Abstract
Semi-holography has been proposed as an effective nonperturbative framework which can combine perturbative and nonperturbative effects consistently for theories like QCD. It is postulated that the strongly coupled nonperturbative sector has a holographic dual in the form of a classical gravity theory in the large N limit, and the perturbative fields determine the gravitational boundary conditions. In this work, we pursue a fundamental derivation of this framework particularly showing how perturbative physics by itself can determine the holographic dual of the infrared, and also the interactions between the perturbative and the holographic sectors. We firstly demonstrate that the interactions between the two sectors can be constrained through the existence of a conserved local energy-momentum tensor for the full system up to hard-soft coupling constants. As an illustration, we set up a bi-holographic toy theory where both the UV and IR sectors are strongly coupled and holographic with distinct classical gravity duals. In this construction, the requirement that an appropriate gluing can cure the singularities (geodetic incompletenesses) of the respective geometries leads us to determine the parameters of the IR theory and the hard-soft couplings in terms of those of the UV theory. The high energy scale behaviour of the hard-soft couplings is state-independent but their runnings turn out to be state-dependent. We discuss how our approach can be adapted to the construction of the semi-holographic framework for QCD.
Highlights
Semiholography has been recently proposed as an effective framework in which one can include both perturbative and nonperturbative effects consistently in a wide range of energy scales
The second assertion implies that the perturbative degrees of freedom determine the leading asymptotic behavior of the classical gravity fields forming the holographic dual of the nonperturbative sector
We will take first steps towards a derivation of the general semiholographic framework from first principles, i.e. from the fundamental theory describing the microscopic dynamics. This amounts to answering the following questions: (a) Which principles tell us how the perturbative degrees of freedom determine the leading asymptotic behaviors of the gravitational fields forming the holographic dual of the nonperturbative sector? (b) How do we find the appropriate classical gravity theory which provides the dual holographic description of the nonperturbative sector?
Summary
Semiholography has been recently proposed as an effective framework in which one can include both perturbative and nonperturbative effects consistently in a wide range of energy scales. We will take first steps towards a derivation of the general semiholographic framework from first principles, i.e. from the fundamental theory describing the microscopic dynamics This amounts to answering the following questions: (a) Which principles tell us how the perturbative degrees of freedom determine the leading asymptotic behaviors of the gravitational fields forming the holographic dual of the nonperturbative sector? It has been argued that decoding holography as a form of non-Wilsonian RG flow which preserves Ward identities for single-trace operators (like the energy-momentum tensor) and can selfdetermine microscopic data via appropriate infrared endpoint conditions naturally gives rise to a more general semiholographic framework in which the ultraviolet can be asymptotically free so that it is described by perturbative quantum field dynamics rather than by a classical gravity theory [13,14,15]. We will conclude with discussions on the potential phenomenological applications of the biholographic framework
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