Chaos in Chiral Condensates in Gauge Theories

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 Nc limit provides a classicalization (other than the standard ℓ→0) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates qq and q5q in an N=2 supersymmetric QCD with the SU(Nc) gauge group at large Nc and at a large 't Hooft coupling λ≡NcgYM2 exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E (6×102)×mq4(Nc/λ2), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ,E) and find that the N=2 supersymmetric QCD is more chaotic for smaller Nc.