Nonarchimedean String Dynamics

Brekke, Lee; Freund, Peter G.O.; Olson, Mark; Witten, Edward

doi:10.1016/0550-3213(88)90207-6

Nonarchimedean String Dynamics

Lee Brekke
(
- Chicago U., EFI and
- Chicago U.
)
,
Peter G.O. Freund
(
- Chicago U., EFI and
- Chicago U.
)
,
Mark Olson
(
- Chicago U., EFI and
- Chicago U.
)
,
Edward Witten
(
- Princeton, Inst. Advanced Study
)

Dec 30, 1987

38 pages

Published in:

Nucl.Phys.B 302 (1988) 365-402

Published: 1988

DOI:

10.1016/0550-3213(88)90207-6

Report number:

EFI-87-101-CHICAGO

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Abstract: (Elsevier)

Explicit formulas for the N -point tree amplitudes of the non-archimedean open string are derived. These amplitudes can be generated from a simple non-local lagrangian involving a single scalar field (the tachyon) in ambient space-time. This lagrangian is studied and is found to possess a tachyon free vacuum with no “particles” but with soliton solutions. The question of generalizing the adelic product formular to N -point amplitudes is taken up. The infinite product of 5-point amplitudes is shown to converge in a suitably chosen kinematic region whence it can be analytically continued. Though the precise form of the product formula for the 5-point (and N -point)amplitudes is not found, it is shown that the product is not equal to one as it is for the 4-point amplitudes but rather involves the famous zeros of the Riemann zeta function. Chan-Paton rules for non-archimedean open strings are given. A string over the (global) field of rational numbers is constructed. Other problems that are addressed are the introduction of supersymmetry, the nature of a p -adic string lagrangian, and the possibility of strings over other locally compact fields.

MODEL: STRING
SCATTERING AMPLITUDE
FIELD THEORY: EFFECTIVE LAGRANGIANS
SUPERSYMMETRY
MATHEMATICAL METHODS: NUMBER THEORY
MATHEMATICAL METHODS: ANALYTIC PROPERTIES