D3-brane Potentials from Fluxes in AdS/CFT

TL;DR

Baumann, Dymarsky, Kachru, Klebanov, and McAllister develop a comprehensive, 10D supergravity framework to compute the D3-brane potential in warped throats with stabilized moduli. By classifying IASD flux perturbations on Calabi–Yau cones and mapping them to dual CFT operators in the Klebanov–Witten theory, they identify the leading flux- and curvature-induced contributions, including an eta-term, and expose new irrational scaling terms. They show that gaugino condensation on D7-branes can source IASD flux, geometrizing nonperturbative 4D effects within a single ten-dimensional description and enabling a direct link between 4D supergravity potentials and 10D flux backgrounds. The results unify major D3-brane potential contributions discussed in the literature, provide a method to compute Planck-suppressed corrections in a Wilsonian-like framework, and illuminate a path toward a geometric transition for D7-branes. Overall, the paper advances a coherent holographic approach to Planck-scale physics in string compactifications relevant for D-brane inflation and moduli stabilization.

Abstract

We give a comprehensive treatment of the scalar potential for a D3-brane in a warped conifold region of a compactification with stabilized moduli. By studying general ultraviolet perturbations in supergravity, we systematically incorporate `compactification effects' sourced by supersymmetry breaking in the compact space. Significant contributions to the D3-brane potential, including the leading term in the infrared, arise from imaginary anti-self-dual (IASD) fluxes. For an arbitrary Calabi-Yau cone, we determine the most general IASD fluxes in terms of scalar harmonics, then compute the resulting D3-brane potential. Specializing to the conifold, we identify the operator dual to each mode of flux, and for chiral operators we confirm that the potential computed in the gauge theory matches the gravity result. The effects of four-dimensional curvature, including the leading D3-brane mass term, arise directly from the ten-dimensional equations of motion. Furthermore, we show that gaugino condensation on D7-branes provides a local source for IASD flux. This flux precisely encodes the nonperturbative contributions to the D3-brane potential, yielding a promising ten-dimensional representation of four-dimensional nonperturbative effects. Our result encompasses all significant contributions to the D3-brane potential discussed in the literature, and does so in the single coherent framework of ten-dimensional supergravity. Moreover, we identify new terms with irrational scaling dimensions that were inaccessible in prior works. By decoupling gravity in a noncompact configuration, then systematically reincorporating compactification effects as ultraviolet perturbations, we have provided an approach in which Planck-suppressed contributions to the D3-brane effective action can be computed.

Figures (6)

• Figure 1: Three descriptions of D3-branes in warped throats: the ten-dimensional supergravity perspective is explored in §\ref{['sec:10dSUGRA']}, §\ref{['sec:flux']} and §\ref{['sec:spectrum']}, the dual four-dimensional conformal field theory is discussed in §\ref{['sec:cft']}, and connections to four-dimensional supergravity are made in §\ref{['sec:4dSUGRA']} and §\ref{['sec:speculations']}.
• Figure 2: Compactification can induce very general UV perturbations of the warped conifold solution, but in the infrared only the lowest-dimension perturbations contribute meaningfully to the D3-brane potential.
• Figure 3: Schematic of the conifold geometry. The five angular coordinates on the base $X_5=T^{1,1}$ are denoted by $\Psi =\{\theta_i, \phi_i, \psi \}$. The geometry is noncompact, but we imagine that eventually this space smoothly attaches to a compact bulk space at $r_{\rm UV}$; cf. Fig. \ref{['fig:BDKMMM']}.
• Figure 4: Schematic of a finite throat with an embedded stack of D7-branes wrapping a four-cycle. The four-cycle is compact and resides partially in the bulk and partially in the throat. Gaugino condensation on the D7-branes induces a potential for the D3-brane.
• Figure 5: Schematic of a configuration in which nonperturbative effects on D7-branes wrapping a small four-cycle are represented, at long distances, by IASD fluxes $G_-$.