High Energy Theory Group Meeting: Dispersion Relations in Conformal Field Theories
Dean Carmi, Perimeter Institute
We derive a dispersion relation for the 4-point correlator of a CFT. The dispersion relation relates the 4-point correlator with an integral over it’s double discontinuity multiplied by a kernel. The kernel is derived by plugging the CFT Lorenzian inversion formula inside the conformal block expansion and performing the resulting integrals and sums. For the 4-point function of scalars of equal scaling dimensions, the kernel is a remarkably simple function (a specific combination of elliptic integral functions) of the cross ratios z and z ̄. The dispersion relation is the analog of the well known dispersion relation which occurs e.g for the 4-particle scattering amplitude M(s, t). We perform various checks of the dispersion relation for simple test correlators (generalized free fields, tree level N = 4 susy at strong coupling), and get perfect matching.