TY - JOUR

T1 - Non-archimedean string dynamics

AU - Brekke, Lee

AU - Freund, Peter G.O.

AU - Olson, Mark

AU - Witten, Edward

N1 - Funding Information:
1 Address after January 1, 1988: Department of Physics, The University of Arizona, Tucson, AZ 85721, USA. Work partially supported by DOE grant no. DE AC02 80ER 10587. 2 Work partially supported by NSF grants no. 85-21588. 3 Work partially supported by NSF grants no. 80-19754 and 86-20266; on leave from Princeton University.

PY - 1988/6/6

Y1 - 1988/6/6

N2 - 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.

AB - 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.

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U2 - 10.1016/0550-3213(88)90207-6

DO - 10.1016/0550-3213(88)90207-6

M3 - Article

AN - SCOPUS:33744771726

SN - 0550-3213

VL - 302

SP - 365

EP - 402

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 3

ER -