Abstract
We review some of the recent results which can be useful for better understanding of the problem of stability of vacuum and in general classical solutions in higher derivative quantum gravity. The fourth derivative terms in the purely gravitational vacuum sector are requested by renormalizability already in both semiclassical and complete quantum gravity theories. However, because of these terms, the spectrum of the theory has unphysical ghost states which jeopardize the stability of classical solutions. At the quantum level, ghosts violate unitarity, and thus ghosts look incompatible with the consistency of the theory. The “dominating” or “standard” approach is to treat higher derivative terms as small perturbations at low energies. Such an effective theory is supposed to glue with an unknown fundamental theory in the high energy limit. We argue that the perspectives for such a scenario are not clear, to say the least. On the other hand, recently, there was certain progress in understanding physical conditions which can make ghosts not offensive. We survey these results and discuss the properties of the unknown fundamental theory which can provide these conditions satisfied.
Highlights
Numerous tests and verifications performed during the last century have shown that GeneralRelativity (GR) is a complete theory of classical gravitational phenomena
The presence of singular regions in physically relevant solutions of GR indicates the need for extending the theory
All higher derivative terms, including the terms in the classical action which are subject of renormalization, local and nonlocal quantum corrections, running parameter, etc., are regarded as small perturbations over the basic Einstein–Hilbert term of GR
Summary
Numerous tests and verifications performed during the last century have shown that General. GR is not valid at all scales, especially at very short distances and/or when the curvature becomes very large In this situation, one can expect that the gravitational phenomena should be described by a more extensive and complicated theory. (ii) Quantize only matter fields on classical curved background (semiclassical approach). In the case of (super)string theory, both matter and gravity are induced, and the fundamental object of quantization is the two-dimensional (2D) string, which lives in the external D-dimensional background and defines its geometry and dynamics.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
