Non-relativistic duality and $$ T\overline{T} $$ deformations

We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformation and the recently introduced hard rod deformation. We show that all three deformations can be interpreted as coupling the non-relativistic QFT to a specific Newton-Cartan geometry, similar to the Jackiw-Teitelboim-like gravity in the relativistic case. Using the gravity formulations, we derive closed-form deformed classical Lagrangians of the Schrödinger model with a generic potential. We also extend the dynamical change of coordinate interpretation to the non-relativistic case for all three deformations. The dynamical coordinates are then used to derive the deformed classical Lagrangians and deformed quantum S-matrices.

Section: Jhep04(2021)186mentioning

confidence: 84%

Geometrizing non-relativistic bilinear deformations

Hansen

Jiang

2021

“…There is a growing interest in non-Lorentzian field theories from a variety of view points and applications, for some recent studies see [8][9][10][11][12][13][14][15][16]. Our own interest stems from a novel form of conformal compactification, which appears to be able to reproduce aspects of the original non-compact six-dimensional SCFT from a five-dimensional Lagrangian theory with a Kaluza-Klein-like tower [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Non-Lorentzian avatars of (1,0) theories

Lambert

Orchard

2021

We construct five-dimensional non-Lorentzian Lagrangian gauge field theories with an SU(1, 3) conformal symmetry and 12 (conformal) supersymmetries. Such theories are interesting in their own right but can arise from six-dimensional (1, 0) superconformal field theories on a conformally compactified Minkowski spacetime. In the limit that the conformal compactification is removed the Lagrangians we find give field theory formulations of DLCQ constructions of six-dimensional (1, 0) conformal field theories.

“…This presents a very nice completion of the questions raised by the results of [21] and reviewed in the introduction. Schematically, we have established the following for classical theories of free bosons and their TT-deformations: The limit λ → ∞ was interpreted as ultra-relativistic (also called Carollian) limit in [19]. There, it was further argued that the chiral decoupling seen in this limit is a JHEP02(2021)028 natural expectation based on the classification given in Since the non-local action obtained in eq.…”

Section: Discussionmentioning

confidence: 92%

“…Various aspects of the so-called TT deformation -triggered at each step of the "flow" by the determinant of the stress tensor [1,2] -such as the finite-volume spectrum [3] and the S-matrix of the deformed theory [4][5][6] are known exactly. These deformations have been studied from a various points of view, for example holography [7][8][9][10][11], supersymmetric quantum field theories [12][13][14][15][16][17], and string theory [18,19]. An excellent introduction to this field can be found in [20].…”

Section: Introductionmentioning

confidence: 99%

Irrelevant deformations of chiral bosons

Chakrabarti

Gupta

Manna

et al. 2021

We study $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformations of chiral bosons using the formalism due to Sen. For arbitrary numbers of left- and right-chiral bosons, we find that the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed Lagrangian can be computed in closed form, giving rise to a novel non-local action in Sen’s formalism. We establish that at the limit of infinite $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ coupling, the equations of motion of deformed theory exhibits chiral decoupling. We then turn to a discussion of $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed chiral fermions, and point out that the stress tensor of the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ -deformed free fermion coincides with the undeformed seed theory. We explain this behaviour of the stress tensor by noting that the deformation term in the action is purely topological in nature and closely resembles the fermionic Wess-Zumino term in the Green-Schwarz formalism. In turn, this observation also explains a puzzle in the literature, viz. why the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformation of multiple free fermions truncate at linear order. We conclude by discussing the possibility of an interplay between $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ deformations and bosonisation.