The Effective Field Theory of Codimension-two Branes

TL;DR

This work establishes a regulator-insensitive effective field theory for codimension-two branes by analyzing a bulk-brane scalar system and extending the analysis to electromagnetism and localized kinetic terms. Through thick-brane regularization and a Green's-function EFT approach, the authors derive consistent classical RG flows for brane-bulk couplings that render brane correlators finite away from the brane while absorbing brane-induced divergences into renormalized couplings. They demonstrate that all relevant and marginal operators are renormalizable at tree level and show that loop corrections preserve finiteness of brane observables, indicating full renormalizability against codimension-two divergences. The framework is then applied to electromagnetic interactions and brane-localized kinetic terms, yielding Euler-Heisenberg-type brane actions and a controlled series of higher-derivative brane operators with RG-consistent couplings. Overall, the paper provides a robust, regulator-independent method to study physics on codimension-two branes and lays groundwork for implications in gravity localization and brane-world cosmology.

Abstract

Distributional sources of matter on codimension-two and higher branes are only well-defined as regularized objects. Nevertheless, intuition from effective field theory suggests that the low-energy physics on such branes should be independent of any high-energy regularization scheme. In this paper, we address this issue in the context of a scalar field model where matter fields (the standard model) living on such a brane interact with bulk fields (gravity). The low-energy effective theory is shown to be consistent and independent of the regularization scheme, provided the brane couplings are renormalized appropriately at the classical level. We perform explicit computations of the classical renormalization group flows at tree and one-loop level, demonstrate that the theory is renormalizable against codimension-two divergences, and extend the analysis to several physical applications such as electrodynamics and brane localized kinetic terms.

Figures (7)

• Figure 1: Thick brane regularization
• Figure 2: Corrections to the bulk field two-point function arising from the brane mass term $\lambda_2$. The blue dashed lines represent the free bulk field propagator $D_k(r,r')$ while the dotted line is that corrected for the mass term i.e. $\tilde{D}_k(r,r')$.
• Figure 3: Coupling corrections to the two-point functions. The blue dotted lines represent the propagator for the bulk field $\tilde{D}_k(r,r')$, while the red plain lines are the propagator for the brane field $\chi$: $H_k$. Lines carrying a circle represent the "dressed" propagators $G^{\phi \phi} (r,r')$ (top diagram) and $G^{\chi \chi}$ (bottom) and take into account the tree-level corrections arising from the coupling $\lambda$ between the bulk and the brane field.
• Figure 4: Three-point functions. The blue dotted lines represent the propagator for the bulk field $\phi$, while the red plane lines are the propagator for the brane field $\chi$.
• Figure 5: Classical contributions to the four-point functions. The second term on the bottom line is finite, but the third diagram involves a divergent piece proportional to $\lambda_3^2 \tilde{D}_k (0,0)$ which needs to be absorbed into the coupling $\beta_4$.