2017/05/08 by M. Beccaria, A. A. Tseytlin
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep06(2017)002
30 pages. v2: minor corrections and refs added; v3: new section 6 with independent confirmation of the main result for anomalies of higher derivative vector multiplet and new appendix C
arxiv created 2017/05/08 · arxiv updated 2017/06/28
In arXiv:1510.02685 we proposed linear relations between the Weyl anomaly c1, c2, c3 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 ξ and its value was then conjectured using some additional assumptions. A different value for ξ was recently suggested in arXiv:1702.03518 using a different method. Here we confirm that this latter value is indeed the correct one by providing an additional data point: the Weyl anomaly coefficient c3 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 c3 which is proportional to the coefficient CT 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 computation of the Renyi entropy and CT from the partition function on S1 × \mathbb 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 higher derivative vector multiplet from the Seeley-DeWitt coefficients on an Einstein background.