Chaos in chiral condensates in gauge theories

Abstract

Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem, because the notion of Lyapunov exponent, which is useful for singling out chaotic behaviors, works only in classical systems. We address the issue by using the AdS/CFT correspondence, as the large $N_c$ limit provides a classicalization (other than the standard $\hslash \to 0$) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: Time evolution of homogeneous quark condensates $⟨\bar{q}q⟩$ and $⟨\bar{q}{\gamma }_{5}q⟩$ in an $\mathcal{N}=2$ supersymmetric QCD with the $SU(N_c)$ gauge group at large $N_c$ and at large 't Hooft coupling $\lambda \equiv N_c{g}_{\mathrm{YM}}^2$ exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density $E\gtrsim (6\times 10^2)\times m_q^4(N_c/{\lambda }^2)$ where $m_q$ is the quark mass. We evaluate the largest Lyapunov exponent as a function of $(N_c,\lambda ,E)$ and find that the $\mathcal{N}=2$ supersymmetric QCD is more chaotic for smaller $N_c$.

9 pages, 5 figures. v2: Analysis of Lyapunov exponent of linear sigma model added, references and a footnote added. v3: Published version. An appendix added for explaining relation between classical chaos and out-of-time-ordered correlator. Title modified, abstract refined v4: Typos and grammatical errors corrected

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Cited by in corpus (29)

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• Entanglement production in bosonic systems: Linear and logarithmic growth
• Out-of-time-order correlator in coupled harmonic oscillators
• Bound on the exponential growth rate of out-of-time-ordered correlators
• Violation of bound on chaos for charged probe in Kerr-Newman-AdS black hole
• Chaos of Wilson Loop from String Motion near Black Hole Horizon
• Non-integrability on AdS${}_3$ supergravity backgrounds
• The fate of chaotic strings in a confining geometry
• Non-integrability and Chaos with Unquenched Flavor
• Chaos of QCD string from holography
• Anisotropic and frame dependent chaos of suspended strings from a dynamical holographic QCD model with magnetic field
• Extracting classical Lyapunov exponent from one-dimensional quantum mechanics
• A bound on energy dependence of chaos
• Quasinormal Modes and Universality of the Penrose Limit of Black Hole Photon Rings
• Chaotic spin chains in AdS/CFT
• Phase diagram of QCD chaos in linear sigma models and holography
• Analytic Non-Integrability and S-Matrix Factorization
• Configurational entropy and spectroscopy of pomeron resonances in dynamical AdS/QCD
• Interplay of magnetic field and chemical potential induced anisotropy and frame dependent chaos of a $Q\bar{Q}$ pair in holographic QCD
• Classical and quantum chaos of closed strings on a charged confining holographic background
• Out-of-time-order correlator as a detector of baryonic phase structure in holographic QCD with instanton
• Quantum quench, large N, and symmetry restoration
• Saturation of Chaos Bound in a Phenomenological Rotating Black Hole--Effective Matter System at Low-Temperature Limit
• Chaos in balanced and unbalanced holographic s+p superconductors
• Chaos in the holographic matrix models for meson and baryon
• Bound on the Lyapunov exponent in Kerr-Newman black holes via a charged particle