D3-brane potentials from fluxes in AdS/CFT

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 automatically and 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 JHEP06 (2010)072 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. This is the companion paper to [1].

Inflation and String Theory

“…The geometric perspective afforded by compactifications, and by D-branes moving inside them, complements the more algebraic tools used to construct effective theories in particle physics. The effective theories in D-brane inflation [41,42], DBI inflation [38], fibre inflation [43], and axion monodromy inflation [34], for example, all exist in their own right as low-energy theories, but would likely have gone undiscovered without the approach provided by string theory. Generating effective theories from the top down in string theory also leads to modified notions of what constitutes a natural inflationary model, or a minimal one.…”

“…For Gaussian initial conditions, complete information about the temperature map is contained in the correlations between the temperatures at pairs of distinct points n and n , 42) where cos θ ≡ n · n , and the angle brackets denote an ensemble average. 3 It is convenient to describe the same information in harmonic space, by expanding the temperature field in spherical harmonics, The angular power spectrum, C , is the Legendre transform of the two-point function (1.42):…”

“…When the scales appearing in the input statistical distributions are taken to be comparable, i.e. when F rms ∼ Z rms ∼ U rms , (3.149) 42 The fine print is that the correlations cannot be too numerous [464], and the statistical distributions must have appropriately bounded moments. Universality has been formulated and established rigorously in many settings -cf.…”

“…For example, in [42] it was shown that the leading contribution to the action for a D3-brane in a warped region arises at quadratic order in an expansion in the strength of sources in the bulk of the compactification.…”

“…e.g. [42,240,534]. 19 See §2.3.2 for an explanation of the cutoff value δ ∼ 6 in small-field inflation.…”