<p>We generalize the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> regularization scheme in order to develop a framework for systematically studying regularization of loops in quantum field theory. This allows us to“solve” a set of gauge consistency conditions for families of gauge invariant regularization schemes. We recover several known examples such as dimensional and denominator regularizations, as well as some more general solutions. We also study anomalies in chiral theories in order to carefully describe how our formalism should be properly implemented.</p>

United Kingdom

Antonio Padilla

Robert G.C. Smith

Gauge invariance and generalized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> regularization

<p>We advance the study of pure de Sitter supergravity by introducing a finite formulation of unimodular supergravity via the super-Stückelberg mechanism. Building on previous works, we construct a complete four-dimensional action of spontaneously broken <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> supergravity to all orders in the Stückelberg fields, which allows for de Sitter solutions. The introduction of finite supergravity transformations extends the super-Stückelberg procedure beyond the second order, offering a recursive solution to all orders in the Goldstino sector. This work bridges the earlier perturbative approaches and the complete finite theory, opening new possibilities for de Sitter vacua in supergravity models and eventually string theory.</p>

Austria

Sukṛti Bansal

Silvia Nagy

Ivonne Zavala

Stückelberg path to pure de Sitter supergravity

We propose a scenario of a de Sitter universe living on an End-of-the-World brane. Motivated by the Swampland programme and in particular the Cobordism Conjecture, we consider a compact region of AdS nucleating from nothing, with a dS living on its boundary. We show that it can equivalently be interpreted as an up-tunnelling from AdS with cosmological constant Λ → −∞, following Brown and Dahlen’s proposal for ‘nothing’. Their picture naïvely leads to the conclusion that the brane has infinite negative tension. But we show that it becomes finite and positive once we employ holographic renormalization, recovering the Bubble of Something where the domain wall becomes a boundary of spacetime. The same holds true in any number of dimensions and, moreover, at the level of metric perturbations. This provides motivation for alternative routes of obtaining cosmology from quantum gravity or string theory using domain walls, departing from conventional vacuum approaches.

Benjamin Muntz

Paul Saffin

Do we live on the End of the World?

We present a type IIB 4D string model with stabilised moduli which is able to describe the history of the universe from inflation to quintessence. The underlying Calabi-Yau volume is controlled by two moduli which are stabilised by perturbative effects. The lighter of them drives Fibre Inflation at a large energy scale. The two associated axions are ultra-light since they are lifted only at the non-perturbative level. The lighter of them can drive quintessence if its decay constant is large enough to prevent quantum diffusion during inflation from ruining the initial conditions. The right dark energy scale can be obtained via a large suppression from poly-instanton effects. The heavier axion gives a negligible contribution to dark matter since it starts oscillating after matter-radiation equality. If instead none of the two axions has a large decay constant, a mild alignment allows the lighter axion to drive quintessence, while the heavier can be at most a few percent of dark matter due to isocurvature and UV bounds. In both cases dark matter can also come from either primordial black holes or the QCD axion.

Italy

Michele Cicoli

Francesc Cunillera

Francisco Pedro

From inflation to quintessence: a history of the universe in string theory

We perform a thorough analysis of de Sitter solutions in <math><mi>O</mi><mo>(</mo><mi>d</mi><mo>,</mo><mi>d</mi><mo>)</mo></math> invariant cosmologies. Starting with a homogeneous and isotropic framework we examine conditions for the existence of such solutions to the vacuum field equations, nonperturbative in <math><msup><mi>α</mi><mo>′</mo></msup></math> in both the string frame and the Einstein frame. We elucidate the nature of the instability in the string frame vacuum. For the Einstein frame, we demonstrate that the de Sitter solutions cannot be eternal. We then extend our analysis to include Bianchi I universes where the <math><mi>O</mi><mo>(</mo><mi>d</mi><mo>,</mo><mi>d</mi><mo>)</mo></math> symmetry includes scale factor exchange as well as scale factor duality. We show how the theory can be extended to the anisotropic case so that it admits de Sitter solutions, noting the crucial role played by the <math><mi>O</mi><mo>(</mo><mi>d</mi><mo>,</mo><mi>d</mi><mo>)</mo></math> symmetry in satisfying any additional constraints.

Yang Liu

Paul M. Saffin

de Sitter vacua in <math><mi>O</mi><mo>(</mo><mi>d</mi><mo>,</mo><mi>d</mi><mo>)</mo></math> invariant cosmology

We examine the descent via membrane nucleation through a landscape of vacua where the cosmological constant is given by a combination of four-form fluxes. It has been shown that this descent can be slowed exponentially for very low curvature vacua close to Minkowski space in a wide class of models satisfying certain parametric conditions, providing a possible solution to the cosmological constant problem. We explore in detail whether or not those parametric conditions are compatible with the membrane weak gravity conjecture. Whilst it is true that there is often tension, we show that this is not always the case and present an explicit model where Minkowski space is absolutely stable and the weak gravity conjecture is satisfied. This corresponds to an extension of the Bousso-Polchinski model into a generalised DBI action for four-forms. We also clarify how the landscape should be populated in a consistent model.

The cosmological constant and the weak gravity conjecture

Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultraviolet regularization scheme for loop integrals in quantum field theory which we call <math><mi>η</mi></math> regularization. This reveals a connection between the elimination of divergences in divergent series of powers and the preservation of gauge invariance in the regularization of loop integrals in quantum field theory. In particular, we note that a method for regularizing the series of natural numbers so that it converges to minus one-twelfth inspires a regularization scheme for non-Abelian gauge theories coupled to Dirac fermions that preserves the Ward identity for the vacuum polarization tensor and other higher point functions. We also comment on a possible connection to Schwinger proper time integrals.

Robert G. C. Smith

Smoothed asymptotics: From number theory to QFT

We consider a wide class of four-dimensional effective field theories in which gravity is coupled to multiple four-forms and their dual scalar fields, with membrane sources charged under the corresponding three-form potentials. Four-form flux, quantised in units of the membrane charges, generically generates a landscape of vacua with a range of values for the cosmological constant that is scanned through membrane nucleation. We list various ways in which the landscape can be made sufficiently dense to be compatible with observations of the current vacuum without running into the empty universe problem. Further, we establish the general criteria required to ensure the absolute stability of the Minkowski vacuum under membrane nucleation and the longevity of those vacua that are parametrically close by. This selects the current vacuum on probabilistic grounds and can even be applied in the classic model of Bousso and Polchinski, albeit with some mild violation of the membrane weak gravity conjecture. We present other models where the membrane weak gravity conjecture is not violated but where the same probabilistic methods can be used to tackle the cosmological constant problem.

The cosmological constant is probably still zero

We investigate the combined effect of fluxes and higher-order curvature corrections, in the form of the Gauss-Bonnet term, on the existence of de Sitter vacua in a heterotic string inspired framework, compactified on spheres and tori. We first gain some intuition on the effects of these corrections by studying a perturbative expansion in the small Gauss-Bonnet coupling. Then, for choices of potential closer to the string theory predictions, we show that the inclusion of quadratic curvature corrections actually reduces the parametric likelihood of de Sitter solutions.

Czechia

William Emond

Portugal

Antoine Lehébel

Quadratic curvature corrections to stringy effective actions and the absence of de Sitter vacua

We argue that, for string compactifications broadly consistent with swampland constraints, dark energy is likely to signal the beginning of the end of our universe as we know it, perhaps even through decompactification, with possible implications for the cosmological coincidence problem. Thanks to the scarcity (absence?) of stable de Sitter vacua, dark energy in string theory is assumed to take the form of a quintessence field in slow roll. As it rolls, a tower of heavy states will generically descend, triggering an apocalyptic phase transition in the low energy cosmological dynamics after at most a few hundred Hubble times. As a result, dark energy domination cannot continue indefinitely and there is at least a percentage chance that we find ourselves in the first Hubble epoch. We use a toy model of quintessence coupled to a tower of heavy states to explicitly demonstrate the breakdown in the cosmological dynamics as the tower becomes light. This occurs through a large number of corresponding particles being produced after a certain time, overwhelming quintessence. We also discuss some implications for early universe inflation.