Abstract
Motivated by $T\bar T$, we introduce and study a wide class of solvable deformations of quantum-mechanical theories. These deformations map the Hamiltonian to a function of itself. We solve these theories by computing all finite-temperature correlation functions of the deformed theory in terms of the correlators of the undeformed theory. Applications to AdS/CFT, SYK, and the Schwarzian theory are considered. We write down the deformed Schwarzian action for an arbitrary Hamiltonian deformation and find that the maximal Lyapunov exponent is unchanged.
Highlights
Calculable deformations of well-understood physical systems form the basis of much of theoretical physics
Upon computing fluctuations around the saddle of these theories and the out-of-time-order correlator (OTOC), we find that the Lyapunov exponent remains maximal
In [2], we proposed a formulation of the 1d TTdeformation (3.10) in terms of worldline gravity
Summary
Calculable deformations of well-understood physical systems form the basis of much of theoretical physics. In this paper we will introduce and study an infinite class of nonperturbative deformations to quantum field theories that can be solved exactly These deformations map the Hamiltonian to a function of itself, H → fðHÞ. One can consider Dirac’s classical theory of an electron in a background electromagnetic field [3] He wrote down an equation for the worldline of the particle that involved the third time derivative of its position, and to exclude unphysical states he imposed a future boundary condition (analogous to our spatial boundary condition to obtain the physical wave functions). Upon computing fluctuations around the saddle of these theories and the out-of-time-order correlator (OTOC), we find that the Lyapunov exponent remains maximal
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