On D3-brane Dynamics at Strong Warping

TL;DR

This work addresses the problem of deriving a controlled, low-energy effective action for a D3-brane in strongly warped Type IIB compactifications, including both open string moduli $Y^i$ and closed string moduli $u^I$. Using the ADM/Hamiltonian formalism, the authors extract the kinetic terms and identify gauge-invariant perturbations, leading to a warped Kähler potential that couples the D3-brane position to the universal Kähler modulus $c$ via a combined modulus $\rho$. They provide an explicit form of the warped Kähler potential $\kappa_4^2\mathcal{K}(\rho,Y) = -3 \log(\rho+\bar{\rho}-\gamma k(Y,\bar{Y})+2 V_W^0/V_{CY})$ with $\rho = c + (\gamma/2) k(Y,\bar{Y}) + i\chi$, and show that including D3 backreaction modifies the warp factor to restore holomorphy of the D7 gauge coupling, thereby resolving the rho problem in warped backgrounds. The results have implications for precise inflaton potentials in D-brane inflation, moduli stabilization, and the consistency of gauge couplings in strongly warped geometries.

Abstract

We study the dynamics of a D3 brane in generic IIB warped compactifications, using the Hamiltonian formulation discussed in arXiv:0805.3700 [hep-th]. Taking into account of both closed and open string fluctuations, we derive the warped Kahler potential governing the motion of a probe D3 brane. By including the backreaction of D3, we also comment on how the problem of defining a holomorphic gauge coupling on wrapped D7 branes in warped background can be resolved.