CT for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories

In [8] we proposed the linear relations between the Weyl anomaly c(1), c(2), c(3) coefficients and the 4 coefficients in the chiral anomaly polynomial for (1,0) superconformal 6d theories. These relations were determined up to one free parameter xi and its value was then conjectured using some additional assumptions. A different value for xi was recently suggested in arXiv: 1702.03518 using an alternative method. Here we confirm that this latter value is indeed the correct one by providing an additional data point: the Weyl anomaly coefficient c(3) for the higher derivative (1,0) superconformal 6d vector multiplet. This multiplet contains the 4-derivative conformal gauge vector, 3-derivative fermion and 2-derivative scalar. We find the corresponding value of c(3) which is proportional to the coefficient C-T in the 2-point function of stress tensor using its relation to the first derivative of the Renyi entropy or the second derivative of the free energy on the product of thermal circle and 5d hyperbolic space. We present some general results of the computation of the Renyi entropy and C-T from the partition function on S-1 x Hd-1 for higher derivative conformal scalars, spinors and vectors in even dimensions. We also give an independent derivation of the conformal anomaly coefficients of the 6d higher derivative vector multiplet from the Seeley-DeWitt coefficients on an Einstein background.