p-Adic String
[151] "The p-Adic String N-Point Function" by P.H. Frampton and Y. Okada.
Phys. Rev. Lett. 60, 484 (1988).
When a novel (p-Adic) expression for the Veneziano formula was suggested in
I. Volovich, Class. Quant. Grav. 4, L83 (1987), it created excitement especially
after Peter Freund and Edward Witten, Phys. Rev. Lett. B199, 191 (1987) rewrote
the 4 legged function as an infinite product.
The open question we addressed in [151] was how to extend this from the 4 to N?
One started from the Bardakci-Ruegg form of the N-Point dual resonance model to arrive
at a very simple N-point p-Adic string. A few weeks later, Freund and Witten arrived at an
entirely equivalent result in Nucl. Phys. B302, 365 (1988) though in a considerably more
complicated version because, unluckily for them, they started from the fully symmetrical
Koba-Nielsen form, instead of the Bardakci-Ruegg form, of the dual resonance model.
[153] "Effective Scalar Field Theory of p-Adic String" by P.H. Frampton and Y. Okada.
Phys. Rev. D37, 3077 (1988).
Paper[153] derived for the first
time the non-local field theory which yields the p-Adic
string Feynman rules. This Frampton-Okada lagrangian was used many years later
for studies of the bosonic string tachyon*.
[156] "On Adelic Formulas for p-Adic Strings" by P.H. Frampton, Y. Okada and
M.R. Ubriaco. Phys. Lett. 213B, 269 (1988).
Here are open questions about p-Adic string:
(1) the adelic formula for the four-point function was first shown in this paper[156]
to be inconsistent everywhere in the Mandelstam s-t plot because the infinite product
has an impenetrable natural boundary as a function of the complex variables s and t.
Why is the product nonanalytic?
(2)What is a physical interpretation of a p-Adic string (for finite p)?
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*Ashoke Sen, Int. J Mod. Phys.A20, 5513 (2004) hep-th/0410103
Ashoke Sen, JHEP 0408:034 (2004) hep-th/0403200.
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