Chiral symmetry breaking in cascading gauge theory plasma

TL;DR

This work analyzes chiral symmetry breaking in the finite-temperature cascade of gauge theories dual to warped IIB supergravity. By constructing and studying a KS-effective action and its KT truncation, the authors identify a tachyonic chiral fluctuations sector that becomes unstable below $T_{\chi\mathrm{SB}}$, implying spontaneous $U(1)$ chiral breaking in the deconfined plasma. They show that the would-be homogeneous and isotropic χSB ground state is unattainable, as attempts to realize a homogeneous KS black hole with χSB fail and the tachyons prefer finite-momentum condensation, signaling an inhomogeneous phase. The analysis also reveals a violation of the correlated stability conjecture in this holographic context and clarifies the role of mass-deformed (explicit) chiral breaking in kinetic equilibrium states. Overall, the paper provides a detailed holographic account of chiral symmetry breaking in a non-conformal plasma, including UV/IR structure, quasinormal mode spectra, and endpoint behavior of tachyon condensation.

Abstract

N=1 supersymmetric SU(K+P)xSU(K) cascading gauge theory of Klebanov et.al [1,2] undergoes a first-order finite temperature confinement/deconfinement phase transition at T_c=0.6141111(3) Lambda, where Lambda is the strong coupling scale of the theory. The deconfined phase of the theory, with the unbroken chiral symmetry, extends down to T_u=0.8749(0) T_c, where it becomes perturbatively unstable due to the condensation of the hydrodynamic (sound) modes. We show that at T_cSB =0.882503(0) T_c > T_u the deconfined phase of the cascading plasma is perturbatively unstable towards development of the chiral symmetry breaking condensates. We present evidence that the ground state of the cascading plasma for T<T_cSB can not be homogeneous and isotropic.

Figures (4)

• Figure 1: (Colour online) Dispersion relation of the $\chi$SB quasinormal modes of the Klebanov-Tseytlin black hole as a function of $\ln \frac{T}{\Lambda}$ at high temperature. The solid blue line represent the dispersion relation of the $\chi$SB fluctuations with $(i\mathfrak{w}=0,\mathfrak{q}^2)$. The red dashed line is a fit \ref{['fitred']} to the data.
• Figure 2: (Colour online) Dispersion relation of the $\chi$SB quasinormal modes of the Klebanov-Tseytlin black hole as a function of $\frac{T}{\Lambda}$. The solid blue lines represent the dispersion relation of the $\chi$SB fluctuations at the threshold of instability: $(\mathfrak{w}=0,\mathfrak{q}^2)$. The blue dashed vertical lines represent the onset of instability: $T=T_{\chi\rm{SB}}$, such that $(i\mathfrak{w}=0,\mathfrak{q}^2=0)$. The vertical dashed green and red lines indicate $T=T_c$ and $T=T_u$ correspondingly. The green dots indicate quasinormal modes with $(i\mathfrak{w}=0.01, \mathfrak{q}^2)$ as a function of $\frac{T}{\Lambda}$. The red dots indicate quasinormal modes with $(i\mathfrak{w}=-0.01, \mathfrak{q}^2)$ as a function of $\frac{T}{\Lambda}$.
• Figure 3: A minimum of the mismatch vector $||\vec{v}_{mismatch}||$\ref{['mismatch']} as a function of the 'tachyon deformation amplitude' $A$\ref{['deform']} for $A\ne 0$ would identify seed values of parameters \ref{['paruvir']} leading to a homogeneous and isotropic KS BH solution with spontaneously broken chiral symmetry. We use $k_s=-0.8$. Clearly, such minimum is not present.
• Figure 4: One of the chiral condensates ($f_{a30}$) in mass-deformed cascading plasma as a function of mass-parameters $K_{110}$ with $f_{a10}=0$ (left plot) and $f_{a10}$ with $K_{110}=0$ (right plot) (see \ref{['solfixed']} for the precise relation to gaugino masses) for $k_s=-0.8$. Notice that the condensate vanishing linearly in the chiral limit.