Signs and Stability in Higher-Derivative Gravity

Perturbatively renormalizable higher-derivative gravity in four space-time dimensions with arbitrary signs of couplings has been considered. Systematic analysis of the action with arbitrary signs of couplings in lorentzian flat space-time for no-tachyons, fixes the signs. Feynman $+i\epsilon$ prescription for these sign further grants necessary convergence in path-integral, suppressing the field modes with large action. This also leads to a sensible wick rotation where quantum computation can be performed. Running couplings for these sign of parameters makes the massive tensor ghost innocuous leading to a stable and ghost-free renormalizable theory in four space-time dimensions. The theory has a transition point arising from renormalisation group (RG) equations, where the coefficient of $R^2$ diverges without affecting the perturbative quantum field theory. Redefining this coefficient gives a better handle over the theory around the transition point. The flow equations pushes the flow of parameters across the transition point. The flow beyond the transition point is analysed using the one-loop RG equations which shows that the regime beyond the transition point has unphysical properties: there are tachyons, the path-integral loses positive definiteness, Newton's constant $G$ becomes negative and large, and perturbative parameters become large. These shortcomings indicate a lack of completeness beyond the transition point and need of a non-perturbative treatment of the theory beyond the transition point.Comment: 13 pages, 0 figures. V2: minor text modification, references added, minor typos and affiliation edited. Published in IJMP

AdS backgrounds and induced gravity

In this paper we look for AdS solutions to generalised gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein-Hilbert gravity is induced when the scalar acquires a non-zero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.Comment: 17 pages. Journal versio

Unitary and Renormalizable Theory of Higher Derivative Gravity

In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which includes standard cosmology. The running of gravitational constant which includes contribution of graviton is computed. It is shown that generically Newton's constant vanishes at short distance in this perturbatively renormalizable and unitary theory.Comment: 4 pages. To appear in JPCS-IOP. Proceedings of the conference COSGRAV12, held at Indian Statistical Institute, Kolkat

Physical states in the canonical tensor model from the perspective of random tensor networks

Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for $N=2,3$, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general $N$. Then, by generalizing this form, we also obtain various solutions for general $N$. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased $N$. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in $N=3$, and comment on an extension of Airy function related to the solutions.Comment: 41 pages, 1 figure; typos correcte

Ultraviolet complete dark energy model

We consider a local phenomenological model to explain a non-local gravity scenario which has been proposed to address dark energy issues. This non-local gravity action has been seen to fit the data as well as $\Lambda$-CDM and therefore demands a more fundamental local treatment. The induced gravity model coupled with higher-derivative gravity is exploited for this proposal, as this perturbatively renormalizable model has a well-defined ultraviolet (UV) description where ghosts are evaded. We consider a generalised version of this model where we consider two coupled scalar fields and their non-minimal coupling with gravity. In this simple model, one of the scalar field acquires a Vacuum Expectation Value (VEV), thereby inducing a mass for one of the scalar fields and generating Newton's constant. The induced mass however is seen to be always above the running energy scale thereby leading to its decoupling. The residual theory after decoupling becomes a platform for driving the accelerated expansion under certain conditions. Integrating out the residual scalar generates a non-local gravity action. The leading term of which is the non-local gravity action used to fit the data of dark energy.Comment: published version: 11 pages, two columns, minor modification of title, text and references added, typos fixe

An OSpOSp extension of Canonical Tensor Model

Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally constrained system with a number of first-class constraints, which have a similar algebraic structure as the constraints of the ADM formalism of general relativity. In this paper, we formulate a super-extension of CTM as an attempt to incorporate fermionic degrees of freedom. The kinematical symmetry group is extended from $O(N)$ to $OSp(N,\tilde N)$, and the constraints are constructed so that they form a first-class constraint super-Poisson algebra. This is a straightforward super-extension, and the constraints and their algebraic structure are formally unchanged from the purely bosonic case, except for the additional signs associated to the order of the fermionic indices and dynamical variables. However, this extension of CTM leads to the existence of negative norm states in the quantized case, and requires some future improvements as quantum gravity with fermions. On the other hand, since this is a straightforward super-extension, various results obtained so far for the purely bosonic case are expected to have parallels also in the super-extended case, such as the exact physical wave functions and the connection to the dual statistical systems, i.e. randomly connected tensor networks.Comment: 27pages, 27 figure

Charge Renormalization due to Graviton Loops

The leading term in the gauge coupling beta function comes due to interaction of gauge field with gravitons. It is shown to be a universal quantity for all gauge theories. At one-loop it is found to be zero in four dimensions. This is independent of the gravity action with metric as the field variable, gauge fixing condition and regularization scheme. This term being universally same for all gauge groups is further studied in the case of abelian gauge theories, where due to self-duality this term is shown to be zero to all loops, on-shell. Consequences of this are discussed.Comment: 1+10 pages, 1 figure, Published in JHE