BCFW Deformation and Regge Limit

It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are (generalised) BrittoCachazo-Feng-Witten shifts, as well as the monodromy relations for open string theory and the Kawai-Lewellen-Tye relations for closed string theory. The roots of the scattering amplitudes and especially their appearance in the residues at the kinematic poles are central to the story. These residues determine the amplitudes through on-shell recursion relations. Several checks of the formalism are presented, including a computation of the Koba-Nielsen amplitude in the bosonic string. Furthermore the question of target space unitarity is (re-)investigated. For the Veneziano amplitude this question is reduced by Poincaré invariance, unitarity and locality to that of positivity of a particular numerical sum. Interestingly, this analysis produces the main conditions of the no-ghost theorem on dimension and intercept from the first three poles of this amplitude.

Section: Completeness Of the Basismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

String theory in target space

Boels

Hansen

2014

“…In general, superconvergence occurs in scattering of particles of spins J1 and J2 whenever J1 +J2 −1 > J0, where J0 is the Regge intercept of the theory, see e.g [38,61]…”

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confidence: 99%

Causality constraints on corrections to Einstein gravity

Caron-Huot

Parra-Martinez

et al. 2023

We study constraints from causality and unitarity on 2 → 2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G → 0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

“…underlies the connection to Regge behavior discussed in [53]. Meanwhile, the little group factors used to remove the z dependence from the (n − 1)-point amplitude give rise to an asymmetry between particles 1 and 2 that distinguishes which shifts are allowed.…”

Section: Jhep01(2023)151mentioning

confidence: 91%

“…Indeed we see that the Mandelstam invariants scale ass = 2p1 • p2 = 1 2 [12 ] ∼ z 0 and t = 2p1 • p3 = 1 3 [13] ∼ z,which is a crossing image of the standard Regge limit. As shown in[53], the BCFW shift configuration can be described by Regge behavior of the amplitude. From the celestial perspective the Regge limit implies a collinear limit but not vice versa.…”

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confidence: 98%

Celestial recursion

Hu¹,

Pasterski²

2023

We examine the BCFW recursion relations for celestial amplitudes and how they inform the celestial bootstrap program. We start by recasting the celestial incarnation of the BCFW shift as a generalization of the action of familiar asymptotic symmetries on hard particles, before focusing on two limits: z → ∞ and z → 0. We then discuss how the celestial CFT data encodes the large-z behavior determining which shifts are allowed, while the infinitesimal limit is tied to the celestial bootstrap program via the BG equations that constrain the MHV sector. The extension to super-BCFW is also presented. We close by remarking on several open questions for future study.