Target Spaces from Chiral Gauge Theories

TL;DR

This work analyzes (0,2) chiral gauge theories in two dimensions, showing that integrating out anomalous massive multiplets generates log interactions that encode gauge anomalies in the infrared. The authors derive a complete set of (0,2) supergraph rules, compute the one‑loop effective action, and extract the resulting non‑linear sigma model data. They demonstrate that the IR target spaces are generally non‑Kähler with finite‑distance boundaries and nontrivial H‑flux, and they construct an invariant metric Ĝ that provides a conventional geometric description. The results reveal a rich landscape of heterotic‑type target spaces with boundaries and flux, arising naturally from charged log interactions and gauge anomaly cancellation, and they outline how these structures could support conformal/torsional heterotic vacua and possibly novel dual descriptions.

Abstract

Chiral gauge theories in two dimensions with (0,2) supersymmetry are central in the study of string compactifications. Remarkably little is known about generic (0,2) theories. We consider theories with branches on which multiplets with a net gauge anomaly become massive. The simplest example is a relevant perturbation of the gauge theory that flows to the CP(n) model. To compute the effective action, we derive a useful set of Feynman rules for (0,2) supergraphs. From the effective action, we see that the infra-red geometry reflects the gauge anomaly by the presence of a boundary at finite distance. In generic examples, there are boundaries, fluxes and branes; the resulting spaces are non-Kahler.

Figures (12)

• Figure 1: Plots of $|\phi|^2 \mp \log |\phi|$ against $|\phi|$.
• Figure 2: Contour plots of $|\phi^1|$ versus $|\phi^0|$ for $r=2$ and $r=4$.
• Figure 3: The only contribution to the effective action in unitary gauge.
• Figure 4: The remaining contributions to the effective action without gauge-fixing.
• Figure 5: A plot depicting the solutions of $(\ref{['defineA']})$ as we increase $|z|$ from $0$ to $|z|_{max}$, with the latter value corresponding to the unique minimum.