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Paper IPM / Physic / 11245  


Abstract:  
The HoravaLifshitz gravity, having broken the symmetry of space and time, includes three objects: the spatial metric g_ij, the lapse variable N, and the shift variable N_i. Each of these objects have their own scaling dimensions. The action of the theory is required to be invariant under this scaling, and spatial diffeomorphism, and the temporal foliation symmetry. Noting that action can nontrivially depend on the lapse variable, we suggest to consider the Horva's approach to quantum gravity in higher dimensions such that an extra spacial coordinate (not time) possesses a scaling dimension different from that of rest. In so so doing, we nominate a new power counting renormalizable theory for quantum gravity in its UV point. The leading IR limit of the proposal coincides to EinsteinHilbert action in an extra dimensional universe where the symmetry between the extra dimension and ordinary dimensions is broken at the subleading corrections.
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