Nonlocality in string theory

Physical Review D, 2015

In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension d at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number 0 < α < d, we find that the spatial spectral dimension reduces to ds ≃ α at small scales. The spatial Hausdorff dimension of such class of states varies between 1 and d, while the walk dimension takes the usual value dw = 2. Therefore, these quantum geometries may be considered as fractal only when α = 1, where the "magic number" Ds ≃ 2 for the spectral dimension of spacetime, appearing so often in quantum gravity, is reproduced as well. These results apply, in particular, to special superpositions of spin-network states in loop quantum gravity, and they provide more solid indications of dimensional flow in this approach.

2014

Recently, evidence has been collected that a class of gravitational theories with certain non-local operators is renormalizable. We consider one such model which, at the linear perturbative level, reproduces the effective non-local action for the light modes of bosonic closed string field theory. Using the property of asymptotic freedom in the ultraviolet and fixing the classical behaviour of the scale factor at late times, an algorithm is proposed to find general homogeneous cosmological solutions valid both at early and late times. Imposing a power-law classical limit, these solutions (including anisotropic ones) display a bounce instead of a big-bang singularity, and super-accelerate near the bounce even in the absence of an inflaton or phantom field.

International Journal of Modern Physics D, 2016

We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory, when the system is probed at a given resolution. This picture has three main advantages: (a) it clarifies the role of the mass term in the derivation of the spectral dimension; (b) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where instead of a transition amplitude one has a probability density solving a non-relativistic diffusion equation in an abstract diffusion time; (c) it solves the problem of negative probabilities known for higher-order and non-local dispersion relations in classical and quantum gravity; (d) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension d S of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value d UV S ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value d UV S = 2 for any dimension D.

The European Physical Journal C

Effects from nonstandard corrections to Newtonian gravity, at large scale, can be investigated using the cosmological structure formation. In particular, it is possible to show if and how a logarithmic correction (as that induced from nonlocal gravity) modifies the clustering properties of galaxies and of clusters of galaxies. The thermodynamics of such systems can be used to obtain important information about the effects of such modification on clustering. We will compare its effects with observational data and it will be demonstrated that the observations seem to point to a characteristic scale where such a logarithmic correction might be in play at galactic scales. However, at larger scales such statistical inferences are much weaker, so that a fully reliable statistical evidence for this kind of corrections cannot be stated without further investigations and the use of more varied and precise cosmological and astrophysical probes.

Journal of High Energy Physics

We study spontaneous gauge symmetry breaking and the Higgs mechanism in nonlocal field theories. Motivated by the level truncated action of string field theory, we consider a class of nonlocal field theories with an exponential factor of the d’Alembertian attached to the kinetic and mass terms. Modifications of this kind are known to make mild the UV behavior of loop diagrams and thus have been studied not only in the context of string theory but also as an alternative approach to quantum gravity. In this paper we argue that such a nonlocal theory potentially includes a ghost mode near the nonlocal scale in the particle spectrum of the symmetry broken phase. This is in sharp contrast to local field theories and would be an obstruction to making a simple nonlocal model a UV complete theory. We then discuss a possible way out by studying nonlocal theories with extra symmetries such as gauge symmetries in higher spacetime dimensions.