Generalized Veneziano and Virasoro amplitudes

Abstract

We analyze so-called generalized Veneziano and generalized Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an over-determined set of non-linear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a two-parameter family which includes the Veneziano amplitude, the one-parameter family of Coon amplitudes, and a larger two-parameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum.

On unitarity of the Coon amplitude

“…The former approach has been recently pioneered in [25] for the Veneziano amplitude, which served as our main source of inspiration to address this question for Coon. It would be very interesting to extend our analysis to the new classes of four-point amplitudes recently constructed in [22,23]. Of course, it would also be very interesting to explore higher-point amplitudes, which we expect will lead to much more stringent constraints on unitarity than four-point amplitudes do.…”

“…More recently, the authors of [21] have attempted to reproduce such accumulation-like aspects of the Coon amplitude by virtue of open string scattering on D-branes in an AdS background. Also, multi-parameter spaces of four-point amplitudes satisfying the above constraints (i)-(iii) have been introduced in [22,23] with further modified spin-dependent Regge trajectories.…”

Positivity of the hypergeometric Coon amplitude

“…(4. 19) is manifestly positive when N > 50, and it is straightforward to check that c (10) N,0 in eq. (4.16) is non-negative when N ≤ 50.…”

“…It seems like these new amplitudes are challenging the uniqueness of perturbative string amplitudes [8][9][10][11]. However, since we lack a physical understanding of these amplitudes that originate from a bottom-up way, 1 we are not sure if they are of physical interest or just mathematical solutions to the S-matrix bootstrap, and so we need impose additional conditions.…”

Cornering large-Nc QCD with positivity bounds

“…This would allow us to understand if the Lovelace-Shapiro amplitude (with subtracted scalars, or scalars and vectors) is indeed extremal or not. Here it would be useful to further understand which deformations of known amplitudes are consistent with unitarity, along the lines of [62][63][64].…”