AdS/CFT for 3D higher-spin gravity coupled to matter fields

作者：Fujisawa Ippei^*; Nakagawa Kenta; Nakayama Ryuichi

来源：Classical and Quantum Gravity, 2014, 31(6): 065006.

DOI：10.1088/0264-9381/31/6/065006

• 3D higher-spin gravity
• AdS/CFT correspondence
• 3D Vasiliev gravity

Newholographic prescription for themodel of 3d higher-spin gravity coupled to real matter fields B-mu nu and C, which was introduced in Fujisawa and Nakayama (2014 Class. Quantum Grav. 31 015003), is formulated. By using a local symmetry, two of the components of B-mu nu are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, B-phi rho, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields A(mu), (A) over bar (mu). In this model, solutions to the classical equations of motion for A(mu) and (A) over bar (mu) are non-flat due to the interactions with matter fields. The solutions for the gauge fields can, however, be split into two parts, flat gauge fields A(mu), (A) over bar (mu), and those terms that depend on the matter fields. The equations for the matter fields then coincide with covariantly-constancy equations in the flat backgrounds A(mu) and (A) over bar (mu), which are exactly the same as those in linearized 3d Vasiliev gravity. The two-and three-point correlation functions of the singletrace operators and the higher-spin currents in the boundary CFT are computed by using an on-shell action tr (B-phi rho C). This term does not depend on coordinates due to the matter equations of motion, and it is not necessary to take the nearboundary limit rho -> infinity. Analysis is presented for SL(3,R) x SL(3,R) as well as HS[1/2] xHS[1/2] higher-spin gravity. In the latter model, scalar operators with scaling dimensions Delta(+) = 3/2 and Delta(-)= 1/2 appear in a single quantization.

• 出版日期2014-3-21