Spinning S-matrix Bootstrap in 4d

Hebbar, Aditya; Karateev, Denis; Penedones, João

doi:10.48550/arxiv.2011.11708

Cited by 11 publications

(33 citation statements)

References 55 publications

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“…Note that helicities (or equivalently tensor structures in higher dimensions) may not be Z 2 × Z 2 invariant and we might need to impose Z 2 × Z 2 invariance. However, for most of the non-crossing symmetric helicity amplitudes that we consider in this work, the Z 2 × Z 2 symmetry has already been taken care of [41]. The S-matrix which is invariant under the Z 2 × Z 2 invariance is often referred to as "Quasi-invariant" S-matrix.…”

Section: Crossing Symmetric Amplitudesmentioning

confidence: 99%

“…We will consider the sub cases whether Parity is preserved or not. We will be following the notations and conventions of [41].…”

Section: Photons and Gravitonsmentioning

confidence: 99%

“…Note that for scattering of four identical photons and gravitons, we have η * 1 η * 2 η 3 η 4 = (|η| 2 ) 2 = 1 trivially. These conditions reduce the number of independent parity preserving helicity amplitudes which are given by [41],…”

Section: P Invariant Theoriesmentioning

confidence: 99%

“…(2.10) 6 These linearly independent set of five amplitudes are the basis of Quasi-invariant S-matrices defined in the previous section. They transform in irreducible representations of S 3 which we determine from the following crossing equation [37,41].…”

Section: P Invariant Theoriesmentioning

confidence: 99%

“…We will fix them in this section using constraints from consistency of crossing equations and comparing against explicit helicity amplitudes in literature. Note that (2.11) differs from the equivalent equation of [41] (eqns 2.81 and 2.82). This is due to the fact that we assume the following assignment for the Wigner-d angles…”

Section: P Invariant Theoriesmentioning

confidence: 99%

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Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Chowdhury¹,

Ghosh²,

Haldar³

et al. 2021

Preprint

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We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.

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Section: Crossing Symmetric Amplitudesmentioning

confidence: 99%

“…We will consider the sub cases whether Parity is preserved or not. We will be following the notations and conventions of [41].…”

Section: Photons and Gravitonsmentioning

confidence: 99%

Section: P Invariant Theoriesmentioning

confidence: 99%

Section: P Invariant Theoriesmentioning

confidence: 99%

Section: P Invariant Theoriesmentioning

confidence: 99%

See 3 more Smart Citations

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Chowdhury¹,

Ghosh²,

Haldar³

et al. 2021

Preprint

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The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

Kruczenski

Murali

2021

J. High Energ. Phys.

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The S-matrix bootstrap is extended to a 1+1d theory with O(N) symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed R-matrices is an infinite dimensional convex space from which we plot a two dimensional section given by a convex domain on a 2d plane. In certain cases, at the boundary of the domain, we find vertices corresponding to integrable R-matrices with no free parameters. In other cases, when there is a one-parameter family of integrable R-matrices, the whole boundary represents integrable theories. We also consider R-matrices which are analytic in an extended region beyond the physical cuts, thus forbidding poles (resonances) in that region. In certain models, this drastically reduces the allowed space of R-matrices leading to new vertices that again correspond to integrable theories. We also work out the dual problem, in particular in the case of extended analyticity, the dual function has cuts on the physical line whenever unitarity is saturated. For the periodic Yang-Baxter solution that has zero transmission, we computed the R-matrix initially using the bootstrap and then derived its previously unknown analytic form.

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Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude

Bern¹,

Kosmopoulos²,

Zhiboedov

2021

J. Phys. A: Math. Theor.

118

162

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We analyze constraints from perturbative unitarity and crossing on the leading contributions of higher-dimension operators to the four-graviton amplitude in four spacetime dimensions, including constraints that follow from distinct helicity configurations. We focus on the leading-order effect due to exchange by massive degrees of freedom which makes the amplitudes of interest infrared finite. In particular, we place a bound on the coefficient of the R 3 operator that corrects the graviton three-point amplitude in terms of the R 4 coefficient. To test the constraints we obtain nontrivial effective field-theory data by computing and taking the large-mass expansion of the one-loop minimally-coupled four-graviton amplitude with massive particles up to spin 2 circulating in the loop. Remarkably, we observe that the leading EFT coefficients obtained from both string and one-loop field-theory amplitudes lie in small islands. The shape and location of the islands can be derived from the dispersive representation for the Wilson coefficients using crossing and assuming that the lowest-spin spectral densities are the largest. Our analysis suggests that the Wilson coefficients of weakly-coupled gravitational physical theories are much more constrained than indicated by bounds arising from dispersive considerations of 2 → 2 scattering. The one-loop four-graviton amplitudes used to obtain the EFT data are computed using modern amplitude methods, including generalized unitarity, supersymmetric decompositions and the double copy.

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Spinning S-matrix Bootstrap in 4d

Cited by 11 publications

References 55 publications

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude

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