Arguably, the simplest chiral gauge theories are SO(10) with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> fermion fields in the spinor representation <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn mathvariant="bold">16</mn></mrow></math>. We study their dynamics using their supersymmetric limits perturbed by an infinitesimal anomaly mediated supersymmetry breaking as a guide. We predict the theory is gapped for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>=</mo><mn>1</mn></math>, 2, while the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><msub><mi>N</mi><mi>f</mi></msub><mo stretchy="false">)</mo></math> global symmetry is broken to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><msub><mi mathvariant="normal">N</mi><mi>f</mi></msub><mo stretchy="false">)</mo></math> for moderately large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>≥</mo><mn>3</mn></math>.

Japan

Dan Kondo

United States

Hitoshi Murayama

Cameron Sylber

Dynamics of the simplest chiral gauge theories

We point out that a QCD-like dark sector can be coupled to the Standard Model by gauging the topological Skyrme current, which measures the dark baryon number in the infrared, to give a technically natural model for dark matter. This coupling allows for a semi-annihilation process $\textit{χχ}$ → $\textit{χX}$ , where $\textit{X}$ is the gauge boson mediator and $\textit{χ}$ a dark pion field, which plays the dominant role in setting the dark matter relic abundance. The topological interaction is purely $\textit{p}$-wave and so free from indirect detection constraints. We show that the dark matter pion mass needs to be in the range 10 MeV ≲ $\textit{m}$ ≲ 1 TeV; towards the lighter end of this range, there can moreover be significant self-interactions. We discuss prospects for probing this scenario at collider experiments, ranging from the LHC to low-energy $\textit{e}$ $\textit{e}$ colliders, future Higgs factories, and beam-dump experiments.

Switzerland

Joe Davighi

Serah Moldovsky

Christiane Scherb

Italy

Nudžeim Selimović

Topological freeze-out by semi-annihilation

We present a careful study of the chiral symmetry breaking minima and other potential minima in supersymmetric symplectic QCD (Sp($\textit{N}$ ) with $\textit{N}$ flavors) perturbed by Anomaly Mediated Supersymmetry Breaking (AMSB). Although the case of $\textit{N}$ = $\textit{N}$ + 1 requires particular care due to the inherently strongly coupled nature of the quantum modified moduli space, we are able to show that all Sp($\textit{N}$ ) theories to which AMSB can be applied ($\textit{N}$ $\textit{<}$ 3($\textit{N}$ + 1)) possess stable chiral symmetry breaking minima, which are plausibly continuously connected to the vacua of QCD-like Sp($\textit{N}$ ) theories for large SUSY breaking, and are protected from runaways to incalculable minima.

Digvijay Varier

China

Zijian Gu

Bea Noether

AMSB in Sp($\textit{N}$ $\textit{c}$ ) gauge theories

Gauge theories can be solved exactly slightly away from the supersymmetric (SUSY) limit softly broken by anomaly mediation when the size of SUSY breaking is much smaller than the dynamical scale (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>≪</mo><mi mathvariant="normal">Λ</mi></math>). We show empirical evidence that the near-SUSY limit is continuously connected to the non-SUSY limit (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>≫</mo><mi mathvariant="normal">Λ</mi></math>) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><msub><mi>N</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math> gauge theories with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math> quarks in the fundamental representation. The evidence includes the behavior of quark bilinear condensate and gluon condensates, light hadron spectra, and consistency with the large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math> limit including the Witten-Veneziano relations between the topological susceptibility and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><msup><mi>η</mi><mo>′</mo></msup></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub></math>. In addition, we present new predictions when <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub><mo>/</mo><msub><mi>N</mi><mi>c</mi></msub><mo>≳</mo><mi>O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math>.

Near-SUSY to non-SUSY crossover

We calculate the $\textit{θ}$ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is $$ \mathcal{N} $$ = 2 SU(2) gauge theory with $\textit{N}$ = 0, 1, 2, 3 flavors of fundamentals, explicitly broken to $$ \mathcal{N} $$ = 1 via an adjoint superpotential, and coupled to anomaly mediated supersymmetry breaking (AMSB). The hierarchy $\textit{m}$ ≪ $\textit{μ}$ ≪ Λ ensures the validity of our IR analysis. As expected from ordinary QCD, the vacuum energy is a function of $\textit{θ}$ which undergoes 1st order phase transitions between different vacua where the various dyons condense. For $\textit{N}$ = 0 we find the expected phase transition at $\textit{θ}$ = $\textit{π}$, while for $\textit{N}$ = 1, 2, 3 we find phase transitions at fractional values of $\textit{π}$.

Csaba Csáki

Teruhiko Kawano

Israel

Ofri Telem

Phase transitions at unusual values of $\textit{θ}$

We present a composite QCD axion model where the Peccei-Quinn symmetry emerges as a high-quality, accidental symmetry. The axion potential is only modified by eight-fermion, dimension-12 operators, which if present at the Planck scale, allow for axion dark matter from misalignment while solving the strong <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> problem. The model is an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><msub><mi>N</mi><mi>c</mi></msub><mo stretchy="false">)</mo></math> gauge theory with ten flavors where the Pati-Salam unified subgroup <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo><mo>×</mo><mi>SO</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo><mo>⊂</mo><mi>SU</mi><mo stretchy="false">(</mo><mn>10</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Sp</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo><mo>⊂</mo><mi>SU</mi><mo stretchy="false">(</mo><mn>10</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub></math> are weakly gauged. The dynamics breaks <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mn>10</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>SU</mi><mo stretchy="false">(</mo><mn>10</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub><mo stretchy="false">→</mo><mi>SU</mi><mo stretchy="false">(</mo><mn>10</mn><msub><mo stretchy="false">)</mo><mi>V</mi></msub></math> and the weakly gauged groups to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>⊃</mo><mi>SU</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>c</mi></msub><mo>×</mo><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>Y</mi></msub></math>, with the QCD axion identified as one of the Nambu-Goldstone bosons. This axion has a relatively large coupling to photons while a residual <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mover accent="true"><mi>θ</mi><mo stretchy="false">¯</mo></mover><mi>eff</mi></msub></math> may be just below the current limit on the neutron electric dipole moment. If the dimension-12 operators are present near the grand unified theory scale, they can cause domain wall networks to decay, allowing for axion dark matter even for the postinflationary scenario.

Tony Gherghetta

Pablo Quílez

High-quality composite Pati-Salam axion

Inverse decays are an interesting avenue for producing dark matter in the early Universe. We study in detail various phases of dark matter parameter space where inverse decays control its abundance, expanding on our work of inverse decay (INDY) dark matter and going beyond. The role of initial conditions and the impact of departure from kinetic equilibrium are investigated as well. We show how these inverse decay phases can arise in theories of a kinetically mixed dark photon and dark Higgs, with promising prospects for detection at upcoming experiments.

Ronny Frumkin

Yonit Hochberg

Eric Kuflik

Phases of dark matter from inverse decays

We present exact nonperturbative vacuum solutions to chiral gauge theories based on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>6</mn></msub></math> gauge group and several matter fermions in the fundamental <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn mathvariant="bold">27</mn></mrow></math>-dimensional representation. They are obtained when supersymmetric versions are perturbed by small supersymmetry breaking by anomaly mediation. The universality classes obtained are very different from what can be conjectured by the tumbling hypothesis. In particular, the case with three <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn mathvariant="bold">27</mn><mi mathvariant="normal">s</mi></mrow></math> may have an unbroken SU(3) symmetry with massless composite fermions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn mathvariant="bold">10</mn></mrow></math> of SU(3). For this case, we employed numerical techniques to obtain the exact ground state.

Andrew Goh

Gup Singh

Bethany Suter

Jason Wong

Dynamics of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>6</mn></msub></math> chiral gauge theories

We present exact results in softly broken supersymmetric <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><msub><mi>N</mi><mi>C</mi></msub><mo stretchy="false">)</mo></math> chiral gauge theories with charged fermions in one antisymmetric, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>F</mi></msub></math> fundamental, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>C</mi></msub><mo>+</mo><msub><mi>N</mi><mi>F</mi></msub><mo>−</mo><mn>4</mn></math> antifundamental representations. We achieve this by considering the supersymmetric version of these theories and utilizing anomaly mediated supersymmetry breaking at a scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo>≪</mo><mi mathvariant="normal">Λ</mi></math> to generate a vacuum. The connection to nonsupersymmetric theories is then conjectured in the limit <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi><mo stretchy="false">→</mo><mi>∞</mi></math>. For odd <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>C</mi></msub></math>, we determine the massless fermions and unbroken global symmetries in the infrared. For even <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>C</mi></msub></math>, we find global symmetries are nonanomalous and no massless fermions. In all cases, the symmetry breaking patterns differ from what the tumbling hypothesis would suggest.

Czechia

Jacob M. Leedom

Exact results in softly broken supersymmetric chiral gauge theories with flavor

We show that near the edges of the conformal window of supersymmetric SU($\textit{N}$ ) QCD, perturbed by Anomaly Mediated Supersymmetry Breaking (AMSB), chiral symmetry can be broken depending on the initial conditions of the RG flow. We do so by perturbatively expanding around Banks-Zaks fixed points and taking advantage of Seiberg duality. Interpolating between the edges of the conformal window, we predict that non-supersymmetric QCD breaks chiral symmetry up to $\textit{N}$ ≤ 3$\textit{N}$ − 1, while we cannot say anything definitive for $\textit{N}$ ≥ 3$\textit{N}$ at this moment.

Broken conformal window