Exact Results in Chiral Gauge Theories with Flavor (2503.08772v2)

Abstract: We present exact results in softly-broken supersymmetric $\text{SU}(N_C)$ chiral gauge theories with charged fermions in one antisymmetric, $N_F$ fundamental, and $N_C+N_F-4$ anti-fundamental representations. We achieve this by considering the supersymmetric version of these theories and utilizing anomaly mediated supersymmetry breaking at a scale $m \ll \Lambda$ to generate a vacuum. The connection to non-supersymmetric theories is then conjectured in the limit $m \rightarrow \infty$. For odd $N_C$, we determine the massless fermions and unbroken global symmetries in the infrared. For even $N_C$, we find global symmetries are non-anomalous and no massless fermions. In all cases, the symmetry breaking patterns differ from what the tumbling hypothesis would suggest.

Analysis of Exact Results in Chiral Gauge Theories with Flavor

The paper "Exact Results in Chiral Gauge Theories with Flavor" by Jacob M. Leedom et al. explores the intricacies of $SU(N_C)$ chiral gauge theories featuring charged fermions across various representations. By leveraging supersymmetric (SUSY) methodologies alongside anomaly-mediated supersymmetry breaking (AMSB), the paper delivers exact insights into the dynamics of these theories, specifically regarding the infrared behavior and symmetry-breaking patterns.

Core Contributions

The authors commence their paper by examining the dynamics of $SU(N_C)$ chiral gauge theories with antifundamental representations. They employ a strategy involving supersymmetric versions of these theories, leveraging SUSY's holomorphicity and global symmetries to attain a level of computational control otherwise unattainable in their non-SUSY counterparts. Anomalies break SUSY at scales $m \ll \Lambda$ to generate a vacuum state, and a meaningful extrapolation to non-SUSY theories is achieved by considering the limit $m \rightarrow \infty$.

One significant achievement of the paper is the exact determination of massless fermions and unbroken global symmetries in scenarios where $N_C$ is odd. Conversely, for even $N_C$, the authors report symmetry patterns that conflict with prevalent hypotheses like the tumbling hypothesis. Specifically, the tumbling hypothesis predicts fermion bilinear condensates within the most attractive channel under a simplistic gauge boson exchange potential, which subsequently informs specific patterns of chiral symmetry breaking. Such patterns were not observed in the paper's findings—indicating a substantial deviation that may inspire future theoretical developments.

Numerical Results and Anomaly Matching

The analysis presents a rigorous numerical exploration to supplement the theoretical proposals, ensuring the vacuum structure aligned with the posited SUSY and AMSB frameworks. By doing so, they validate the existence of massless composite fermions when $N_C$ is odd, through both the mass spectra and 't Hooft anomaly matching for global symmetries. Through their anomaly evaluation, the authors ensure consistency between UV and IR descriptions, with particularly notable results in odd-$N_C$ scenarios, where fermions exhibit non-trivial transitions.

Theoretical and Practical Implications

The theoretical insights provided by this research have profound implications for both fundamental particle physics and the broader fields of high-energy physics. Firstly, the precise conditions under which certain symmetry-breaking patterns arise challenge existing paradigms, notably those relying on the most attractive channel for predictive guidance. The disparity between these results and the predictions of the tumbling hypothesis necessitate a reevaluation of chiral gauge theory methods. Furthermore, such exact results can contribute significantly to models that bridge BSM theories and conventional QCD-like interactions, thus enriching our comprehension of confinement, chiral symmetry breaking, and anomaly mediation in non-Abelian gauge theories.

Future Developments

The methodology and results offered in this paper pave the way for a range of future research directions. Additional exploration into the $m \rightarrow \infty$ non-SUSY limit may elucidate phase transitions or robustness of symmetry structures. Moreover, expanding the classes of chiral gauge theories studied with these techniques could offer deeper insights into the universality of the symmetry-breaking patterns discovered and further test the resilience of the tumbling hypothesis in diverse settings. Additionally, experimental accessibility of some predictions could be investigated in future work, potentially impacting the search for novel physics within collider environments.

In conclusion, the paper provides insightful, exact results concerning chiral gauge theories with extensive implications for our theoretical understanding and opens several avenues for ongoing research in non-perturbative gauge dynamics.