PU High Energy Theory Seminar

This talk will be held in-person in Jadwin Hall, PCTS Room 407 and on Zoom:
https://princeton.zoom.us/j/97248927011?pwd=SWFiNWFwZWE5SUR4OUxvV0ZacVdWQT09#success

Abstract: For each prime number p, there exists a p-adic version of the Veneziano amplitude and its higher-point generalizations. Multiplying together all the p-adic amplitudes and their real counterparts, one obtains the adelic amplitudes, objects intended to join together string theory and analytic number theory.

In this talk I will provide a gentle review of this story and subsequently demonstrate how for special kinematic configurations the adelic 5-point amplitude can be explicitly evaluated in terms of ratios of the Riemann zeta function. This result teaches us that adelic amplitudes are non-analytic, and in light of this fact we should consider reevaluating previous adelic product formulas in the physics literature, which rely on analytic continuation. I will present an alternative formalism for computing the 4-point adelic product, resulting in a non-constant amplitude that is piecewise analytic in the three scattering channels. By decomposing the residues of this amplitude into sums of Gegenbauer polynomials, I will determine a range of dimensions for which the amplitude appears unitary.