the string bits have no space to move. Let-ting each string bit be an adjoint of a "color" group U(N), we then analyze the physics of 't Hooft's limit N -> infinity, in which closed chains of many string bits behave like free lightcone IIB superstrings with d compact coordinate bosonic worldsheet fields x(k) , and s pairs of Grassmann fermionic fields theta(a)(L,R) , a = 1,..., s. The coordinates x(k) emerge because, on the long chains, flavor fluctuations enjoy the dynamics of d anisotropic Heisenberg spin chains. It is well-known that the low energy excitations of a many-spin Heisenberg chain are identical to those of a string worldsheet coordinate compactified on a circle of radius R (k) , which is related to the anisotropy parameter -1 <= Delta (k <=) sign 1 of the corresponding Heisenberg system. Furthermore there is a limit of this parameter, Delta(k) -> +/- 1, in which R-k -> infinity. As noted in earlier work [Phys. Rev. D 89 (2014) 105002], these multi-string-bit chains are strictly stable at N = infinity when d < s and only marginally stable when d = s. (Poincare supersymmetry requires d = s = 8, which is on the boundary between stability and instability.).
- 出版日期2014-11-20
