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Planar quark scattering at strong coupling and universality

Zohar Komargodski, Shlomo S. Razamat

TL;DR

This paper investigates planar, strong-coupling quark scattering in AdS/CFT, extending Alday–Maldacena’s minimal-area prescription from gluons to fundamental matter. By exploiting color decomposition, the authors show that quark amplitudes in two distinct N=2 theories reduce to the same minimal-area problem bounded by light-like segments, mirroring the gluon case. They analyze both a D3-D7 setup and an exactly conformal USp(2N) theory to argue for a universal behavior of scattering amplitudes at strong coupling in the planar limit. The results illuminate why the strong-coupling amplitudes for gluons and quarks share universal features across a class of conformal theories.

Abstract

We discuss scattering of fundamental matter in the planar and strong coupling limit via the AdS/CFT correspondence, generalizing the recently proposed calculation for adjoint matter due to Alday and Maldacena [arXiv:0705.0303]. Color decomposition of quark amplitudes is a key property allowing to repeat the procedure in the case of fundamental matter and to derive the relation of these strong coupling amplitudes to minimal area problems. We present the results for two different D3-D7 systems, one is only conformal in the planar limit and the other is exactly conformal. Our results suggest a universal behavior of scattering amplitudes at strong coupling and planar limit (both for gluons and quarks).

Planar quark scattering at strong coupling and universality

TL;DR

This paper investigates planar, strong-coupling quark scattering in AdS/CFT, extending Alday–Maldacena’s minimal-area prescription from gluons to fundamental matter. By exploiting color decomposition, the authors show that quark amplitudes in two distinct N=2 theories reduce to the same minimal-area problem bounded by light-like segments, mirroring the gluon case. They analyze both a D3-D7 setup and an exactly conformal USp(2N) theory to argue for a universal behavior of scattering amplitudes at strong coupling in the planar limit. The results illuminate why the strong-coupling amplitudes for gluons and quarks share universal features across a class of conformal theories.

Abstract

We discuss scattering of fundamental matter in the planar and strong coupling limit via the AdS/CFT correspondence, generalizing the recently proposed calculation for adjoint matter due to Alday and Maldacena [arXiv:0705.0303]. Color decomposition of quark amplitudes is a key property allowing to repeat the procedure in the case of fundamental matter and to derive the relation of these strong coupling amplitudes to minimal area problems. We present the results for two different D3-D7 systems, one is only conformal in the planar limit and the other is exactly conformal. Our results suggest a universal behavior of scattering amplitudes at strong coupling and planar limit (both for gluons and quarks).

Paper Structure

This paper contains 5 sections, 23 equations, 4 figures.

Table of Contents

  1. Introduction and summary
  2. Color decomposition of quark scattering
  3. Adding fundamental matter to ${\mathcal{N}}=4$
  4. $n$-point quark scattering
  5. ${\mathcal{N}}=2$ conformal field theory

Figures (4)

  • Figure 1: Example of quark scattering diagram, (a) the Feynman diagram (b) its double line notation.
  • Figure 2: The $D3-D7$ system.
  • Figure 3: The $D3-D7$ system before backreaction considered. (a) The massive case, here the $D7$ wraps the sphere in a non-trivial way, $\cos(\psi) = c\cdot z$. (b) The massless case, the $D7$ brane lies along the $\psi=\frac{1}{2} \pi$ direction, and spans all values of $z$.
  • Figure 4: The disc four point amplitude before (left) and after (right) the action of the $T$-duality. The spike singularities which arise if $z$ is allowed to vary along the blue lines on the left hand side figure, are depicted as blue dashed lines.