Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry

作者：Afshar Hamid^*; Creutzig Thomas; Grumiller Daniel; Hikida Yasuaki; Ronne Peter B

来源：The Journal of High Energy Physics, 2014, 2014(6): 063.

DOI：10.1007/JHEP06(2014)063

• Higher Spin Symmetry
• Conformal and W Symmetry
• AdS-CFT Correspondence

We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Sernikhatov W-n((2))-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n = 2 and n = 4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k + n = (n + 1)/(n - 1). At these points, the W-n((2))-algebra is nothing but a compactified free boson. This family of W-algebras admits an %26apos;t Hooft limit. Further, in the case of n = 4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product.

• 出版日期2014-6-11