2021/03/01 by Arnab Kundu, Kundu, Arnab, Ayan Patra +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.2103.00824
openalex publication_date 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently introduced reparametrization mode operators in CFTs have been shown\nto govern stress tensor interactions via the shadow operator formalism and\nseem to govern the effective dynamics of chaotic systems. We initiate a study\nof Ward identities of reparametrization mode operators i.e. how two\ndimensional CFT Ward identities govern the behaviour of insertions of\nreparametrization modes \ε in correlation functions:\n\⟨\ε\ε\φ\φ\⟩. We find that in the semi-classical\nlimit of large c they dictate the leading \O(c-1) behaviour.\nWhile for the 4pt function this reproduces the same computation as done by\nHeahl, Reeves & Rozali in citeHaehl:2019eae, in the case of 6pt function of\npair-wise equal operators this provides an alternative way of computing the\nVirasoro block in stress-tensor comb channel. We compute a maximally out of\ntime ordered correlation function in a thermal background and find the expected\nbehaviour of an exponential growth governed by Lyapunov index\n\λL=2\π/\β lasting for twice the scrambling time of the system\nt^*=\(\β)/(2\π)\log ,c for the maximally braided type of\nout-of-time-ordering. However when only the internal operators of the\ncomb channel are \out-of-time-ordered, the correlator sees no exponential\nbehaviour despite the inclusion of the Virasoro contribution. From a bulk\nperspective for the \out-of-time-ordered 4pt function we find that the\nCasimir equation for the stress tensor block reproduces the linearised back\nreaction in the bulk.\n