### References & Citations

# High Energy Physics - Theory

# Title: Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT$_2$

(Submitted on 1 Mar 2021 (v1), revised 22 Apr 2021 (this version, v2),

*latest version 7 Sep 2021*(v3))Abstract: Recently introduced reparametrization mode operators in CFTs have been shown to govern stress tensor interactions $via$ the shadow operator formalism and seem to govern the effective dynamics of chaotic system. We initiate a study of Ward identities of reparametrization mode operators $i.e.$ how two dimensional CFT Ward identities govern the behaviour of insertions of reparametrization modes $\epsilon$ in correlation functions: $\langle\epsilon\epsilon\phi\phi\rangle$. We find that in the semi-classical limit of large $c$ they dictate the leading $\mathcal{O}(c^{-1})$ behaviour. While for the $4$pt function this reproduces the same computation as done by Heahl, Reeves \& Rozali in [1], in the case of 6pt function of pair-wise equal operators this provides an alternative way of computing the Virasoro block. We compute a maximally out of time ordered correlation function in a thermal background and find the expected behaviour of an exponential growth governed by Lyapunov index $\lambda_L=2\pi/\beta$ lasting for twice the scrambling time of the system $t^*=\frac{\beta}{2\pi}\log\,c$. From a bulk perspective for the out of time ordered $4$pt function we find that the Casimir equation for the stress tensor block reproduces the linearised back reaction in the bulk.

## Submission history

From: Rohan Poojary [view email]**[v1]**Mon, 1 Mar 2021 07:48:16 GMT (39kb)

**[v2]**Thu, 22 Apr 2021 09:45:33 GMT (40kb)

**[v3]**Tue, 7 Sep 2021 08:39:25 GMT (487kb,D)

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