Relating non-relativistic string theories

Harmark, Troels; Hartong, Jelle; Menculini, Lorenzo; Obers, Niels A.; Oling, Gerben

doi:10.1007/jhep11(2019)071

Cited by 123 publications

(273 citation statements)

References 67 publications

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“…Consequently, it should for example exhibit maximal chaos [22]. The limit that we propose can also be taken directly in string theory, giving rise to non-relativistic string theories on U(1)-Galilean target space [6,7,23,24] 1 and D-branes [27]. The explicit construction presented in this note will allow one to explore this very interesting corner of holography in quantitative detail.…”

Section: Discussionmentioning

confidence: 89%

Nonrelativistic Corners of N=4 Supersymmetric Yang-Mills Theory

Harmark¹,

Wintergerst²

2020

Phys. Rev. Lett.

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We show that N = 4 super Yang-Mills (SYM) theory on R×S 3 with gauge group SU(N ) is described in a near-BPS limit by a simple lower-dimensional non-relativistic field theory with SU(1, 1) × U(1) invariant interactions. In this limit, a single complex adjoint scalar field survives, and part of its interaction is obtained by exactly integrating out the gauge boson of the SYM theory. Taking into account normal ordering, the interactions match the one-loop dilatation operator of the SU(1, 1) sector, establishing the consistency of the limit at the quantum level. We discover a tantalizing field-theoretic structure, corresponding to a (1 + 1)-dimensional complex chiral boson on a circle coupled to a non-dynamical gauge field, both in the adjoint representation of SU(N ). Our findings equivalently apply to other BPS bounds and point towards the existence of new non-relativistic field theories that correspond to non-relativistic corners of N = 4 super Yang-Mills theory, paving the way for a new approach to understand its strongly coupled finite-N dynamics.

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Section: Discussionmentioning

confidence: 89%

Nonrelativistic Corners of N=4 Supersymmetric Yang-Mills Theory

Harmark¹,

Wintergerst²

2020

Phys. Rev. Lett.

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“…Moreover, we outline that our method is not only applicable non-relativistic symmetries corresponding to point particle limits, but also to extended objects where the D covariant dimensions are split into p + 1 and D − p − 1 directions for a p-brane [34,35]. Similar constructions in the case without a cosmological constant have been considered previously in [36,24,8,37]. Note added.…”

Section: Introductionmentioning

confidence: 90%

“…As in the particle case, higher values of N give rise to post-Newtonian extensions of the brane Newton-Hooke algebra. In the case of vanishing cosmological constant, these reduce to the non-relativistic expansion of the p-brane Galilean algebra [78][79][80], which have been studied in [37].…”

Section: A Further Generalisationsmentioning

confidence: 99%

Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

Gomis

Kleinschmidt

Palmkvist

et al. 2020

J. High Energ. Phys.

117

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We construct finite-and infinite-dimensional non-relativistic extensions of the Newton-Hooke and Carroll (A)dS algebras using the algebra expansion method, starting from the (anti-)de Sitter relativistic algebra in D dimensions. These algebras are also shown to be embedded in different affine Kac-Moody algebras. In the three-dimensional case, we construct Chern-Simons actions invariant under these symmetries. This leads to a sequence of non-relativistic gravity theories, where the simplest examples correspond to extended Newton-Hooke and extended (post-)Newtonian gravity together with their Carrollian counterparts.

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“…The cause of the surprise was a connection between two very different sounding topics. The first is the description of strings in non-relativistic Newton-Cartan backgrounds, which has recently been explored extensively in (for instance) [1][2][3][4][5][6][7][8][9][10][11][12][13]. This is in part inspired by motivations from holography [14,15], but also recalls older studies of non-relativistic limits of string theory [16][17][18], in which one might hope to find a novel corner of string theory in which at least some aspects of the full theory become simpler to understand.…”

Section: Introductionmentioning

confidence: 99%

A worldsheet supersymmetric Newton-Cartan string

Blair

2019

J. High Energ. Phys.

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We construct a (locally) supersymmetric worldsheet action for a string in a non-relativistic Newton-Cartan background. We do this using a doubled string action, which describes the target space geometry in an O(D, D) covariant manner using a doubled metric and doubled vielbeins. By adopting different parametrisations of these doubled background fields, we can describe both relativistic and non-relativistic geometries. We focus on the torsional Newton-Cartan geometry which can be obtained by null duality/reduction (such null duality is particularly simple for us to implement). The doubled action we use gives the Hamiltonian form of the supersymmetric Newton-Cartan string action automatically, from which we then obtain the equivalent Lagrangian. We extract geometric quantities of interest from the worldsheet couplings and write down the supersymmetry transformations. Our general results should apply to other non-relativistic backgrounds. We comment on the usefulness of the doubled approach as a tool for studying non-relativistic string theory.

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Relating non-relativistic string theories

Cited by 123 publications

References 67 publications

Nonrelativistic Corners of N=4 Supersymmetric Yang-Mills Theory

Nonrelativistic Corners of N=4 Supersymmetric Yang-Mills Theory

Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity

A worldsheet supersymmetric Newton-Cartan string

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