Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Chowdhury, Subham Dutta; Ghosh, Kausik; Haldar, Parthiv; Raman, Prashanth; Sinha, Aninda

doi:10.21468/scipostphys.13.3.051

Cited by 39 publications

(15 citation statements)

References 51 publications

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“…More concretely, keeping spins up to j seems to be enough until s ≲ j+1 in the range of energies plotted in the above figure. A version of low-spin dominance was previously observed in field theory and tree-level string scattering, where only spin-0 dominates across all energies [35,36], see also [37].…”

Section: Low-spin Dominancementioning

confidence: 60%

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Unitarity cuts of the worldsheet

Eberhardt¹,

Mizera²

2023

SciPost Phys.

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We compute the imaginary parts of genus-one string scattering amplitudes. Following Witten’s i\varepsiloniε prescription for the integration contour on the moduli space of worldsheets, we give a general algorithm for computing unitarity cuts of the annulus, Möbius strip, and torus topologies exactly in \alpha'α′. With the help of tropical analysis, we show how the intricate pattern of thresholds (normal and anomalous) opening up arises from the worldsheet computation. The result is a manifestly-convergent representation of the imaginary parts of amplitudes, which has the analytic form expected from Cutkosky rules in field theory, but bypasses the need for performing laborious sums over the intermediate states. We use this representation to study various physical aspects of string amplitudes, including their behavior in the (s,t)(s,t) plane, exponential suppression, decay widths of massive strings, total cross section, and low-energy expansions. We find that planar annulus amplitudes exhibit a version of low-spin dominance: at any finite energy, only a finite number of low partial-wave spins give an appreciable contribution to the imaginary part.

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Section: Low-spin Dominancementioning

confidence: 60%

“…We checked up to s < 1 that low-spin dominance also occurs for the Möbius strip, non-planar annulus, and torus topologies. A version of low-spin dominance was previously observed at tree-level and in field theory amplitudes, albeit with only spin-0 dominance [35,36], see also [37].…”

Section: Introductionmentioning

confidence: 56%

Unitarity cuts of the worldsheet

Eberhardt¹,

Mizera²

2023

SciPost Phys.

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“…As discussed in section 4, this is not a problem in the eikonal regime (where polynomial behaviour under crossing is not expected), but if a causal crossing-symmetric unitary UV-completion exists for this amplitude, it must -after crossing -regulate the exponential divergence coming from the cosine and sine functions. One could also try to crossing-symmetrize the amplitude by hand, and see if the low energy expansion coefficients satisfy positivity constraints [77][78][79][80][81][82][83]. However, it turns out that the resulting amplitude does not possess enough of these low energy coefficients to draw a conclusion on this point.…”

Section: Discussionmentioning

confidence: 99%

“…Note also that this amplitude does not have sufficiently many terms in its Laurent expansion to be checked against positivity constraints (cf., [77][78][79][80][81][82][83]), though it would be interesting to further explore this using 'reverse bootstrap' ideas [84] or the non-projective EFT-hedron [85]. Since it is fair to expect that our amplitude will show signs of acausal behaviour (due to its relation to over-spun Kerr), it could suggest derivations for further positivity constraints which could be used to discard the amplitude on causality grounds.…”

Section: Born Amplitudementioning

confidence: 98%

The ultrarelativistic limit of Kerr

Adamo

Cristofoli

Tourkine

2023

J. High Energ. Phys.

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The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by Balasin and Nachbagauer, does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism.

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“…[7,8]. Recently, similar bounds [13,[30][31][32][33][34][35][36] were organized into a novel geometric structure termed the EFT-hedron [14] (see also refs. [15,18,37]), related to the Weak Gravity Conjecture [38][39][40], the analytic bootstrap in AdS/CFT [16,41], and applied to the Standard Model EFT and pion scattering [42][43][44][45].…”

Section: Jhep01(2023)113mentioning

confidence: 99%

Effective Field Theory islands from perturbative and nonperturbative four-graviton amplitudes

Bern¹,

Herrmann²,

Kosmopoulos³

et al. 2023

J. High Energ. Phys.

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Theoretical data obtained from physically sensible field and string theory models suggest that gravitational Effective Field Theories (EFTs) live on islands that are tiny compared to current general bounds determined from unitarity, causality, crossing symmetry, and a good high-energy behavior. In this work, we present explicit perturbative and nonperturbative 2 → 2 graviton scattering amplitudes and their associated low-energy expansion in spacetime dimensions D ≥ 4 to support this notion. Our new results include a first example of gravity weakly coupled to a nonperturbative effective action. We show that, at energies below the mass of its nonperturbative matter, the D = 4, $$ \mathcal{N} $$ N = 1 supersymmetric field theory in the confined phase lies on the same islands identified using four-dimensional perturbative models based on string theory and minimally-coupled matter circulating a loop. Furthermore, we generalize the previous four-dimensional perturbative models based on string theory and minimally-coupled massive spin-0 and spin-1 states circulating in the loop to D dimensions. Remarkably, we again find that the low-energy EFT coefficients lie on small islands. These results offer a useful guide towards constraining possible extensions of Einstein gravity.

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Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

Cited by 39 publications

References 51 publications

Unitarity cuts of the worldsheet

Unitarity cuts of the worldsheet

The ultrarelativistic limit of Kerr

Effective Field Theory islands from perturbative and nonperturbative four-graviton amplitudes

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