Partition functions and Casimir energies in higher spin AdSd_{+1}/CFT_{d}
Abstract
Recently, the oneloop free energy of higher spin (HS) theories in Euclidean AdS_{d +1} was calculated and matched with the order N^{0} term in the free energy of the large N "vectorial" scalar CFT on the S^{d} boundary. Here we extend this matching to the boundary theory defined on S^{1}×S^{d 1}, where the length of S1 may be interpreted as the inverse temperature. It has been shown that the large N limit of the partition function on S^{1}×S^{2} in the U(N) singlet sector of the CFT of N free complex scalars matches the oneloop thermal partition function of the Vasiliev theory in AdS4, while in the O(N) singlet sector of the CFT of N real scalars it matches the minimal theory containing even spins only. We extend this matching to all dimensions d. We also calculate partition functions for the singlet sectors of free fermion CFTs in various dimensions and match them with appropriately defined higher spin theories, which for d >3 contain massless gauge fields with mixed symmetry. In the zerotemperature case R×S^{d 1} we calculate the Casimir energy in the scalar or fermionic CFT and match it with the oneloop correction in the global AdSd_{+1}. For any odddimensional CFT the Casimir energy must vanish on general grounds, and we show that the HS duals obey this. In the U(N) symmetric case, we exhibit the vanishing of the regularized oneloop Casimir energy of the dual HS theory in AdSd_{+1}. In the minimal HS theory the vacuum energy vanishes for odd d while for even d it is equal to the Casimir energy of a single conformal scalar in R×S^{d 1} which is again consistent with AdS/CFT, provided the minimal HS coupling constant is ̃1/(N1). We demonstrate analogous results for singlet sectors of theories of N Dirac or Majorana fermions. We also discuss extensions to CFTs containing N_{f} flavors in the fundamental representation of U(N) or O(N).
 Publication:

Physical Review D
 Pub Date:
 July 2014
 DOI:
 10.1103/PhysRevD.90.024048
 arXiv:
 arXiv:1402.5396
 Bibcode:
 2014PhRvD..90b4048G
 Keywords:

 04.50.h;
 11.25.Tq;
 04.62.+v;
 Higherdimensional gravity and other theories of gravity;
 Gauge/string duality;
 Quantum field theory in curved spacetime;
 High Energy Physics  Theory
 EPrint:
 43 pages. v3: minor changes, references added. Version published in PRD