$$ T\overline{T} $$ deformations of supersymmetric quantum mechanics

Ebert, Stephen; Ferko, Christian; Sun, Haoyu; Sun, Zhengdi

doi:10.1007/jhep08(2022)121

Cited by 21 publications

(20 citation statements)

References 145 publications

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“…Since the dimensional reduction of ModMax yields a Root-T T flow [10,69,70] with a particularly simple seed action, one may suspect that supersymmetry persists for any supersymmetric seed. This is certainly the case for the irrelevant T T deformation [71][72][73][74][75][76][77]. In that case, it was useful to understand the whole deformation in terms of superfields; it may be important to do the same here.…”

Section: Discussionmentioning

confidence: 99%

On the Classical Integrability of Root-$T \overline{T}$ Flows

Borsato¹,

Ferko²,

Sfondrini³

2022

Preprint

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The Root-T T flow was recently introduced as a universal and classically marginal deformation of any two-dimensional translation-invariant field theory. The flow commutes with the (irrelevant) T T flow and it can be integrated explicitly for a large class of actions, leading to non-analytic Lagrangians reminiscent of the four-dimensional Modified-Maxwell theory (ModMax). It is not a priori obvious whether the Root-T T flow preserves integrability, like it is the case for the T T flow. In this paper we demonstrate that this is the case for a large class of classical models by explicitly constructing a deformed Lax connection. We discuss the principal chiral model and the non-linear sigma models on symmetric and semi-symmetric spaces, without or with Wess-Zumino term. We also construct Lax connections for the two-parameter families of theories deformed by both Root-T T and T T for all of these models.

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Section: Discussionmentioning

confidence: 99%

On the Classical Integrability of Root-$T \overline{T}$ Flows

Borsato¹,

Ferko²,

Sfondrini³

2022

Preprint

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“…7 4 JT gravity can be written in terms of a BF gauge theory. The deformed BF formalism and related supersymmetric quantum mechanics was found in [42,43]. 5 An alternative perspective on deriving this flow equation may be found through the Wheeler-de Witt equation derived in [23] for higher-dimensional large-N CFTs.…”

Section: Jhep08(2022)026mentioning

confidence: 99%

$$ T\overline{T} $$-deformed free energy of the Airy model

Ebert

Sun

2022

J. High Energ. Phys.

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Sharpening the correspondence of Jackiw-Teitelboim (JT) gravity and its dual matrix model description at a finite radial cutoff λ through the $$ T\overline{T} $$ T T ¯ deformation is of interest. To proceed, we simplify the problem by considering the Airy model and deform Airy correlators in the same way as in $$ T\overline{T} $$ T T ¯ -deformed JT gravity. We use those correlators to compute the annealed and quenched free energies for both λ > 0 and λ < 0 from an integral representation of the replica trick. At the leading order in λ and low temperatures, we confirm that the genus-zero quenched free energy monotonically decreases as a function of temperature when perturbation theory is valid. We then study the all-genus quenched free energy at low temperatures, where we discover and discuss subtleties due to non-perturbative effects in the Airy model, as well as the contributions from the non-perturbative branch under the $$ T\overline{T} $$ T T ¯ deformation.

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“…Furthermore, the T T operator in 2d preserves several symmetries of a given seed theory. For example, some preserved symmetries include integrability [43,49] and supersymmetry [62][63][64][65][66]; for additional results on manifestly supersymmetric T T -like flows, see [67][68][69][70][71][72]. However, conformal symmetry is not preserved because the flow parameter λ introduces a dimensionful scale in the theory.…”

Section: Introductionmentioning

confidence: 99%

$T\bar{T}$ in JT Gravity and BF Gauge Theory

et al. 2022

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JT gravity has a first-order formulation as a two-dimensional BF theory, which can be viewed as the dimensional reduction of the Chern-Simons description of 3d3d gravity. We consider {T\overbar{T}}TT¯-type deformations of the (0+1)(0+1)-dimensional dual to this 2d2d BF theory and interpret the deformation as a modification of the BF theory boundary conditions. The fundamental observables in this deformed BF theory, and in its 3d3d Chern-Simons lift, are Wilson lines and loops. In the 3d3d Chern-Simons setting, we study modifications to correlators involving boundary-anchored Wilson lines which are induced by a {T\overbar{T}}TT¯ deformation on the 2d2d boundary; results are presented at both the classical level (using modified boundary conditions) and the quantum-mechanical level (using conformal perturbation theory). Finally, we calculate the analogous deformed Wilson line correlators in 2d2d BF theory below the Hagedorn temperature where the principal series dominates over the discrete series.

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$$ T\overline{T} $$ deformations of supersymmetric quantum mechanics

Cited by 21 publications

References 145 publications

On the Classical Integrability of Root-$T \overline{T}$ Flows

On the Classical Integrability of Root-$T \overline{T}$ Flows

$$ T\overline{T} $$-deformed free energy of the Airy model

$T\bar{T}$ in JT Gravity and BF Gauge Theory

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