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Crossing Symmetric Dispersion Relations for Mellin Amplitudes

Journal Article · · Physical Review Letters
 [1];  [2];  [2]
  1. International Centre for Theoretical Sciences (ICTS) (India); Stony Brook University
  2. Indian Institute of Science (India)
+ Show Author Affiliations
We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories. This allows us to set up the nonperturbative Polyakov bootstrap for the conformal field theories in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks. Our new approach employs certain “locality” constraints replacing the requirement of crossing symmetry in the usual fixed-t dispersion relation. Using these constraints, we show that the sum rules based on the two channel dispersion relations and the present dispersion relations are identical. Our framework allows us to connect with the conceptually rich picture of the Polyakov blocks being identified with Witten diagrams in anti-de Sitter space. We also give two sided bounds for Wilson coefficients for effective field theories in anti-de Sitter space.
Research Organization:
Stony Brook Univ., NY (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
FG02-88ER40388
OSTI ID:
2280777
Journal Information:
Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 21 Vol. 126; ISSN 0031-9007
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (21)

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Crossing Symmetric Dispersion Relations in Quantum Field Theories journal May 2021
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Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
conformal field theory
quantum field theory