$$ T\overline{T} $$ and $$ J\overline{T} $$ deformations in quantum mechanics

Chakraborty, Soumangsu; Mishra, Amiya

doi:10.1007/jhep11(2020)099

Cited by 14 publications

(7 citation statements)

References 23 publications

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“…It would also be interesting to understand the behavior of the bulk theory at finite cutoff in the presence of matter: for example, the existence of a U(1) chiral current could provide a deformation of the Schwarzian quantum mechanics analogous to the J T deformation in two-dimensional CFTs [39]. In [40], such a deformation has been proposed leading, for some choice of the parameters, to a positive-definite spectral density.…”

Section: Discussionmentioning

confidence: 99%

Nonperturbative effects and resurgence in JT gravity at finite cutoff

Griguolo,

Panerai,

Papalini

et al. 2021

Preprint

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We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a T T -deformed Schwarzian quantum mechanics. Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. We show that the perturbative series is asymptotic and that it admits a precise completion exploiting the analytical properties of its Borel transform, as prescribed by resurgence theory. The final result is then naturally interpreted in terms of the nonperturbative branch of the T T -deformed spectrum. The finite-cutoff trumpet partition function is computed by applying the same strategy. In the second part of the paper, we propose an extension of this formalism to arbitrary topologies, using the basic gluing rules of the undeformed case. The Weil-Petersson integrations can be safely performed due to the nonperturbative corrections and give results that are compatible with the flow equation associated with the T T deformation. We derive exact expressions for general topologies and show that these are captured by a suitable deformation of the Eynard-Orantin topological recursion. Finally, we study the "slope" and "ramp" regimes of the spectral form factor as functions of the cutoff parameter.

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Section: Discussionmentioning

confidence: 99%

Nonperturbative effects and resurgence in JT gravity at finite cutoff

Griguolo,

Panerai,

Papalini

et al. 2021

Preprint

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show abstract

“…Since the deformation is irrelevant, the density of states of the deformed theory in the UV exhibits Hagedorn growth behavior, which implies the TT deformation is non-local in the UV [2,9,10]. With many intriguing properties discovered, the TT deformation has subsequently been generalized to many directions, for instance, to other integrable deformations such as the JT deformation [11][12][13], to supersymmetric cases [14][15][16][17], to various dimensions [18][19][20][21] and spin chain models [22][23][24][25][26]. For some other developments of the TT deformation, please refer to [27][28][29][30][31][32][33][34][35].…”

Section: Jhep09(2021)061mentioning

confidence: 99%

“…Since |P (z)| 2 is no longer analytic, we can not expand it in terms of ζ(z) as what we did for P (z) 2 . Instead, we will adopt the following 21 In this case lim…”

Section: Jhep09(2021)061mentioning

confidence: 99%

T $$ \overline{T} $$-flow effects on torus partition functions

Sun

Zhang

2021

J. High Energ. Phys.

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In this paper, we investigate the partition functions of conformal field theories (CFTs) with the T$$ \overline{T} $$ T ¯ deformation on a torus in terms of the perturbative QFT approach. In Lagrangian path integral formalism, the first- and second-order deformations to the partition functions of 2D free bosons, free Dirac fermions, and free Majorana fermions on a torus are obtained. The corresponding Lagrangian counterterms in these theories are also discussed. The first two orders of the deformed partition functions and the first-order vacuum expectation value (VEV) of the first quantum KdV charge obtained by the perturbative QFT approach are consistent with results obtained by the Hamiltonian formalism in literature.

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“…This paper will study an analog of the T T deformation in the one-dimensional quantum mechanical theory proposed by [4,5]. For example, one can refer to [6,7] for recent developments. In particular, we focus on a particular realization of the T T deformation of the SYK 4 model in the form of f (H), where H is the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos, scrambling and operator growth in $$ T\overline{T} $$ deformed SYK models

Lau

Xian

et al. 2022

J. High Energ. Phys.

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In this work, we investigate the quantum chaos in various $$ T\overline{T} $$ T T ¯ -deformed SYK models with finite N, including the SYK4, the supersymmetric SYK4, and the SYK2 models. We numerically study the evolution of the spectral form factor (SFF), the out-of-time ordered correlator (OTOC), and the Krylov complexity. We find that the characteristic evolution of the SFF, OTOC and K-complexity of both the SYK4 and SSYK4 models remains unchanged under the deformation, which implies that the properties of quantum chaos is preserved. We also identify a many-body localization behavior in the deformed SYK2 model.

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$$ T\overline{T} $$ and $$ J\overline{T} $$ deformations in quantum mechanics

Cited by 14 publications

References 23 publications

Nonperturbative effects and resurgence in JT gravity at finite cutoff

Nonperturbative effects and resurgence in JT gravity at finite cutoff

T $$ \overline{T} $$-flow effects on torus partition functions

Quantum chaos, scrambling and operator growth in $$ T\overline{T} $$ deformed SYK models

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