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

Abstract

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.

Dual EFT bootstrap: QCD flux tubes

“…Nevertheless, we do expect that such bound must exist because an arbitrarily negative γ 3 would produce a negative phase (2.3), which would signal non-analyticities in the UHP. 22 As we have learned in this paper, such expectation is precisely addressed by the dual EFT bootstrap approach which sets the bound γ 3 −1/768. An amplitude with a γ 3 below such value is not feasible: it is either non-analytic in the UHP or it violates unitarity for some energy regime.…”

“…Many works have exploited positivity, including: the original studies in the context of the chiral Lagrangian [2][3][4], many interesting applications on RG-flows and the phenomenology of EFT interactions, see e.g. [5][6][7][8][9][10][11][12][13][14][15], as well as new developments [16][17][18][19][20][21][22][23].…”

Positivity and geometric function theory constraints on pion scattering

“…The constraints in EFT Wilson coefficients were worked out in [19][20][21][22][23][24][25][26][27][28][29][30][31], using positivity of the partial wave and null conditions. 4 In our case, we don't use the null constraints; instead, we use positivity (of the partial wave expansion) and bounds in the Taylor series coefficients of the amplitudes in z-variable that appear from the geometric function theory.…”

Standard Model EFTs via on-shell methods

“…In the recent years, onshell methods have proven to be the most powerful techniques in a variety of settings, such as collider physics [37,38], the study of the ultraviolet (UV) behaviour of N = 8 supergravity [39,40], the study of the inspiral phase of binary systems of celestial objects [41][42][43][44][45][46][47][48], the perturbative exploration of supersymmetric gauge theories [49][50][51] and also the perturbative study of off-shell quantities such as form factors [52][53][54][55][56][57][58][59][60][61]. Besides the classification of effective field theory (EFT) interactions themselves, S-matrix properties, such as unitarity, causality and analyticity, have been used to constrain Wilson coefficients associated to EFTs [16,[62][63][64], including the SMEFT [65][66][67]. Moreover, on-shell techniques also provide powerful strategies to study the UV mixing in (non-supersymmetric) EFTs, as first pointed out in [68] using techniques developed for the study of the anomalous dimension of operators in N = 4 super-Yang-Mills [69][70][71][72] (for a review, see [73] and references therein) from scattering amplitudes and form factors [74][75]…”