Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Localized Backreacted Flavor Branes in Holographic QCD

Benjamin A. Burrington, Vadim S. Kaplunovsky, Jacob Sonnenschein

Abstract

We investigate the perturbative (in $g_s N_{D8}$) backreaction of localized D8 branes in D4-D8 systems including in particular the Sakai Sugimoto model. We write down the explicit expressions of the backreacted metric, dilaton and RR form. We find that the backreaction remains small up to a radial value of $u \ll \ell_s/(g_s N_{D8})$, and that the background functions are smooth except at the D8 sources. In this perturbative window, the original embedding remains a solution to the equations of motion. Furthermore, the fluctuations around the original embedding, describing scalar mesons, do not become tachyonic due to the backreaction in the perturbative regime. This is is due to a cancelation between the DBI and CS parts of the D8 brane action in the perturbed background.

Localized Backreacted Flavor Branes in Holographic QCD

Abstract

We investigate the perturbative (in ) backreaction of localized D8 branes in D4-D8 systems including in particular the Sakai Sugimoto model. We write down the explicit expressions of the backreacted metric, dilaton and RR form. We find that the backreaction remains small up to a radial value of , and that the background functions are smooth except at the D8 sources. In this perturbative window, the original embedding remains a solution to the equations of motion. Furthermore, the fluctuations around the original embedding, describing scalar mesons, do not become tachyonic due to the backreaction in the perturbative regime. This is is due to a cancelation between the DBI and CS parts of the D8 brane action in the perturbed background.

Paper Structure

This paper contains 19 sections, 121 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Brief review of the general setup
  3. Sakai-Sugimoto (SS) model
  4. Massive type IIA and 8 branes
  5. Backreaction of D8 branes
  6. Finding the equations: ansatz and separation
  7. Gauge Freedom
  8. Solutions: the linearized backreaction
  9. $U_K=0$ decompactification limit
  10. $U_K=0$ with $x_4$ compactified
  11. $U_K\neq0$
  12. Analysis of equations: Stability
  13. DBI and CS equations of motion: $x_4=0$ ($\pi R_x)$ solution
  14. $U_K=0$ decompactification limit
  15. Stability of the Sakai Sugimoto model
  16. ...and 4 more sections

Figures (7)

  • Figure 1: The three cases studied: a) the uncompactified $x_4$ case, b) the compactified $x_4$ case, and c) the near extremal "cigar" case.
  • Figure 2: The dominant configurations of the D8 and anti-D8 probe branes in the Sakai-Sugimoto model at zero temperature, which break the chiral symmetry. The same configurations will turn out to be relevant also at low temperatures. On the left a generic configuration with an asymptotic separation of $L$, that stretches down to a minimum at $u=u_0$, is drawn. The figure on the right describes the limiting antipodal case $L=\pi R_x$, where the branes connect at $u_0=U_{K}$.
  • Figure 3: Graphs of $K_i(q)$, setting $N_2=N_3=0$.
  • Figure 4: $F_1/U_K$ as a function of $x_4/R_x$ for $u/U_K=100$ using images from $n=-50\cdots 50$, $F_2/U_K$ as a function of $x_4/R_x$ for $u/U_K=100$, $n=-500\cdots 500$ and $\hat{\phi}_1/U_K$ as a function of $x_4/R_x$ for $u/U_K=10,000$, $n=-500\cdots 500$.
  • Figure 5: Graphs of $\phi_1/U_K$, $A_1/U_K$, $B_1/U_K=G_1/U_K$, $C_1/U_K$ graphed as a function of $x_4/R_x$. Each graph represents a different $u$ value of $u=1,5,10,20,40$ in ROYGB order. All graphs use the first 150 modes ($m=0...150$), of which only even m are non zero.
  • ...and 2 more figures