Abstract
Light-cone gauge formulation of fields in AdS space and conformal field theory in flat space adapted for the study of AdS/CFT correspondence is developed. Arbitrary spin mixed-symmetry fields in AdS space and arbitrary spin mixed-symmetry currents, shadows, and conformal fields in flat space are considered on an equal footing. For the massless and massive fields in AdS and the conformal fields in flat space, simple light-cone gauge actions leading to decoupled equations of motion are found. For the currents and shadows, simple expressions for all 2-point functions are also found. We demonstrate that representation of conformal algebra generators on space of currents, shadows, and conformal fields can be built in terms of spin operators entering the light-cone gauge formulation of AdS fields. This considerably simplifies the study of AdS/CFT correspondence. Light-cone gauge actions for totally symmetric arbitrary spin long conformal fields in flat space are presented. We apply our approach to the study of totally antisymmetric (one-column) and mixed-symmetry (two-column) fields in AdS space and currents, shadows, and conformal fields in flat space.
Highlights
AdS field theory in ref. [5] and light-cone gauge formulation of AdS superstring theory in refs. [6, 7] were developed
Our presentation for thecolumn andcolumn AdS fields demonstrates how the field content and explicit form of the operator M z which are required for the light-cone gauge formulation of mixedsymmetry arbitrary spin AdS field can be specified
This is to say that, by analogy with the light-cone gauge formulation of massive field in Rd,1, in order to develop the light-cone gauge formulation of massive field in AdSd+1 we can use field content which is realized as irreducible representation of the so(d) algebra
Summary
AdS field theory in ref. [5] and light-cone gauge formulation of AdS superstring theory in refs. [6, 7] were developed. Massless and massive fields propagating in AdSd+1 space are associated with unitary positive-energy lowest weight irreducible representations of the so(d, 2) algebra. The short shadows in Rd−1,1 can be used to build the conformal invariant Lagrangian dynamics of fields propagating in Rd−1,1. The long shadows with some particular values of ∆sh can be used to build the conformal invariant Lagrangian dynamics of fields propagating in Rd−1,1. Such fields will be referred to as long conformal fields. Most of conformal fields enter higher-derivative Lagrangian dynamics and are associated with non-unitary representations of the so(d, 2) algebra labeled by ∆, h.
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