Nonrelativistic giant magnons from Newton Cartan strings

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: 88%

Section: Geometric Contentmentioning

confidence: 99%

Geometrizing non-relativistic bilinear deformations

Hansen

Jiang

2021

“…The Newton-Cartan geometry has only recently been embedded in string theory at the classical level, that is at the tree level of the world-sheet non-linear sigma model [15,17,18]. Nonrelativistic string theory on a TNC background with R × S 2 topology has been studied in [19][20][21][22]. A parallel and separate line of work [23][24][25][26] which started by the original paper of Gomis and Ooguri [27] realized the Galilean symmetry in the context of closed string theory in a particular contraction limit and continued by the very recent papers [28,29] that ask the same question we ask here but in the context of the Gomis-Ooguri theory.…”

Section: Jhep09(2020)172mentioning

confidence: 99%

Torsional Newton Cartan gravity from non-relativistic strings

Gallegos

Gürsoy

Zinnato

2020

121

We study propagation of closed bosonic strings in torsional Newton-Cartan geometry based on a recently proposed Polyakov type action derived by dimensional reduction of the ordinary bosonic string along a null direction. We generalize the Polyakov action proposal to include matter, i.e. the 2-form and the 1-form that originates from the Kalb- Ramond field and the dilaton. We determine the conditions for Weyl invariance which we express as the beta-function equations on the worldsheet, in analogy with the usual case of strings propagating on a pseudo-Riemannian manifold. The critical dimension of the TNC space-time turns out to be 25. We find that Newton’s law of gravitation follows from the requirement of quantum Weyl invariance in the absence of torsion. Presence of the 1-form requires torsion to be non vanishing. Torsion has interesting consequences, in particular it yields a mass term and an advection term in the generalized Newton’s law. U(1) mass invariance of the theory is an important ingredient in deriving the beta functions.

“…However, a detailed understanding of similar phenomena from the perspective of strong coupling (g 1) physics is still lacking in the literature. The understanding of strong coupling phenomena requires a dual nonrelativistic (NR) stringy counterpart [10]- [12] living in AdS 5 × S 5 which for our case would correspond to constructing a null reduced sigma model action over torsional Newton-Cartan (TNC) geometry [13]- [24] and thereby taking 1/c limit of the world-sheet degrees of freedom.…”

Section: Jhep11(2020)044mentioning

confidence: 99%

Nonrelativistic spinning strings

Roychowdhury

2020

Self Cite

We construct nonrelativistic spinning string solutions corresponding to SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5. Considering various nonrelativistic spinning string configurations both in AdS5 as well as S5 we obtain corresponding dispersion relations in the strong coupling regime of SMT where the strong coupling ($$ \sim \sqrt{\mathfrak{g}} $$ ∼ g ) corrections near the BPS bound have been estimated in the slow spinning limit of strings in AdS5. We generalize our results explicitly by constructing three spin folded string configurations that has two of its spins along AdS5 and one along S5. Our analysis reveals that the correction to the spectrum depends non trivially on the length of the NR string in AdS5. The rest of the paper essentially unfolds the underlying connection between SU(1, 2|3) Spin-Matrix theory (SMT) limit of strings in AdS5× S5 and the nonrelativistic Neumann-Rosochatius like integrable models in 1D. Taking two specific examples of NR spinning strings in R × S3 as well as in certain sub-sector of AdS5 we show that similar reduction is indeed possible where one can estimate the spectrum of the theory using 1D model.