<p>The dynamics of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></mrow></math> supersymmetric gauge theories with matter in adjoint and fundamental representations and the superpotentials given by Arnold’s ADE singularities has been extensively studied in the literature. It was also conjectured that supersymmetric models with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>W</mi></mrow><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msub></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>W</mi></mrow><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub></mrow></msub></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>W</mi><msub><mi>E</mi><mn>7</mn></msub></msub></math> superpotentials possess a dual description. In this paper, we revisit the analysis of the moduli space of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>A</mi><mi>k</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub></mrow></math> models by considering the duality along nilpotent directions on the moduli space. While our analysis provides additional evidence for the duality conjecture in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>W</mi><msub><mi>A</mi><mi>k</mi></msub></msub></math> models, we show that the duality conjecture fails for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>W</mi><msub><mi>D</mi><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub></msub></math> models.</p>

United States

Eric Bryan

Arvind Rajaraman

Yuri Shirman

Potency of nilpotence

We present the first analytical calculation that shows that perturbations with angular dependence can lead to an instability in gauged Q-balls. We find an explicit condition on the parameters for the Q-ball to become unstable. We compare our predictions to the numerical calculation in Kinach et al., and show agreement, including a correct prediction of the instability/stability of the two parameter points analyzed in that paper.

Instabilities of gauged Q-balls

Q-balls are non-topological solitons arising in scalar field theories. Solutions for rotating Q-balls (and the related boson stars) have been shown to exist when the angular momentum is equal to an integer multiple of the Q-ball charge Q. Here we consider the possibility of classically long-lived metastable rotating Q-balls with small angular momentum, even for large charge, for all scalar theories that support non-rotating Q-balls. This is relevant for rotating extensions of Q-balls and related solitons such as boson stars as it impacts their cosmological phenomenology.

Kuwait

Yahya Almumin

Julian Heeck

Christopher Verhaaren

Slowly rotating Q-balls

We perform a general analysis of thin-wall <math><mi>Q</mi></math>-balls in anti–de Sitter (AdS) space. We provide numeric solutions and highly accurate analytic approximations over much of the parameter space. These analytic solutions show that AdS <math><mi>Q</mi></math>-balls exhibit significant differences from the corresponding flat-space solitons. This includes having a maximum radius beyond which the <math><mi>Q</mi></math>-balls are unstable to a new type of state where the <math><mi>Q</mi></math>-ball coexists with a gas of massive particles. The phase transition to this novel state is found to be a zero-temperature third-order transition. This, through the AdS/CFT correspondence, has implications for a scalar condensate in the boundary theory.

Alexander Stewart

Christopher B. Verhaaren

<math><mi>Q</mi></math>-balls in anti–de Sitter space

We present an efficient method for finding the independent invariant tensors of a gauge theory. Our method uses a theorem relating invariant tensors and D-flat directions in field space. We apply our method to several examples — SO(3) with symmetric tensors, SU(2) with a dimension-4 representation, and SU(3) with matter in the sextet — and find the set of independent invariant tensors in these theories.

Jason Baretz

On the Calculation of Invariant Tensors in Gauge Theories

We consider the search for gamma rays produced by the annihilation or decay of low-mass dark matter which couples to quarks. In this scenario, most of the photons are produced from the decays of <math><msup><mi>π</mi><mn>0</mn></msup></math> or <math><mi>η</mi></math> mesons. These decays produce distinctly different photon signatures due to the difference in meson mass. We assess the ability of the future MeV-range observatories to constrain the hadronic final states produced by dark matter annihilation or decay from the shape of the resulting photon spectrum. We then comment on how this information can be used to determine properties of the dark matter coupling to the quark current, based on the approximate symmetries of low-energy QCD.

J. G. Christy

Jason Kumar

Indirect detection of low-mass dark matter through the <math><msup><mi>π</mi><mn>0</mn></msup></math> and <math><mi>η</mi></math> windows

Complex scalars in U(1)-symmetric potentials can form stable Q-balls, non-topological solitons that correspond to spherical bound-state solutions. If the U(1) charge of the Q-ball is large enough, it can support a tower of unstable radial excitations with increasing energy. Previous analyses of these radial excitations were confined to fixed parameters, leading to excited states with different charges Q. In this work, we provide the first characterization of the radial excitations of solitons for fixed charge, providing the physical spectrum for such objects. We also show how to approximately describe these excited states analytically and predict their global properties such as radius, energy, and charge. This enables a complete characterization of the radial spectrum. We also comment on the decay channels of these excited states.

Excited Q-balls

We investigate a novel interplay between the decay and annihilation of a particle whose mass undergoes a large shift during a first order phase transition, leading to the particles becoming trapped in the false vacuum and enhancing their annihilation rates as the bubbles of true vacuum expand. This opens up a large region of the parameter space where annihilations can be important. We apply this scenario to baryogenesis, where we find that annihilations can be enhanced enough to generate the required baryon asymmetry even for relatively tiny annihilation cross sections with modest CP asymmetries.

Jason Arakawa

Tim Tait

Annihilogenesis

Non-topological solitons such as Q-balls and Q-shells have been studied for scalar fields invariant under global and gauged U(1) symmetries. We generalize this frame-work to include a Proca mass for the gauge boson, which can arise either from spontaneous symmetry breaking or via the Stückelberg mechanism. A heavy (light) gauge boson leads to solitons reminiscent of the global (gauged) case, but for intermediate values these Proca solitons exhibit completely novel features such as disconnected regions of viable parameter space and Q-shells with unbounded radius. We provide numerical solutions and excellent analytic approximations for both Proca Q-balls and Q-shells. These allow us to not only demonstrate the novel features numerically, but also understand and predict their origin analytically.

Rebecca Riley

Proca Q-balls and Q-shells

Nontopological gauged soliton solutions called <math><mi>Q</mi></math>-balls arise in many scalar field theories that are invariant under a <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> gauge symmetry. The related, but qualitatively distinct, <math><mi>Q</mi></math>-shell solitons have only been shown to exist for special potentials. We investigate gauged solitons in a generic sixth-order polynomial potential (that contains the leading effects of many effective field theories) and show that this potential generically allows for both <math><mi>Q</mi></math>-balls and <math><mi>Q</mi></math>-shells. We argue that <math><mi>Q</mi></math>-shell solutions occur in many, and perhaps all, potentials that have previously only been shown to contain <math><mi>Q</mi></math>-balls. We give simple analytic characterizations of these <math><mi>Q</mi></math>-shell solutions, leading to excellent predictions of their physical properties.