It has been known for some time that the cosmological bound on the invisible axion scale can be avoided by an early phase of strong QCD. While most approaches rely on theories where the strong coupling constant is determined through the expectation value of some scalar field, we show that this mechanism can also be implemented into the benchmark Kim-Shifman-Vainshtein-Zakharov and Dine-Fischler-Srednicki-Zhitnitsky models when the early phase of strong QCD emerges by the modification of the running coupling during inflation. For both models the physics that are responsible for making QCD strong do not displace the axions minimum by too much, so that the efficiency of the relaxation is controlled by parameters of the theory and the number of inflationary <math><mi>e</mi></math>-folds. In particular, we consider the case of very efficient relaxation where the axion abundance is dominated by inflationary quantum and postinflationary thermal fluctuations. Within this situation we identify the parameter space compatible with all cosmological constrains and derive conditions on the reheating temperature and the QCD scale during inflation that result in the axion making up all the dark matter. Because of duality below the Peccei-Quinn scale and a minor influence of the Kim-Shifman-Vainshtein-Zakharov and Dine-Fischler-Srednicki-Zhitnitsky fields on the running, our findings also apply to a minimal two-form implementation of the axion.

Germany

Emmanouil Koutsangelas

Removing the cosmological bound on the axion scale in the Kim-Shifman-Vainshtein-Zakharov and Dine-Fischler-Srednicki-Zhitnitsky models

We construct on-shell <math><mi>N</mi><mo>=</mo><mn>2</mn></math> nonlinear sigma models on <math><mrow><mi>S</mi><mi>O</mi><mo>(</mo><mn>2</mn><mi>N</mi><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math> and <math><mrow><mi>S</mi><mi>p</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math> by holomorphically embedding the models in the hyper-Kähler nonlinear sigma model on the cotangent bundle of the Grassmann manifold <math><mrow><msup><mrow><mi>T</mi></mrow><mrow><mo>*</mo></mrow></msup><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn><mi>N</mi><mo>,</mo><mi>N</mi></mrow></msub></mrow></math> in the <math><mi>N</mi><mo>=</mo><mn>1</mn></math> superspace formalism. We apply the moduli matrix formalism to the mass-deformed nonlinear sigma models on the quadrics to study three-pronged junctions by using a recently proposed diagram method.

South Korea

Taegyu Kim

Sunyoung Shin

Junctions of mass-deformed nonlinear sigma models on <math><mrow><mi>S</mi><mi>O</mi><mo>(</mo><mn>2</mn><mi>N</mi><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math> and <math><mrow><mi>S</mi><mi>p</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math>

We construct three-pronged junctions of mass-deformed nonlinear sigma models on SO(2N)/U(N) and Sp(N )/U(N ) for generic N. We study the nonlinear sigma models on the Grassmann manifold or on the complex projective space. We discuss the relation between the nonlinear sigma model constructed in the harmonic superspace for- malism and the nonlinear sigma model constructed in the projective superspace formalism by comparing each model with the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 nonlinear sigma model constructed in the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 superspace formalism.