Generalization of the Froissart-Martin bounds to scattering in a space-time of general dimension

Chaichian, M.; Fischer, Ján; Vernov, Yu. S.

doi:10.1016/0550-3213(92)90674-z

Cited by 29 publications

(51 citation statements)

References 14 publications

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“…To remind, the scattering amplitude F (s, t) is analytic in t in quasi topological product {|t| < R = 4m 2 }⊗ cut s-plane. Thus we have provided proof of the two assumptions used in [25,26] in the present investigation. We have not determined how many subtractions are required in the dispersion relation i.e.…”

Section: The Partial Wave Expansion and Asymptotic Behavior Of Amplitudementioning

confidence: 55%

“…Moreover, eventually, when one derives the bound [25,26] on σ t , the factor s −λ+1/2 disappears in the expression for the bound. C λ l (x) are the Gegenbauer polynomials satisfying orthogonality conditions with weight factor (1 − x 2 ) λ−1/2 , −1 ≤ x ≤ +1 [28].…”

Section: The Partial Wave Expansion and Asymptotic Behavior Of Amplitudementioning

confidence: 99%

“…First thing to note is that the partial wave amplitudes in the expansion for F λ (s, t) fall off exponentially beyond a cut off L. This is a very crucial feature and we shall dwell upon this aspect in sequel. Moreover, in the above mentioned work [25,26], as is obvious from the bound on σ t , the growth is still a power of lns. Furthermore, there are some interesting results where scattering amplitude and slope associated with the forward amplitude are constrained.…”

Section: Introductionmentioning

confidence: 97%

“…The statements (a1) -(a4) have been proved in the frame work of axiomatic field theory. In the context of higher dimensional field theories, the analog of Froissart bound has been derived for scattering of massive spinless particles [25,26]. There is only one scattering angle for spinless scattering although for the most general case, the amplitude is to expressed in terms of complete set of basis functions (see Section 4 for detailed discussions) for representation of SO(D − 1) rotation group.…”

Section: Introductionmentioning

confidence: 99%

“…(lns) 2 . Let us briefly discuss the essentials steps for derivation of (5) in [25,26]. The amplitude for scattering of massive spinless particles in D-dimensional spacetime admits a partial wave amplitude expansion [27] F λ (s, t) = A 1 s −λ+1/2 ∞ l=0 (l + λ)f λ l (s)C λ l (t)(1 + 2t/s) (6) where λ = 1 2 (D − 3) and (s, t) are the usual Mandelstam variables.…”

Section: Introductionmentioning

confidence: 99%

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Analyticity properties and asymptotic behavior of scattering amplitude in higher dimensional theories

Maharana

2017

Journal of Mathematical Physics

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The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is adopted. The analyticity properties of the causal, the retarded and the advanced functions associated with the four point elastic amplitudes are studied. The analog of the Lehmann-Jost-Dyson representation is obtained in higher dimensional field theories. The generalized J-L-D representation is utilized to derive the t-plane analyticity property of the amplitude. The existence of an ellipse analogous to the Lehmann ellipse is demonstrated. Thus a fixed-t dispersion relation can be written down with finite number of subtractions due to the temperedness of the amplitudes. The domain of analyticity of scattering amplitude in s and t variables is extended by imposing unitarity constraints. A generalized version of Martin's theorem is derived to prove the existence of such a domain in D-dimensional field theories. It is shown that the amplitude can be expanded in a power series in t which converges for |t| < R; R being sindependent. The positivity properties of absorptive amplitudes are derived to prove the t-plane analyticity of amplitude. In the extended analyticity domain dispersion relations are written with two subtractions. The bound on the total cross section is derived from LSZ axioms without any extra ad hoc assumptions.

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Section: The Partial Wave Expansion and Asymptotic Behavior Of Amplitudementioning

confidence: 55%

Section: The Partial Wave Expansion and Asymptotic Behavior Of Amplitudementioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analyticity properties and asymptotic behavior of scattering amplitude in higher dimensional theories

Maharana

2017

Journal of Mathematical Physics

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Swampland conditions for higher derivative couplings from CFT

Kundu

2022

J. High Energ. Phys.

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There are effective field theories that cannot be embedded in any UV complete theory. We consider scalar effective field theories, with and without dynamical gravity, in D-dimensional anti-de Sitter (AdS) spacetime with large radius and derive precise bounds (analytically) on the coupling constants of higher derivative interactions ϕ2□kϕ2 by only requiring that the dual CFT obeys the standard conformal bootstrap axioms. In particular, we show that all such coupling constants, for even k ≥ 2, must satisfy positivity, monotonicity, and log-convexity conditions in the absence of dynamical gravity. Inclusion of gravity only affects constraints involving the ϕ2□2ϕ2 interaction which now can have a negative coupling constant. Our CFT setup is a Lorentzian four-point correlator in the Regge limit. We also utilize this setup to derive constraints on effective field theories of multiple scalars. We argue that similar analysis should impose nontrivial constraints on the graviton four-point scattering amplitude in AdS.

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Geometry of 6D RG flows

Heckman

Morrison

Rudelius

et al. 2015

J. High Energ. Phys.

109

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Abstract:We study renormalization group flows between six-dimensional superconformal field theories (SCFTs) using their geometric realizations as singular limits of F-theory compactified on elliptically fibered Calabi-Yau threefolds. There are two general types of flows: one corresponds to giving expectation values to scalars in the tensor multiplets (tensor branch flow) realized as resolving the base of the geometry. The other corresponds to giving expectation values to hypermultiplets (Higgs branch flow) realized as complex structure deformations of the geometry. To corroborate this physical picture we calculate the change in the anomaly polynomial for these theories, finding strong evidence for a flow from a UV fixed point to an IR fixed point. Moreover, we find evidence against non-trivial dualities for 6D SCFTs. In addition we find non-trivial RG flows for theories realizing small E 8 instantons on ALE spaces.

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Generalization of the Froissart-Martin bounds to scattering in a space-time of general dimension

Cited by 29 publications

References 14 publications

Analyticity properties and asymptotic behavior of scattering amplitude in higher dimensional theories

Analyticity properties and asymptotic behavior of scattering amplitude in higher dimensional theories

Swampland conditions for higher derivative couplings from CFT

Geometry of 6D RG flows

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