Ivano Basile

This short overview aims to summarize some universal aspects of gravitational effective theories arising from string theory. In particular, I will discuss how the consistency conditions on string vacua, formulated within the worldsheet conformal field theory, entail unexpected relations between low-energy data. This includes the vacuum energy, the mass gap to new physics and the species scale, which are the three scales featured by any gravitational theory. The resulting scaling relations hint at parametric inequalities in the form of holographic bounds, which furthermore support swampland-motivated phenomenological scenarios such as the dark dimension. This review is based on a talk given at Niels Bohr Institute in May 2025.

A bstract: Parametric scale separation is notoriously difficult to achieve in flux compactifications of gravitational effective theories. An appealing alternative to conventional Freund-Rubin vacua involves Ricci-flat internal manifolds, where the energy supplied by fluxes is balanced not by curvature but by the Casimir energy. The internal volume can be stabilized by this mechanism producing anti-de Sitter geometries with parametric scale separation, including an explicit example in eleven-dimensional supergravity. We study deformations of these geometries, showing the presence of perturbative and non-perturbative instabilities.

The main goal of string phenomenology is to find realistic models of particle physics and cosmology within string theory. Dark bubble cosmology is an alternative to string compactifications, where our Universe lives on a bubble expanding in a higher-dimensional spacetime. This construction is inherently nonsupersymmetric and can yield a four-dimensional realistic cosmology, where radiation behaves as expected due to its coupling to higher-dimensional fields. We study the coupling of the electroweak and strong sectors to the induced braneworld gravity via the same mechanism. While the electroweak sector is unaffected, the gravitational and inertial masses of the proton differ significantly, severely violating measurements of the equivalence principle.

A bstract: In a recent work, Tachikawa and Zhang proved the existence of a discrete topological term in the unique non-supersymmetric heterotic string with no tachyons in ten dimensions. This theory features NS5-branes, whose chiral degrees of freedom are not well-understood due to the absence of dualities or supersymmetry. In this paper, we test the consistency of a tentative spectrum obtained by anomaly inflow, studying the relation between the worldvolume theory and the discrete topological term in spacetime. Furthermore, we conduct a bottom-up investigation of lower-dimensional gravitational theories with the same methods.

We build a novel realization of dark bubble cosmology in non-supersymmetric string theory. Among the simplest models in ten dimensions, the type 0’B orientifold is the unique option which yields a scale-separated construction. The resulting setting produces a logarithmically varying dynamical dark energy, reflecting its holographic counterpart in terms of running gauge couplings. We analyze in detail the phenomenological consequences of the model for particle physics, inflation and late-time cosmology. We find that, although particle physics may be consistently realized, neither early-time nor late-time cosmology are observationally viable.

Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards Quantum Gravity". The scope was to provide a coherent picture, from its foundation to forefront research, emphasizing connections between different areas. The lectures begin with perturbative quantum gravity and effective field theory. Subsequently, two ultraviolet-complete approaches are presented: Asymptotically safe gravity and string theory. Finally, elements of quantum effects in black hole spacetimes are discussed.

In a recent work, Tachikawa and Zhang proved the existence of a discrete topological term in the unique non-supersymmetric heterotic string with no tachyons in ten dimensions. This theory features NS5-branes, whose chiral degrees of freedom are not well-understood due to the absence of dualities or supersymmetry. In this paper, we test the consistency of a tentative spectrum obtained by anomaly inflow, studying the relation between the worldvolume theory and the discrete topological term in spacetime. Furthermore, we conduct a bottom-up investigation of lower-dimensional gravitational theories with the same methods.

The main goal of string phenomenology is to find realistic models of particle physics and cosmology within string theory. Dark bubble cosmology is an alternative to string compactifications, where our universe lives on a bubble expanding in a higher-dimensional spacetime. This construction is inherently non-supersymmetric and can yield a four-dimensional realistic cosmology, where radiation behaves as expected due to its coupling to higher-dimensional fields. We study the coupling of the electroweak and strong sectors to the induced braneworld gravity via the same mechanism. While the electroweak sector is unaffected, the gravitational and inertial masses of the proton differ significantly, severely violating measurements of the equivalence principle.

It appears to be difficult within string theory to obtain genuine scale separation between spacetime and the internal sector. In this paper, we propose a novel mechanism for scale-separated vacua which hinges on stringy effects that are invisible at the level of effective field theory. We show that (meta)stable vacua can form if a super no-scale one-loop potential combines with generic two-loop contributions to the vacuum energy, in a manner analogous to Banks-Zaks fixed points. Weak string coupling and scale separation arise from the accidental smallness of the one-loop term, which receives contributions only from massive states, relative to the two-loop term. We provide a proof of concept of this mechanism in explicit non-supersymmetric heterotic toroidal orbifolds by balancing the complete one-loop contribution against the estimated two-loop term and numerically minimizing the resulting effective potential in a restricted sector of moduli space. We note that this mechanism is generically possible within any fundamental theory that has a one-loop energy that gets contributions only from massive modes.

It is widely believed that global symmetries must be broken in Quantum Gravity. This includes higher-form symmetries, which are commonplace in supergravity coupled to vector multiplets. Recently, a quantitative criterion for the breaking of (higher-form) symmetries in effective field theories of gravity has been proposed. We studied this criterion in the context of center one-form symmetries broken by BPS states in Calabi–Yau compactifications of type IIA string theory and M-theory. In a simple toy model, we evaluated the parameters quantifying the extent of symmetry breaking for large and small values of the moduli, comparing the scales of significant breaking with other relevant physical scales.