Cubic Interaction Vertices and One-loop Self-energy in the Stable String Bit Model

We provide a formalism to calculate the cubic interaction vertices of the stable string bit model, in which string bits have s spin degrees of freedom but no space to move. With the vertices, we obtain a formula for one-loop self-energy, i.e., the O(1/N2) correction to the energy spectrum. A rough analysis shows that, when the bit number M is large, the ground state one-loop self-energy ΔEG scale as M5-s/4 for even s and M4-s/4 for odd s. Particularly, in s=24, we have ΔEG∼1/M, which resembles the Poincaré invariant relation of 1+1 dimension P-∼1/P+. We calculate analytically the one-loop correction for the ground energies with M=3 and s=1, 2. We then numerically confirm that the large M behavior holds for s≤4 cases.

Note:

33 pages, 14 figures, update to the published version

vertex: stability
propagator
string
energy spectrum
ground state
Grassmann
Poincare
spin

References(15)

Figures(7)

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