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.
Highlights
One of the celebrated facts of string theory is that it defines a consistent theory of quantum gravity in ten target spacetime dimensions
For the F-theory models, we focus on some examples of “rigid gauged linear sigma models (GLSMs)” which are the two-dimensional analogue of non-Higgsable clusters encountered in higherdimensional F-theory vacua
If we focus on the gauge sector, we can describe it as a gauged linear sigma model (GLSM), and in many cases we can argue that the resulting path integral leads to a sensible unitary QFT with a normalizable ground state and low energy behavior described by some compact and unitary conformal field theory (CFT)
Summary
One of the celebrated facts of string theory is that it defines a consistent theory of quantum gravity in ten target spacetime dimensions. Since part of our aim is to maintain an explicit UV completion of any proposed 2D non-critical string theory, we first treat in detail the cases of perturbative string theories with a non-abelian gauge theory sector and at least (0, 2) supersymmetry in two dimensions This includes compactification on a Calabi-Yau fourfold of the type I superstring, and the heterotic Spin(32)/Z2 and E8 × E8 string theories. This includes a general set of rules for extracting the zero mode content in the presence of a non-trivial supersymmetric vector bundle. Motivated by the successful analyses of higher-dimensional cases, we shall primarily focus on the local picture of intersecting 7-branes In both the perturbative and F-theory constructions, we will generically encounter gauge theoretic anomalies, indicating that there are additional degrees of freedom in our models. To the extent we have been able to compare our results with those found in [27], the broad conclusions appear to be compatible
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