New positivity bounds from full crossing symmetry

Abstract

Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the P Q, Dsu, Dstu and $$ {\overline{D}}^{\mathrm{stu}} $$ D ¯ stu bounds. While the PQ bounds and Dsu bounds only make use of the s↔u dispersion relation, the Dstu and $$ {\overline{D}}^{\mathrm{stu}} $$ D ¯ stu bounds are obtained by further imposing the s↔t crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.

Sharp boundaries for the swampland

“…In a local QFT in flat space, the constraints of unitarity and JHEP07(2021)110 causality imply inequalities for the low-energy effective couplings [6,7]. A series of recent papers [8][9][10][11][12] initiated a systematic analysis of the inequalities that follow from consideration of 2 → 2 scattering processes. The analysis begins with canonical assumptions about the S-matrix, such as analyticity, crossing and, crucially, Regge boundedness.…”

S-matrix bootstrap for effective field theories: massless pions

“…The Wilson coefficients depend on the specific microscopic realization of the system and, generically, are very difficult to compute ab initio. For this reason, it is desirable to find universal bounds on these coefficients using only general principles like unitarity and causality [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

“…The same bound has been recently improved in [13] by adding additional positivity constraints -see the grey band in figure 8. Further improvements can be made assuming the validity of perturbation theory also in the physical region z > 4m 2 up to some scale [14].…”

Causality, unitarity and symmetry in effective field theory

“…Generalisation to higher mass dimension, departure from the forward limit and massive particles are obvious future directions [17,[20][21][22]. See e.g.…”

“…For applications of causality constraints to CFTs and holography, see e.g. [8][9][10][11][12][13][14], while for application to EFTs, the subject of discussion here, see [2,[15][16][17][18][19][20][21][22] for a sample of past studies (among many others).…”