<p>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 <i>and</i> 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>.</p>

United States

Jonathan J. Heckman

Cumrun Vafa

Germany

Timo Weigand

China

Fengjun Xu

Dark dimension and the grand unification of forces

In this note, we study the Swampland Distance Conjecture in TCS G 2 manifold compactifications of M-theory. In particular, we are interested in testing a refined version — the Emergent String Conjecture, in settings with 4d N = 1 supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the K3-fiber in a TCS G 2 manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS G 2 compactifications, which might lead to a weakly coupled fundamental type II string theory.

On TCS G 2 manifolds and 4D emergent strings

The existence of light sterile neutrinos is a long-standing question in particle physics. Several experimental “anomalies” might be explained by introducing eV mass scaled light sterile neutrinos. Many experiments are actively searching for such light sterile neutrinos through neutrino oscillation. For long baseline experiments, the matter effect should be treated carefully for precise calculation of the neutrino oscillation probabilities. However, this is usually time-consuming or analytically complex. In this manuscript, we adopt a Jacobi-like method to diagonalize the Hermitian Hamiltonian matrix and derive analytically simplified neutrino oscillation probabilities for 3 (active) + 1 (sterile)-neutrino mixing for a constant matter density. These approximations can reach a considerably high numerical accuracy while retaining their analytical simplicity and fast computing speed. This would be useful for current and future long baseline neutrino oscillation experiments.

Bao-Biao Yue

Wei Li

Jia-Jie Ling

Fan-Rong Xu

A compact analytical approximation for a light sterile neutrino oscillation in matter Jiajie Ling acknowledges the support from National Key R&D program of China (2018YFA0404103) and National Natural Science Foundation of China (11775315). F. Xu is supported partially by NSFC (11605076), as well as the FRFCU (Fundamental Research Funds for the Central Universities in China) (21616309)

We study the structure of gauge and gravitational anomalies in 2d N = (0, 2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory. We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms. These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon. Cancellation of anomalies in the effective theory predicts intricate topological identities which must hold on every elliptically fibered Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but their proof from a purely mathematical perspective remains as an interesting open problem. Some of the identities we find on elliptic 5-folds are related in an intriguing way to previously studied topological identities governing the structure of anomalies in 6d N = (1, 0) and 4d N = 1 theories obtained from F-theory.

CERN

The Green-Schwarz mechanism and geometric anomaly relations in 2d (0,2) F-theory vacua