Dual amplitudes in higher dimensions: a personal view
Claud Lovelace · Cambridge University Press eBooks · 2012
This is a very personal view of the origin of string theory, and it also makes an interesting prediction. When I first encountered the Veneziano model in 1968, I was at CERN working on the phenomenology of strong interactions. I saw an application to pion–pion scattering (Lovelace [Lov68] and Shapiro [Sha69]), which occurred independently to Shapiro and Yellin [SY70] at Berkeley. It attracted considerable attention, but now seems misguided. Later I combined dual amplitudes with Gribov's Reggeon calculus [Lov71b]. This application has been revived recently by people exploiting AdS/CFT duality, and should eventually succeed. All through 1969 people were adding legs to the Veneziano amplitude, or chopping it in half. I will leave this story to other contributors. Amati and coworkers gave a series of seminars at CERN on their SL (2,ℝ) group theoretic formulation which I thought very elegant [AALO71]. This inspired me to drop phenomenology and join them. In modern language, the N -Reggeon vertex [Lov70a] is the open string disc amplitude with arbitrary excited states on all external lines. Several people had written down a complicated formula. I noticed it could be factorized by a single set of oscillators at the centre of the disc, and realized that an easy construction of the complete perturbation expansion to all orders in string loops would follow. Alessandrini and Amati [Ale71, AA71], and I [Lov70b] worked this out. I am eulexic – my favourite way of developing an idea is to cover a table with piles of possibly relevant books and papers, and rapidly turn pages till I catch a scent like the one in my mind.