UV Completions for Non-Critical Strings

TL;DR

This work develops UV-complete frameworks for non-critical two-dimensional strings arising from string compactifications, introducing quasi-topological 8D and 6D theories to govern GLSM vacua in perturbative type I/heterotic and F-theory constructions. It shows that anomaly and tadpole cancellation generically require additional, often strongly coupled, extra sectors—frequently difficult to describe as UV GLSMs—and that, in some cases, enforcing anomaly freedom can break supersymmetry via spacetime-filling anti-branes. The authors construct off-shell 2D $(0,2)$ formulations for the higher‑dimensional gauge theories, derive zero-mode spectra, and classify localized interactions on defects, curves, and points in Calabi–Yau geometries; they illustrate the framework with examples including standard embeddings and rigid F-theory clusters. The results provide a principled UV interpretation of 2D non-critical strings, illuminate the interplay between anomalies, tadpoles, and SUSY, and open avenues for studying protected quantities such as anomaly polynomials and elliptic genera in these rich, localized 2D theories.

Abstract

Compactifications of the physical superstring to two dimensions provide a general template for realizing 2D conformal field theories coupled to worldsheet gravity, i.e. non-critical string theories. Motivated by this observation, in this paper we determine the quasi-topological 8D theory which governs the vacua of 2D N = (0,2) gauged linear sigma models (GLSMs) obtained from compactifications of type I and heterotic strings on a Calabi-Yau fourfold. We also determine the quasi-topological 6D theory governing the 2D vacua of intersecting 7-branes in compactifications of F-theory on an elliptically fibered Calabi-Yau fivefold, where matter fields and interaction terms localize on lower-dimensional subspaces, i.e. defect operators. To cancel anomalies / cancel tadpoles, these GLSMs must couple to additional chiral sectors, which in some cases do not admit a known description in terms of a UV GLSM. Additionally, we find that constructing an anomaly free spectrum can sometimes break supersymmetry due to spacetime filling anti-branes. We also study various canonical examples such as the standard embedding of heterotic strings on a Calabi-Yau fourfold and F-theoretic "rigid clusters" with no local deformation moduli of the elliptic fibration.

Figures (2)

• Figure 1: Depiction of energy scales for 2D effective string theories derived from string compactification. In the deep infrared, we have a 2D conformal fixed point coupled to gravity, leading to an effective string theory. At somewhat higher energy scales, this description passes over to a gauged linear sigma model coupled to extra sectors and gravity, and at even higher energy scales this description also breaks down and is replaced by a 10D supergravity theory. This is in turn replaced at even higher energies by a corresponding UV completion in string theory.
• Figure 2: Depiction of the non-gravitational sector of the 2D model obtained from string compactification. Generically, this consists of a 2D gauged linear sigma model (GLSM) coupled to additional extra sectors. These extra sectors can sometimes be strongly coupled conformal field theories in their own right, leading to a rich class of novel 2D theories.