An Analysis of Fluxes by Duality

TL;DR

The work investigates flux compactifications in M-theory on ${\\mathrm{K3}}\\times{\\mathrm{K3}}$ through a duality with Calabi–Yau threefolds times ${T^2}$, enabling analysis beyond the supergravity limit. It constructs explicit ${G}$-flux configurations (including primitive $(1,1)$ fluxes) and brane–flux transitions, showing how moduli can be obstructed and ${\\mathrm{K3}}$ volumes fixed, with mirror symmetry exchanging the two ${\\mathrm{K3}}$ factors. It also develops smooth ${\\mathrm{K3}}$-based setups with ${U(1)}$ bundles and realizes volume obstructions via ${\\omega_1}, {\\omega_2}$ fluxes in a controlled dual pair ${X_{U(1)}}$ and ${S_1}\\times {S_2}$, including a concrete brane-to-flux transition that reduces M2-brane content while introducing flux. The analysis highlights nonperturbative effects, worldsheet instantons, and strongly coupled regions that alter the moduli geometry beyond primitive flux, and argues for an expanded web of extremal transitions in M-theory on ${\\mathrm{K3}}\\times{\\mathrm{K3}}$ beyond the Calabi–Yau data alone.

Abstract

M-theory on K3xK3 with non-supersymmetry-breaking G-flux is dual to M-theory on a Calabi-Yau threefold times a 2-torus without flux. This allows for a thorough analysis of the effects of flux without relying on supergravity approximations. We discuss several dual pairs showing that the usual rules of G-flux compactifications work well in detail. We discuss how a transition can convert M2-branes into G-flux. We see how new effects can arise at short distances allowing fluxes to obstruct more moduli than one expects from the supergravity analysis.

Figures (3)

• Figure 1: A simple transition to a finite-sized instanton.
• Figure 2: The self-similarity of the type $\mathrm{III}^*$ fibre under a ${\mathbb Z}_2$-quotient.
• Figure 3: A Brane to Flux Transition