(Non)-projective bounds on gravitational EFT

Abstract

In this paper we study both projective and non-projective constraints on gravitational effective fields theories implied from unitarity, causality and crossing. We derive bounds on the Wilson coefficients of D 2n R 4 from its dispersive representation, utilizing both numerical semi-definite programming and analytic geometry analysis. From the former, we derive projective bounds on ratios of couplings and observe that generic boundary spectrums exhibit accumulation points. For the latter we consider the non-projective geometry of the EFThedron, which we relate to the known L-moment problem in the literature. This allows us to move beyond positivity and incorporate the upper bound from unitarity on the spectral functions. This leads to sharp bounds on individual coefficients, which are of order unity when normalized with respect to the UV scale. Finally, the non-projective geometry also allows us to derive optimal bounds reflecting assumptions of low-spin dominance, improving previous results. We complement the analytic derivations with a simple linear programming approach that can efficiently solve such non-projective conditions.

On the unitarity and low energy expansion of the Coon amplitude

“…Firstly, it resonates very neatly with a conjecture of [14] that amplitudes with accumulation points populate the EFT-hedron of gravitational theories away from the small portion where usual theories seem to live. It would be very important to study this problem in more details, in relation with the Coon amplitude.…”

“…In more recent times, the Coon amplitude was brought forward in the bootstrap analysis as an exception to the universality of linear Regge trajectories in [4], coming from the existence of an accumulation point in its spectrum, similar to that of the hydrogen atom, which allows the theory to evade the theorem of [4]. Related bootstrap constraints applied to the Wilson coefficients of effective field theories (EFTs) coming from unitarity, crossing and analyticity are known to impose bounds [5] that carve theory islands [6][7][8][9][10], and it appears that they are bigger than what is required to describe the basic theories of the world around us [11][12][13][14]. Even more interestingly, [14] recently conjectured that the space of gravitational EFTs is actually populated generically of theories with an accumulation point.…”

“…Related bootstrap constraints applied to the Wilson coefficients of effective field theories (EFTs) coming from unitarity, crossing and analyticity are known to impose bounds [5] that carve theory islands [6][7][8][9][10], and it appears that they are bigger than what is required to describe the basic theories of the world around us [11][12][13][14]. Even more interestingly, [14] recently conjectured that the space of gravitational EFTs is actually populated generically of theories with an accumulation point. Since the Coon amplitude has an accumulation point and connects continuously string theory and field theory, it provides an extremely interesting testing ground to investigate some aspects of these questions.…”

UV-Complete Gravity Amplitudes and the Triple Product

“…[11] for the role of Coon's amplitude [12,13] in such context). The existence of such accumulation-point amplitudes was also conjectured to be important in spanning the gravitational EFT [8]. In this work, we aim to construct such amplitudes.…”

“…This is no longer an issue if we assume a perturbative completion, in which case the graviton loops are suppressed. Indeed, working with tree-level completions has led to tremendous insight into the UV spectrum stemming from causality constraints [3], as well as the EFT beyond the leading Einstein-Hilbert action from the combined requirements of causality, unitarity, and crossing [4][5][6][7][8][9]. Moreover, as shown via counting in Ref.…”