Longitudinal Galilean and Carrollian limits of non-relativistic strings

Gerben Oling; Jelle Hartong; Leo Bidussi; Niels A. Obers; Troels Harmark

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Longitudinal Galilean and Carrollian limits of non-relativistic strings

Leo Bidussi, Troels Harmark, Jelle Hartong, Niels A. Obers, Gerben Oling

High Energy Physics - Theory · Submitted 25 Sep 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The second is a completely novel limit leading to a worldsheet theory with a Carrollian structure.

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arXiv ID2309.14467 (version 2)

Pith IDADYIIAH3, Pith's permanent record of this paper and its review

CitationGerben Oling, Jelle Hartong, Leo Bidussi, Niels A. Obers, Troels Harmark. "Longitudinal Galilean and Carrollian limits of non-relativistic strings." arXiv:2309.14467 (2023). https://pith.science/paper/ADYIIAH3

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What the abstract itself states, as probabilities: claims first 0.36 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.76 · mentions code or data availability 0.02.

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It is well known that one can take an infinite speed of light limit that gives rise to non-relativistic strings with a relativistic worldsheet sigma model but with a non-relativistic target space geometry. In this work we systematically explore two further limits in which the worldsheet becomes non-Lorentzian. The first gives rise to a Galilean string with a Galilean structure on the worldsheet, extending previous work on Spin Matrix-related string theory limits. The second is a completely novel limit leading to a worldsheet theory with a Carrollian structure. We find the Nambu-Goto and Polyakov formulations of both limits and explore gauge fixing choices. Furthermore, we study in detail the case of the Galilean string for a class of target space geometries that are related to Spin Matrix target space geometries, for which the Nambu-Goto action (in static gauge) is quadratic in the fields.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	It is well known that one can take an infinite speed of light limit that gives rise to non-relativistic strings with a relativistic worldsheet sigma model but with a non-relativistic target space geometry.	background 1.00	0.04	0.04	asserted 1.00
s1	In this work we systematically explore two further limits in which the worldsheet becomes non-Lorentzian.	contribution 1.00	0.85	0.08	asserted 0.98
s2	The first gives rise to a Galilean string with a Galilean structure on the worldsheet, extending previous work on Spin Matrix-related string theory limits.	contribution 0.73	0.83	0.15	asserted 1.00
s3	The second is a completely novel limit leading to a worldsheet theory with a Carrollian structure.	contribution 0.84	0.88	0.21	asserted 1.00
s4	We find the Nambu-Goto and Polyakov formulations of both limits and explore gauge fixing choices.	contribution 0.63	0.96	0.08	asserted 1.00
s5	Furthermore, we study in detail the case of the Galilean string for a class of target space geometries that are related to Spin Matrix target space geometries, for which the Nambu-Goto action (in static gauge) is quadratic in the fields.	contribution 0.84	0.93	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

It is well known that one can take an infinite speed of light limit that gives rise to non-relativistic strings with a relativistic worldsheet sigma model but with a non-relativistic target space geometry. In this work we systematically explore two further limits in which the worldsheet becomes non-Lorentzian. The first gives rise to a Galilean string with a Galilean structure on the worldsheet, extending previous work on Spin Matrix-related string theory limits. The second is a completely novel limit leading to a worldsheet theory with a Carrollian structure. We find the Nambu-Goto and Polyakov formulations of both limits and explore gauge fixing choices. Furthermore, we study in detail the case of the Galilean string for a class of target space geometries that are related to Spin Matrix target space geometries, for which the Nambu-Goto action (in static gauge) is quadratic in the fields.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A Common Type II Origin of Galilean and Carroll Superstrings
hep-th 2026-10 accept novelty 8.0 of 10

A single non-Lorentzian contraction of the Type II superalgebra, keeping momentum and F1 winding, yields the Galilean and magnetic Carroll superstrings as complementary quotients and polarizations.
Twisted BPS decoupling limits and AdS/CFT
hep-th 2026-09 conditional novelty 6.0 of 10

Twisted BPS decoupling limits of strings on AdS5 x S5 are defined as single-step limits, yielding non-relativistic sigma-models on symplectic U(1)-Galilean spaces, and extended to D-branes and to Spin Matrix theory limits.
An Introduction to String Newton-Cartan Holography and Integrability
hep-th 2026-03 accept novelty 3.0 of 10

String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.

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10 arXiv papers cite this in 26 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 15 sentences without a confident label

Uses its method or tool 2 papers

All global symmetries of the action of strings with relativistic world-sheet propagating in ([ref]) are given by solving the SNC Killing equations described in [ref] .

Non-Relativistic Holography from AdS$_5$/CFT$_4$ · A first test: matching symmetries · 0.92
One possible way to realise this is to take a world-sheet Galilean limit following the recent prescription of [ref] .

Nonrelativistic expansion of Green-Schwarz strings on $ AdS_5 \times S^5 $ · Concluding remarks · 0.88

Cites it as background 5 papers

Carroll strings with worldsheet Carroll symmetry were studied in [ref] , whereas target space Carroll symmetry was studied in [ref] .

Carroll Strings with an Extended Symmetry Algebra · Introduction · 0.90
SMTs are valuable models that interconnect fundamental physics – including the study of Hagedorn phase transitions, giant gravitons, non-relativistic string theory and more [ref] – with condensed matter applications, such as the Heisenberg XXX$_1/2$ spin chain and the Landau-Lifshitz model [ref] .

Finite scalar field theory with SU(1,1) spacetime symmetry from near-BPS limits of $\mathcal{N}=4$ SYM · Introduction · 0.92
See [ref] for reviews of SMT and [ref] for the latest developments.

Worldsheet Formalism for Decoupling Limits in String Theory · Spin Matrix Theory and Nonrelativistic Holography · 0.95

What it cites · 74 sentences without a confident label

Builds on 5 papers

Building on the recent TSNC formulation of NR string theory in [ref] , we find two new classes of sigma models, arising from scaling limits of the TSNC string.

Torsional string Newton-Cartan geometry for non-relativistic strings · Introduction · 0.98
It generalizes previous limits obtained and studied in Refs. [ref] for a less general class of target spacetimes, and has sometimes been referred to as the Spin Matrix Theory (SMT) string.

Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence · Longitudinal limits of non-relativistic string theory · 0.97
It generalizes previous limits obtained and studied in Refs. [ref] for a less general class of target spacetimes, and has sometimes been referred to as the Spin Matrix Theory (SMT) string.

Relating non-relativistic string theories · Longitudinal limits of non-relativistic string theory · 0.97

Uses the method or tool of 2 papers

Using the gauging methods described in e.g. [ref] and [ref] it is then not difficult to show that the longitudinal and transverse boost symmetry [ref] and [ref] of the action [ref] directly follow from the algebra above.

Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry · Symmetry algebra of Galilean string · 0.90
Using the gauging methods described in e.g. [ref] and [ref] it is then not difficult to show that the longitudinal and transverse boost symmetry [ref] and [ref] of the action [ref] directly follow from the algebra above.

Torsional string Newton-Cartan geometry for non-relativistic strings · Symmetry algebra of Galilean string · 0.90

Cites as background 38 papers

We refer to [ref] for details on this algebra and its contraction to FSG, as well as the associated gauging procedure, summarizing here the main results.

Torsional string Newton-Cartan geometry for non-relativistic strings · Gauge symmetry algebras and target spacetime geometry · 0.95
We begin with a brief review of the limit of the NS-NS sector of relativistic string theory (omitting the dilaton) in which one takes the speed of light along the transverse directions to infinity, following [ref] (see also [ref] and more generally [ref] ).

A Non-Relativistic Limit of NS-NS Gravity · Brief review of non-relativistic string theory · 0.92
We begin with a brief review of the limit of the NS-NS sector of relativistic string theory (omitting the dilaton) in which one takes the speed of light along the transverse directions to infinity, following [ref] (see also [ref] and more generally [ref] ).

Non-Relativistic Closed String Theory · Brief review of non-relativistic string theory · 0.92

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