Bulk and brane gauge propagator on 5 d AdS black hole

The bulk gauge fields on 5d AdS black hole are discussed. We construct the bulk (and the corresponding brane) gauge propagator when black hole has large radius. The properties of gauge and ghost propagators are studied in both, minkowski or euclidean signature. In euclidean formulation the propagator structure corresponds to the one of theory at finite temperature (which depends on coordinates). The decoupling of KK modes and localization of gauge fields on flat brane is demonstrated. We show that with such a bulk there is no natural solution of hierarchy problem. PACS: 98.80.Hw,04.50.+h,11.10.Kk,11.10.Wx [email protected] [email protected]. Also at ICREA and IEEC, Barcelona, Spain. 1 1. Assuming that observable Universe is multi-dimensional one the fundamental question appears: What is the form (and number) of extra dimensions? Are they planar or orbifolded? Within the recent braneworld scenario [1] the most likely possibility for Universe is 5d AdS space. The braneworld scenario with bulk 5d AdS is very attractive as it may have the superstring origin. Moreover, in such picture the four-dimensional world represents the brane (where graviton and matter fields are trapped) embedded into AdS bulk. The nice way to solve the hierarchy problem on the brane appears. Nevertheless, one can admit another choice for bulk manifold, for example, AdS black hole. Indeed, like pure AdS space the AdS black hole may be (part of) superstring vacuum. The phase transition which may be interpreted as confinement-deconfinement transition in AdS/CFT set-up may occur between pure AdS and AdS black hole[2]. Moreover, the graviton is localized on the brane embedded in AdS black hole[3]. Hence, it is very interesting to understand the properties of such bulk choice and their possible relation with the phenomenology of the unified theories. In the present Letter we consider bulk abelian gauge fields in 5d AdS black hole. The bulk (brane) gauge propagator is constructed for large black hole with minkowskii or euclidean signature. The decoupling of KK modes and localization of gauge fields on flat brane is demonstrated. It is shown that unlike to pure AdS bulk there is no natural solution for hierarchy problem. Brief discussion of possible phase transition and its consequences for bulk QFT is given. 2. In order to consider the propagators, we start with the action of the abelian gauge theory in the 5-dimensional curved background: S0 = − 1 4 ∫ dx −ggμνgρσFμρFνσ , Fμν = ∂μAν − ∂νAμ . (1) The gauge fixing action Sf and the ghost action Sg are: Sf = 1 2ξ ∫ dx √−g (∇Aμ) , Sg = ∫ dx −gb∇μ∂μc . (2) Note that discussion of bulk gauge fields in AdS braneworlds has been given in refs.[4, 5, 6, 7, 8]. As a curved background, we consider the Schwarzschild-