Holography and entropy bounds suggest that the ultraviolet (UV) and infrared (IR) cutoffs of gravitational effective theories are related to one another as a form of UV/IR mixing. Motivated by this, we derive a bound on the allowed scalar field range in theories with cosmic horizons. We show how this bound challenges several inflationary scenarios, such as $\textit{α}$-attractors and modular-invariant inflation. Besides, we find a relation between the number of extra spatial dimensions and the tensor-to-scalar ratio.

Belgium

Niccolò Cribiori

Italy

Flavio Tonioni

Cosmological constraints from UV/IR mixing

The latest DESI DR2 results, when combined with other independent cosmological data on the Cosmic Microwave Background and supernovas, suggest a preference for dynamical dark energy. We propose a novel cosmological scenario, which features two distinct scalar fields. One governs the magnitude of the present-day dark energy density and is related to the size of extra-dimensions. Accounting for the observed smallness of this energy density requires the scalar to reside near the boundary of field space. The second field, responsible for the time evolution of dark energy and associated with the string coupling, must instead lie in the bulk to remain consistent with the non-observation of light string states. We show that a natural candidate for such dark energy dynamics is a quintessence modular-invariant potential, in which the second scalar field rolls down a negatively curved slope, starting from a self-dual critical point. We find that this scenario is in good agreement with the latest findings by DESI.

United States

Luis Anchordoqui

Thailand

France

Ignatios Antoniadis

Türkiye

Arda Hasar

Germany

Dieter Lüst

Joaquin Masias

Marco Scalisi

Bulk/boundary modular quintessence and DESI

<p>We revisit scale separation for compactifications of ten- and eleven-dimensional supergravity. For cosmological solutions rolling down flux-generated potentials, we observe that scale separation is achieved as time flows, and is fairly generic. This is realized without the need of orientifolds nor corrections to the classical supergravity approximation. We then confront scale separation with the covariant entropy bound (CEB) and the Cohen-Kaplan-Nelson bound. We show that a naive application of these bounds to vacua hints at the existence of at least two extra dimensions. For rolling solutions, we observe that the CEB is not always respected, but since these examples lack a cosmic horizon, the application of entropy bounds remains delicate.</p>

David Andriot

Thomas Van Riet

Scale separation, rolling solutions, and entropy bounds

We argue that scale-separated $$\hbox {AdS}_2$$ vacua with at least two preserved supercharges cannot arise from flux compactifications in a regime of computational control. We deduce this by showing that the $$\hbox {AdS}_2$$ scale is parametrically of the same order as the tension of a fundamental BPS domain wall, which provides an upper bound on the UV cutoff. Since the latter does not need to be associated to any geometric scale, the argument excludes scale separation in a broader sense than what commonly considered. Our claim is exemplified by a bottom-up 2D supergravity analysis as well as top-down models from Type II flux compactifications.

Greece

Fotis Farakos

Nikolaos Liatsos

On scale-separated supersymmetric $$\hbox {AdS}_2$$ flux vacua

It has been recently suggested that the strong Emergence Proposal is realized in M-theory limits by integrating out all light towers of states with a typical mass scale not larger than the species scale, i.e. the eleventh dimensional Planck mass. Within the BPS sector, these are transverse M2- and M5-branes, that can be wrapped and particle-like, carrying Kaluza-Klein momentum along the compact directions. We provide additional evidence for this picture by revisiting and investigating further the computation of R 4-interactions in M-theory à la Green-Gutperle-Vanhove. A central aspect is a novel UV-regularization of Schwinger-like integrals, whose actual meaning and power we clarify by first applying it to string perturbation theory. We consider then toroidal compactifications of M-theory and provide evidence that integrating out all light towers of states via Schwinger-like integrals thus regularized yields the complete result for R 4-interactions. In particular, this includes terms that are tree-level, one-loop and space-time instanton corrections from the weakly coupled point of view. Finally, we comment on the conceptual difference of our approach to earlier closely related work by Kiritsis-Pioline and Obers-Pioline, leading to a correspondence between two types of constrained Eisenstein series.

Ralph Blumenhagen

Aleksandar Gligovic

Antonia Paraskevopoulou

Emergence of R 4-terms in M-theory

The species scale provides a lower bound on the shortest possible length that can be probed in gravitational effective theories. It may be defined by the size of the minimal black hole in the theory and, as such, it has recently been given an interpretation along the lines of the celebrated black hole thermodynamics. In this work, we extend this interpretation to the case of charged species. We provide working definitions of minimal black holes for the case of uncharged and charged species constituents. Then, examining the modifications in the thermodynamic properties of near-extremal charged species compared to the uncharged case, we uncover interesting implications for the cosmology of an expanding universe, particularly within the context of the Dark Dimensions Scenario. Finally, we explore possible microscopic constructions in non-supersymmetric string theories in which towers of charged near-extremal species may arise.

Ivano Basile

Carmine Montella

Minimal black holes and species thermodynamics

We revisit the Emergence Proposal in the vector multiplet moduli space of type IIA N = 2 supersymmetric string vacua in four dimensions, for which the string tree-level prepotential and the string one-loop correction are exactly known via mirror symmetry. We argue that there exists an exact notion of emergence, according to which these four-dimensional couplings can be computed exactly in any asymptotic limit in field space. In such limits, a perturbative quantum gravity theory emerges, whose fundamental degrees of freedom include all complete infinite towers of states with typical mass scale not larger than the species scale. For a decompactification limit, this picture is closely related to and in fact motivated by the computation of Gopakumar-Vafa invariants. In addition, in the same limit our results suggest that the emergent theory will also contain asymptotically tensionless wrapped NS5-branes.

Demystifying the Emergence Proposal

It has been recently proposed that at each infinite distance limit in the moduli space of quantum gravity a perturbative description emerges with fundamental degrees of freedom given by those infinite towers of states whose typical mass scale is parametrically not larger than the ultraviolet cutoff, identified with the species scale. This proposal is applied to the familiar ten-dimensional type IIA and IIB superstring theories, when considering the limit of infinite string coupling. For type IIB, the light towers of states are given by excitations of the <math><mi>D</mi><mn>1</mn></math>-brane, as expected from self-duality. Instead, for type IIA at strong coupling, which is dual to M-theory on <math><msup><mi>S</mi><mn>1</mn></msup></math>, we make the observation that the emergent degrees of freedom are bound states of transversal <math><mi>M</mi><mn>2</mn></math>- and <math><mi>M</mi><mn>5</mn></math>-branes with Kaluza-Klein momentum along the circle. We speculate on the interpretation of the necessity of including all these states for a putative quantum formulation of M-theory.

Emergent M-theory limit

We analyse particle species and the species scale in quantum gravity from a thermodynamic perspective. In close analogy to black hole thermodynamics, we propose that particle species have an entropy and a temperature, which is determined by the species scale. This is identical to the Bekenstein-Hawking entropy of a corresponding minimal black hole and agrees with the number of species in a given tower of states. Through the species entropy, we find that certain entropy bounds are connected to recent swampland constraints. Moreover, the concept of species entropy and temperature allow us to formulate the laws of species thermodynamics, which are argued to govern the variations of moduli in string theory. They can be viewed as general rules that imply certain swampland conjectures, and vice versa.

Species entropy and thermodynamics

We provide a moduli-dependent definition of species scale in quantum gravity based on black hole arguments. Concretely, it is derived from a lower bound on the entropy of extremal black holes with higher curvature corrections, which ensures that the black hole can be reliably described within the effective theory. By demanding that our definition coincides with a recent proposal for a moduli-dependent species scale motivated from the topological string, we conclude that the conjecture <math><msub><mrow><mi>Z</mi></mrow><mrow><mi>B</mi><mi>H</mi></mrow></msub><mo>=</mo><mo>|</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>top</mi></mrow></msub><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></math> relating the black hole to the topological string partition functions should hold, at least within the regime of validity of our analysis.