# Heavy Operators and Hydrodynamic Tails

### Submission summary

 As Contributors: Luca Delacrétaz Arxiv Link: https://arxiv.org/abs/2006.01139v2 (pdf) Date accepted: 2020-08-25 Date submitted: 2020-08-18 13:55 Submitted by: Delacrétaz, Luca Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

### Abstract

The late time physics of interacting QFTs at finite temperature is controlled by hydrodynamics. For CFTs this implies that heavy operators -- which are generically expected to create thermal states -- can be studied semiclassically. We show that hydrodynamics universally fixes the OPE coefficients $C_{HH'L}$, on average, of all neutral light operators with two non-identical heavy ones, as a function of the scaling dimension and spin of the operators. These methods can be straightforwardly extended to CFTs with global symmetries, and generalize recent EFT results on large charge operators away from the case of minimal dimension at fixed charge. We also revisit certain aspects of late time thermal correlators in QFT and other diffusive systems.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 9, 034 (2020)

### List of changes

List of changes (numbers refer to comments from the referee):

1,2- Added Eq. (1.3) with thermal two-point function, and discussion
above on the location of the sound pole.

4- Changed 'light' to 'long-lived'.

5- Changed 'correlator' to 'two-point function' and referred to the
appropriate equation.

6- Replaced "10" with "n".

7- Extra comment below (1.8) explaining how the general result involves
both (1.4) and (1.8).

8- Corrected footnote on p.9.

10- Added a footnote on p.14 with the value of the dimensionless entropy
s_o for the quark-gluon plasma.

11- Added explanation for the derivation of (2.29).

12- The \bar{\ell} was removed from Eq. (2.30).

13- Added definition of J and m above (3.7).

Other changes:

power of k\ell_th in (2.30) and (2.31)

power of c_1 in (4.22) and (4.24)