TY - JOUR

T1 - Operator thermalisation in d > 2

T2 - Huygens or resurgence

AU - Engelsoey, Julius

AU - Larana-Aragon, Jorge

AU - Sundborg, Bo

AU - Wintergerst, Nico

PY - 2020/9/16

Y1 - 2020/9/16

N2 - Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large N free fields subjected to a singlet constraint. This study in dimensions d > 2 motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens' principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens' principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non- perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.

AB - Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large N free fields subjected to a singlet constraint. This study in dimensions d > 2 motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens' principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens' principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non- perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.

KW - 1

KW - N Expansion

KW - AdS-CFT Correspondence

KW - Holography and condensed matter physics (AdS

KW - CMT)

KW - Quantum Dissipative Systems

KW - QUANTUM

KW - TRANSITION

KW - MODELS

U2 - 10.1007/JHEP09(2020)103

DO - 10.1007/JHEP09(2020)103

M3 - Journal article

VL - 2020

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 9

M1 - 103

ER -