ABSTRACT
We revisit Weyl invariance string theories in generalized supergravity backgrounds. A possible counterterm was constructed in a work by Sakamoto, Sakatani, and Yoshida, but it seems to be a point of controversy in some literatures whether or not it is nonlocal. To settle down this issue, we show that the counterterm may be local and exactly cancels out the one-loop trace anomaly in generalized supergravity backgrounds.
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 ââ0) 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 Eâ³(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}.
