Double-trace deformation in Keldysh field theory

TL;DR

This paper introduces a Keldysh field theory framework with double-trace deformations, revealing potential nonthermal fixed points and richer driven-dissipative dynamics beyond traditional thermodynamics.

Contribution

It formulates a general Keldysh action obeying Weinbergian constraints, identifying a natural double-trace Lindblad term that may lead to new nonthermal conformal fixed points in large N limit.

Findings

Identification of a double-trace deformation as a Lindblad term in Keldysh formalism

Potential existence of nonthermal conformal fixed points in driven-dissipative systems

Examples demonstrating the theory in harmonic oscillator and O(N) vector models

Abstract

The Keldysh formalism is capable of describing driven-dissipative dynamics of open quantum systems as nonunitary effective field theories that are not necessarily thermodynamical, thus often exhibiting new physics. Here, we introduce a general Keldysh action that maximally obeys Weinbergian constraints, including locality, Poincar\'e invariance, and two "$CPT$" constraints: complete positivity and trace preserving as well as charge, parity, and time reversal symmetry. We find that the perturbative Lindblad term responsible for driven-dissipative dynamics introduced therein has the natural form of a double-trace deformation $\mathcal{O}^2$, which, in the large $N$ limit, possibly leads to a new nonthermal conformal fixed point. This fixed point is IR when $\Delta<d/2$ or UV when $\Delta>d/2$ given $d$ the dimensions of spacetime and $\Delta$ the scaling dimension of $\mathcal{O}$. Such a UV fixed point being not forbidden by Weinbergian constraints may suggest its existence and even completion of itself, in contrast to the common sense that dissipation effects are always IR relevant. This observation implies that driven-dissipative dynamics is much richer than thermodynamics, differing in not only its noncompliance with thermodynamic symmetry (e.g., the fluctuation-dissipation relation) but its UV/IR relevance as well. Examples including a $(0+1)$-$d$ harmonic oscillator under continuous measurement and a $(4-\epsilon)$-$d$ classic $O(N)$ vector model with quartic interactions are studied.