Baryon Mass and Phase Transitions in Large N Gauge Theory

TL;DR

The work addresses baryon binding and finite-temperature phase behavior in the large-N N=4 gauge theory using holographic duality. It computes the baryon mass by modeling a wrapped D5-brane on S^5 with N attached strings and analyzes how finite temperature and Higgs-phase breaking affect bound states. A key result is that baryons form true bound states at zero temperature, with M_B < N M_q, and that there is a phase transition at a critical temperature where baryons dissolve into N quarks; in the Higgs phase, bound states of W-bosons also arise. The findings illuminate non-perturbative bound-state dynamics in a conformal theory and map a finite-temperature phase diagram via holography with potential implications for strongly coupled gauge theories.

Abstract

We calculate the baryon mass in N=4 large $N$ gauge theory by means of AdS/CFT correspondence and show that it is a truly bound state, at least in some situations. We find that a phase transition occurs at a critical temperature. Furthermore, we find there are bound states of W-bosons in the Higgs phase, where the gauge group is broken to SU(N_1)xSU(N_2).

Figures (4)

• Figure 1: Baryon creation process. (a) If $k$ strings meet, (b) two wrapped D5-branes with opposite orientations are created at a point on the strings. (c) If the number $k$ of the strings is smaller than $N$, $N-k$ strings with opposite orientation are generated between the two wrapped D5-branes to cancel the charge of string endpoints on the D5-branes. (d) Then, one of the wrapped D5-branes reaches to the position of the probe, $r=r_{\rm probe}$, and another is absorbed into the horizon.
• Figure 2: The near horizon geometry of a Higgs phase consist of three regions. W-bosons which belong to the $(N_1,\overline N_2)$ representation are represented by strings stretched from the horizon in region 1 to that in region 2. They are regarded as combinations of $SU(N_1)$ quarks in region 1 and $SU(N_2)$ antiquarks in region 2. W-bosons in the $(\overline N_1,N_2)$ representation correspond to strings with the opposite orientation.
• Figure 3: If $k$ W-bosons belonging to the $(N_1,\overline N_2)$ representation meet, a bound state is created if $k$ is larger than $(5/8)N_1$ or $(5/8)N_2$. (a) When $(5/8)N_1\leq k\leq(5/8)N_2$, it is regarded as combination of an $SU(N_1)$ baryon and $SU(N_2)$ antiquarks. (b) When $k$ is larger than both $(5/8)N_1$ and $(5/8)N_2$, the bound state is regarded as a combination of an $SU(N_1)$ baryon and an $SU(N_2)$ antibaryon.
• Figure 4: $\rho$-dependence of the ratio $M_B/M_q$.