String Theory seminar - Paul McFadden [UNUSUAL DAY: THURSDAY] Seminar

Abstract: This talk will discuss parametric integral representations for the general n-point function of scalar operators in momentum-space conformal field theory. Recently, the n-point function was expressed as a generalised Feynman integral with the topology of a simplex, where the numerator contains an arbitrary function of momentum-space cross ratios. Here, we show the corresponding graph polynomials can be expressed in terms of the first and second minors of the Laplacian matrix for the simplex. Computing the effective resistance between nodes of the corresponding electrical network, an inverse parametrisation is found in terms of the determinant and first minors of the Cayley-Menger matrix. These parametrisations reveal new families of weight-shifting operators, expressible as determinants, that connect n-point functions in spacetime dimensions differing by two.