Absorption of dilaton partial waves by D3-branes

TL;DR

The work addresses the problem of dilaton absorption by a stack of $N$ D3-branes beyond the s-wave, by constructing the complete set of non-abelian world-volume operators ${\cal O}^{i_1 \cdots i_l}$ that couple to the $l$-th partial wave of the dilaton and its derivatives. The authors derive these operators from T-duality and Matrix theory results, including a bosonic, a two-fermion, and a four-fermion sector organized with a symmetrized-trace structure. They compute the leading low-energy two-point functions of these operators in the planar, large-$N$ limit and convert them into absorption cross sections via the discontinuity method, obtaining exact agreement with the semiclassical gravity result for all partial waves: $\sigma^l_{worldvolume} = \sigma^l_{sugra}$. This provides strong evidence for non-renormalization theorems governing these two-point functions and deepens the AdS/CFT and Matrix theory connections, with implications for how bulk dilaton modes are encoded on the D3-brane worldvolume. The work also highlights the role of symmetrized-trace combinatorics and suggests avenues for exploring subleading (stringy) corrections and localization of bulk modes on $S^5$ in the gauge theory description.

Abstract

We calculate the leading term in the low-energy absorption cross section for an arbitrary partial wave of the dilaton field by a stack of many coincident D3-branes. We find that it precisely reproduces the semiclassical absorption cross section of a 3-brane geometry, including all numerical factors. The crucial ingredient in making the correspondence is the identification of the precise operators on the D3-brane world-volume which couple to the dilaton field and all its derivatives. The needed operators are related through T-duality and the IIA/M-theory correspondence to the recently determined M(atrix) theory expressions for multipole moments of the 11D supercurrent. These operators have a characteristic symmetrized trace structure which plays a key combinatorial role in the analysis for the higher partial waves. The results presented here give new evidence for an infinite family of non-renormalization theorems which are believed to exist for two-point functions in ${\cal N} = 4$ gauge theory in four dimensions.