A Stringy Test of Flux-Induced Isometry Gauging

TL;DR

The paper analyzes how fluxes that gauge isometries in 4d ${\cal N}=2$ theories arising from type IIA Calabi–Yau compactifications withstand nonperturbative corrections from brane instantons. It shows that $F_4$ and $H$ fluxes gauge specific isometries via Killing vectors $ (k_F)_i = -2 e_i \partial_a$ and $ k_H = (p^A \tilde{\xi}_A - q_A \xi^A)\partial_a + p^A \partial_{\xi^A} + q_A \partial_{\tilde{\xi}_A}$, while brane instantons could potentially break them; however, Gauss’ law on the brane worldvolume enforces $\sum_i c^i p_i = 0$ for allowed instantons, preserving the gauged isometries. The authors then show that all other isometries are lifted by instanton corrections, with a detailed analysis of instanton configurations (E2 and E2–E0) and the necessary zero modes and vertex operators, including a flux-dependent mass term $V^{\pm}_{\theta\theta}$ and hyperino–brane couplings. The resulting nonperturbative corrections to the curvature–4–fermion coupling depend on $e^{\text{vol}(\Gamma)+ i\int_\Gamma C_3}$ and flux data, confirming that the flux-protected isometries survive while the rest are generically broken, thereby clarifying the consistency of flux-induced gauging in the presence of brane instantons.

Abstract

Supergravity analysis suggests that the effect of fluxes in string theory compactifications is to gauge isometries of the scalar manifold. However, isometries are generically broken by brane instanton effects. Here we demonstrate how fluxes protect exactly those isometries from quantum corrections which are gauged according to the classical supergravity analysis. We also argue that all other isometries are generically broken.

Figures (1)

• Figure 1: A permissible instanton configuration. The ellipses denote E2 branes wrapping homologically different 3 cycles, the connecting lines are E0 branes. The numbers inside the ellipses indicate the quanta of $H$ flux through the respective cycle.