Under the assumption that the recent pulsar timing array evidence for a stochastic gravitational wave (GW) background at nanohertz frequencies is generated by metastable cosmic strings, we analyze the potential of present and future GW observatories for probing the change of particle degrees of freedom caused, e.g., by a supersymmetric (SUSY) extension of the Standard Model (SM). We find that signs of the characteristic doubling of degrees of freedom predicted by SUSY could be detected at Einstein Telescope and Cosmic Explorer even if the masses of the SUSY partner particles are as high as about 10$^{4}$ TeV, far above the reach of any currently envisioned particle collider. We also discuss the detection prospects for the case that some entropy production, e.g. from a late decaying modulus field inducing a temporary matter domination phase in the evolution of the universe, somewhat dilutes the GW spectrum, delaying discovery of the stochastic GW background at LIGO-Virgo-KAGRA. In our analysis we focus on SUSY, but any theory beyond the SM predicting a significant increase of particle degrees of freedom could be probed this way.

Switzerland

Stefan Antusch

Kevin Hinze

Shaikh Saad

Germany

Jonathan Steiner

Probing SUSY at gravitational wave observatories

A reliable determination of the pole parameters and residues of nucleon resonances is notoriously challenging, given the required analytic continuation into the complex plane. We provide a comprehensive analysis of such resonance parameters accessible with Roy–Steiner equations for pion–nucleon scattering—a set of partial-wave dispersion relations that combines the constraints from analyticity, unitarity, and crossing symmetry—most prominently of the <math><mi>Δ</mi><mo>(</mo><mn>1232</mn><mo>)</mo></math> resonance. Further, we study the Roper, <math><mi>N</mi><mo>(</mo><mn>1440</mn><mo>)</mo></math>, resonance, which lies beyond the strict domain of validity, in comparison to Padé approximants, comment on the role of subthreshold singularities in the S-wave, and determine the residues of the <math><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>500</mn><mo>)</mo></math>, <math><mi>ρ</mi><mo>(</mo><mn>770</mn><mo>)</mo></math>, and <math><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> resonances in the t-channel process <math><mi>π</mi><mi>π</mi><mo>→</mo><mover><mrow><mi>N</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>N</mi></math>. The latter allows us to test—for the first time fully model independently in terms of the respective residues—universality of the <math><mi>ρ</mi><mo>(</mo><mn>770</mn><mo>)</mo></math> couplings and the Goldberger–Treiman relation expected if the scalars behaved as dilatons, in both cases revealing large deviations from the narrow-resonance limit.

Martin Hoferichter

Spain

Jacobo Ruiz de Elvira

Bastian Kubis

Ulf-G. Meißner

Nucleon resonance parameters from Roy–Steiner equations

Embedding inflation within a grand unified theory is an intriguing idea towards a more fundamental understanding of particle physics and cosmology. However, within the framework of supersymmetric <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> grand unified theory inflation, models typically feature light color octets and weak triplets that ruin the successful gauge coupling unification of the mimimal supersymmetric Standard Model. We present a new possibility for naturally splitting the electronlike states from the colored ones within vectorlike 10-plets by utilizing their couplings with 40-plets that lack electronlike states. Together with the extra light weak doublets from the double missing partner mechanism, the appearance of the light electronlike states from our proposed generalized missing partner mechanism restores gauge coupling unification. Remarkably, the same vectorlike 10-plets cure the bad mass relations between the down quarks and the charged leptons. Discovering the light relic states at future colliders would provide a “smoking gun” signal of the scenario.

Generalized missing partner mechanism for <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> GUT inflation

In this work, we construct promising model-building routes towards SO(10) grand unified theory inflation and examine their ability to explain the recent pulsar timing arrays (PTAs) results hinting at a stochastic gravitational wave (GW) background at nanohertz frequencies. We consider a supersymmetric framework within which the so-called doublet-triplet splitting problem is solved without introducing fine-tuning. Additionally, realistic fermion masses and mixings, gauge coupling unification, and cosmic inflation are incorporated by utilizing superfields with representations no higher than the adjoint representation. Among the three possible scenarios, two of these cases require a single adjoint Higgs field, and do not lead to cosmic strings. In contrast, the third scenario featuring two adjoints, can lead to a network of metastable cosmic strings that generates a GW background contribution compatible with the recent PTA findings and testable by various ongoing and upcoming GW observatories.

Singling out SO(10) GUT models using recent PTA results

The hyperbolic version of Roy-Steiner equation describing low energy πN scatterings, with larger analyticity domain in the complex s plane is solved. The numerical results on phase shifts of low partial waves are in agreement with that of Hoferichter et al. [Phys. Rept. 625 (2016) 1]. A subthreshold pole in S 11 channel is found located at   <math> <msqrt> <mi>s</mi> </msqrt> </math>  $$ \sqrt{s} $$  = (918 ± 3) − i(163 ± 9) MeV.

China

Xiong-Hui Cao

Qu-Zhi Li

Han-Qing Zheng

A possible subthreshold pole in S 11 channel from πN Roy-Steiner equation analyses

In this note we study CFT$_{2}$ Virasoro conformal blocks with heavy operators in the large-c limit in the context of AdS$_{3}$/CFT$_{2}$ correspondence. We compute the lengths of the holographic Steiner trees dual to the 5-point and 6-point conformal blocks using the superlight approximation when one or more dimensions are much less than the others. These results are generalized for N-point holographic Steiner trees dual to <math><mo>(</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></math>-point conformal blocks with superlight weights.

Russia

Mikhail Pavlov

Large- Conformal ( ≤ 6)-point blocks with superlight weights and holographic Steiner trees

We consider the Steiner tree problem in hyperbolic geometry in the context of the AdS/CFT duality between large-c conformal blocks on the boundary and particle motions in the bulk. The Steiner trees are weighted graphs on the Poincare disk with a number of endpoints and trivalent vertices connected to each other by edges in such a way that an overall length is minimum. We specify a particular class of Steiner trees that we call holographic. Their characteristic property is that a holographic Steiner tree with N endpoints can be inscribed into an N-gon with N − 1 ideal vertices. The holographic Steiner trees are dual to large-c conformal blocks. Particular examples of N = 2, 3, 4 Steiner trees as well as their dual conformal blocks are explicitly calculated. We discuss geometric properties of the holographic Steiner trees and their realization in CFT terms. It is shown that connectivity and cuts of the Steiner trees encode the factorization properties of large-c conformal blocks.

Konstantin Alkalaev

Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk

In quantum field theory with a mass gap correlation function between two spatially separated operators decays exponentially with the distance. This fundamental result immediately implies an exponential suppression of all higher point correlation functions, but the predicted exponent is not optimal. We argue that in a general quantum field theory the optimal suppression of a three-point function is determined by total distance from the operator locations to the Fermat-Steiner point. Similarly, for the higher point functions we conjecture the optimal exponent is determined by the solution of the Euclidean Steiner tree problem. We discuss how our results constrain operator spreading in relativistic theories.