We study semiclassical spiky strings in de Sitter space and the corresponding Regge trajectories, generalizing the analysis in anti-de Sitter space. In particular we demonstrate that each Regge trajectory has a maximum spin due to de Sitter acceleration, similarly to the folded string studied earlier. While this property is useful for the spectrum to satisfy the Higuchi bound, it makes a nontrivial question how to maintain mildness of high-energy string scattering which we are familiar with in flat space and anti-de Sitter space. Our analysis implies that in order to have infinitely many higher spin states, one needs to consider infinitely many Regge trajectories with an increasing folding number.

Japan

Mitsuhiro Kato

Kanji Nishii

Toshifumi Noumi

Toshiaki Takeuchi

Sweden

Siyi Zhou

Spiky strings in de Sitter space

We study the spectrum of semiclassical rotating strings in de Sitter space and its consistency. Even though a naive extrapolation of the linear Regge trajectory on flat space implies a violation of the Higuchi bound (a unitarity bound on the mass of higher-spin particles in de Sitter space), the curved space effects turn out to modify the trajectory to respect the bound. Interestingly, as a consequence of accelerated expansion, there exists a maximum spin for each Regge trajectory, which is helpful to make the spectrum consistent with the Higuchi bound, but at the same time, it could be an obstruction to stringy UV completion based on an infinite higher-spin tower. By pushing further this observation, we demonstrate that the vacuum energy <math><mi>V</mi></math> inflating the Universe has to be bounded by the string scale <math><msub><mi>M</mi><mi>s</mi></msub></math> as <math><mrow><mi>V</mi><mo>≲</mo><msubsup><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>4</mn></mrow></msubsup></mrow></math>, if UV completion is achieved with the leading Regge trajectory of higher spin states up to the 4D Planck scale. Its application to inflation in the early Universe implies an upper bound on the tensor-to-scalar ratio, <math><mrow><mi>r</mi><mo>≲</mo><mn>0.01</mn><mo>×</mo><mo>(</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>/</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>16</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi><msup><mrow><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup></mrow></math>, which is within the scope of the near future CMB experiments. We also discuss another possibility that UV completion is achieved by multiple Regge trajectories.

Hong Kong

String Regge trajectories in de Sitter space and implications for inflation

We construct conformal three-point functions in momentum space with a general tensor and conserved currents of spin 1 and 2. While conformal correlators in momentum space have been studied especially in the connection with cosmology, correlators involving a tensor of general spin and scaling dimension have not been studied very much yet. Such a direction is unavoidable when we go beyond three-point functions because general tensors always appear as an intermediate state. In this paper, as a first step, we solve the Ward-Takahashi identities for correlators of a general tensor and conserved currents. In particular we provide their expression in terms of the so-called triple-K integrals and a differential operator which relates triple-K integrals with different indices. For several correlators, closed forms without the differential operator are also found.

Thailand

Hiroshi Isono

Momentum space conformal three-point functions of conserved currents and a general spinning operator