The Gravitational Sector of 2d (0,2) F-theory Vacua

TL;DR

This work constructs the gravitational sector of 2d $(0,2)$ F-theory vacua from elliptically fibered Calabi–Yau fivefolds by deriving the dilaton supergravity spectrum from Type IIB on Calabi–Yau fourfolds and uplifting to F-theory. It demonstrates anomaly cancellation when including the duality-twisted D3-brane sector and establishes a precise spectrum match with the circle-reduced $N=2$ SQM arising from M-theory on the same fivefold, including Curvature- and M2-/D3-brane–related Chern–Simons couplings via 1d reduction. The analysis clarifies the role of automorphic duality in relating 2d multiplets to 1d SQM multiplets and reveals how M2-brane tadpoles along the elliptic fiber enforce consistency conditions mirroring fundamental strings in the type II duals. These results reinforce the consistency of F-/M-theory duality in two dimensions and provide a concrete framework for the gravitational sector of 2d $(0,2)$ F-theory vacua.

Abstract

F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S^1 reduction of the dual F-theory.