Abstract
Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, 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 ℏ→0) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨q[over ¯]q⟩ and ⟨q[over ¯]γ_{5}q⟩ in an N=2 supersymmetric QCD with the SU(N_{c}) gauge group at large N_{c} and at a large 't Hooft coupling λ≡N_{c}g_{YM}^{2} exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E≳(6×10^{2})×m_{q}^{4}(N_{c}/λ^{2}), where m_{q} is the quark mass. We evaluate the largest Lyapunov exponent as a function of (N_{c},λ,E) and find that the N=2 supersymmetric QCD is more chaotic for smaller N_{c}.
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