We place bounds on the order of enhanced discrete gauge symmetries that act on massless fields and thus arise at subloci of the moduli space in supergravity theories. We focus on supersymmetric theories with 8 or more supercharges which in some cases lead to sharp upper bounds realized by specific string constructions.

United States

Zihni Baykara

Switzerland

Markus Dierigl

South Korea

Hee-Cheol Kim

Cumrun Vafa

Kai Xu

Bounds on discrete gauge symmetries in supergravity

We consider 4d $$ \mathcal{N}=1 $$ supergravity theories with modular symmetry, where the modulus $\textit{τ}$ is the upper half-plane modulo SL(2$\textit{,}$ ) action. We focus on enhanced discrete gauge symmetry points $\textit{τ}$ = $\textit{i,}$ exp(2$\textit{πi/}$3), and argue that, if there are no new additional massless fields at these points, they will always be critical points of the scalar potential. Moreover, we show that whether these correspond to dS, AdS, or Minkowski vacua can be generically determined simply by the weight of the superpotential under modular transformations. We also analyze the asymptotics of the scalar potential and find that compatibility with the Swampland principles implies that, if nonvanishing, the scalar potential decays either exponentially or double-exponentially, and that the asymptotic slope is bounded. The slope is governed by the superpotential weight as well as by real-analytic modular contributions to the Kähler potential.

Amineh Mohseni

Symmetry points of $$ \mathcal{N}=1 $$ modular geometry

In four decades of string theory research, only a handful of nonsupersymmetric tachyon-free strings with only one neutral scalar at tree level were found. We construct new nonsupersymmetric tachyon-free string theories using asymmetric orbifolds that serve as the lower-dimensional counterparts to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>16</mn><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mn>16</mn><mo stretchy="false">)</mo></mrow></math> string in 4, 6, and 8 dimensions, each featuring only one neutral scalar at tree level, chiral matter and positive leading order potential. The 4D construction uses a quasicrystalline orbifold.

Zihni Kaan Baykara

Houri-Christina Tarazi

New Nonsupersymmetric Tachyon-Free Strings

Non-geometric flux vacua have recently been revisited, leading to the remarkable discovery of isolated 4D $$ \mathcal{N} $$ = 1 supersymmetric Minkowski vacua. These constructions rely on the non-renormalization of the superpotential, which is supported by heuristic arguments. Given the significance of verifying the existence of these isolated M-theory-like vacua, we present alternative symmetry-based arguments that arrive at the same conclusion. Additionally, we leverage these symmetries to argue for the existence of unstable dS solutions as well as supersymmetric AdS solutions.

Shi Chen

Damian Heisteeg

Symmetries and M-theory-like vacua in four dimensions

In this work, we investigate a largely unexplored nongeometric corner of the string landscape: the quasicrystalline orbifolds. These exist at special points of the Narain moduli, leading to frozen moduli and large quantum symmetries. Here, we complete the classification and construction of quasicrystalline Narain lattices and use this to explore supersymmetric compactifications in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mo>≤</mo><mi>D</mi><mo>≤</mo><mn>6</mn></math> and with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mo>≤</mo><mi>Q</mi><mo>≤</mo><mn>16</mn></math> supercharges, leading to novel theories, including theories with large quantum symmetries at all points in the moduli space. We anticipate that these constructions will have many applications, and in subsequent work, we apply these techniques to construct new nonsupersymmetric tachyon-free models. Similarly, these constructions can lead to constructing exotic matter representations in the string landscape.

Quasicrystalline string landscape

The dark dimension scenario, predicting one extra mesoscopic dimension in the micron range, has emerged by applying various swampland principles to the dark energy. In this note we find that realizing the grand unification of gauge forces is highly constraining in this context. Without actually constructing any grand unified theory (GUT) models, we argue that the mere assumption of grand unification of forces in this scenario, together with the experimental bounds on massive replicas of the Standard Model gauge bosons, predicts an upper bound for the GUT scale, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>GUT</mi></msub><mo>≲</mo><msup><mn>10</mn><mn>16</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Combined with the experimental bound on the proton lifetime, this predicts that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math> gauge boson mediating proton decay is a 5D solitonic string of Planckian tension stretched across a length scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi><mo>∼</mo><mo stretchy="false">(</mo><mn>1</mn><mi>–</mi><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi><msup><mo stretchy="false">)</mo><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> ending on gauge branes of the same diameter <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mi>L</mi></math>. This leads to a mass of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>X</mi></msub><mo>∼</mo><msup><mn>10</mn><mn>15</mn></msup><mi>–</mi><msup><mn>10</mn><mn>16</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. In particular assuming grand unification in the dark dimension scenario results in a tower of Kaluza-Klein excitations of Standard Model gauge bosons on the gauge branes in the 1–10 TeV range. This suggests that the diameter/separation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>L</mi></math> of the gauge branes correlates with both the weak scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>1</mn><mo>/</mo><mi>L</mi></math> near a TeV and the GUT scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msubsup><mi>M</mi><mn>5</mn><mn>2</mn></msubsup><mi>L</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>16</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Jonathan J. Heckman

Germany

Timo Weigand

China

Fengjun Xu

Dark dimension and the grand unification of forces

In this note, we propose a generalized notion of distance between vacua in the theory of a scalar field ϕ with scalar potential V (ϕ) coupled to gravity. We propose the normalized tension of domain wall connecting different field values, with a varying normalization relative to a local energy scale, as the distance. We show this definition reproduces the usual moduli space distance for zero potential, as well as the d ∝ |log Λ| behavior with the vacuum energy Λ in the AdS case, previously proposed in the literature. In the case of large AdS we also obtain the expected exponent of mass versus distance in one particular case, when the mass of the light tower is m ~ <math> <msqrt> <mi>Λ</mi> </msqrt> </math> $$ \sqrt{\Lambda} $$ and there is a single extra dimension decompactifying. We also discuss the features and shortcomings of alternative but related proposals.

CERN

Spain

Miguel Montero

Irene Valenzuela

On measuring distances in the quantum gravity landscape

The dark dimension scenario, which is motivated from Swampland principles and predicts a single micron scale extra dimension, suggests a consistent framework for the dark sector of the universe. We consider the implications of this scenario for the QCD axion. We find that in the scenario in which the axion is localized on the standard model brane (which we will argue is natural), a combination of theoretical (being bounded by the 5D Planck mass) and observational constraints forces it to have decay constant in a narrow range f ~ 109 – 1010 GeV. This corresponds to a mass for the QCD axion of m  a  ~ (1 – 10) meV. The axion mass surprisingly coincides with the mass scale for the dark energy, the dark matter tower, and the neutrinos. In this scenario axions are not expected to form a large fraction of the dark matter but nevertheless this range of axion parameters is accessible to observations in near future experiments.

Naomi Gendler

Axions in the dark dimension

Noninvertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of noninvertible gauge symmetries? In theories with gravity we find a new form of noninvertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy noninvertible gauge symmetries appear in standard examples such as non-Abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of noninvertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate noninvertible symmetries have implications for swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the distance conjecture, and can sometimes explain the existence of slightly subextremal states which fill in the gaps in the sublattice weak gravity conjecture.

Jacob McNamara

Adar Sharon

Fate of stringy noninvertible symmetries

We propose new constraints for 6d (1, 0) supergravity theories based on consistency conditions on the Kähler moduli spaces of their 5d reductions. The requirement that both the metric and the BPS string tensions in the Kähler moduli space are positive imposes specific restrictions on the Chern-Simons coefficients in the 5d effective Lagrangians that are derived from the Kaluza-Klein reductions of 6d theories. Moreover, the emergence of local interacting 5d CFTs when the moduli space metric degenerates introduces additional constraints coming from the analysis of 5d SCFTs. Focusing on the moduli spaces of 6d supergravity theories without a tensor multiplet and their Higgsings, we show that these constraints require the presence of certain primary states in the 2d worldvolume CFTs on 1/2 BPS strings. We specifically analyze a class of SU(2) models and infinite families of U(1) models using these constraints, and demonstrate that the theories featuring a 1-form symmetry in their massless spectra, unless the 1-form symmetry is gauged, fail to satisfy the constraints and therefore belong to the Swampland.