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Crossing Symmetric Dispersion Relations in Quantum Field Theories

Journal Article · · Physical Review Letters
 [1];  [2]
  1. Indian Institute of Science (IISC) (India). Centre for High Energy Physics; Stony Brook University
  2. Indian Institute of Science (IISC) (India). Centre for High Energy Physics
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For 2-2 scattering in quantum field theories, the usual fixed t dispersion relation exhibits only two-channel symmetry. This Letter considers a crossing symmetric dispersion relation, reviving certain old ideas from the 1970s. Rather than the fixed t dispersion relation, this needs a dispersion relation in a different variable z, which is related to the Mandelstam invariants s, t, u via a parametric cubic relation making the crossing symmetry in the complex z plane a geometric rotation. The resulting dispersion is manifestly three-channel crossing symmetric. We give simple derivations of certain known positivity conditions for effective field theories, including the null constraints, which lead to two sided bounds and derive a general set of new nonperturbative inequalities. We show how these inequalities enable us to locate the first massive string state from a low energy expansion of the four dilaton amplitude in type II string theory. We also show how a generalized (numerical) Froissart bound, valid for all energies, is obtained from this approach.
Research Organization:
Stony Brook Univ., NY (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
FG02-88ER40388
OSTI ID:
2280778
Journal Information:
Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 18 Vol. 126; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
effective field theory
field & string theory models & techniques
quantum field theory
scattering amplitudes