Nonrelativistic strings and limits of the AdS/CFT correspondence

Abstract

Using target space null reduction of the Polyakov action, we find a novel covariant action for strings moving in a torsional Newton-Cartan geometry. Sending the string tension to zero while rescaling the Newton-Cartan clock 1-form, so as to keep the string action finite, we obtain a nonrelativistic string moving in a new type of non-Lorentzian geometry that we call Uð1Þ-Galilean geometry. We apply this to strings on AdS 5 × S 5 for which we show that the zero tension limit is realized by the spin matrix theory limits of the AdS/CFT correspondence. This is closely related to limits of spin chains studied in connection to integrability in AdS/CFT. The simplest example gives a covariant version of the Landau-Lifshitz sigma-model.

Nonrelativistic giant magnons from Newton Cartan strings

“…We further generalize our results considering background NS-NS fluxes and obtain effective NR magnon momentum in the presence of background magnetic field. All these findings strongly indicate towards NR sigma model/SMT correspondence [12]. However, quite surprisingly, we also notice that unlike its relativistic counterpart [28], the NR sigma model lacks of single spike solutions.…”

“…The next step would be to take the so called large c(→ ∞) limit [12] associated with the world-sheet d.o.f. which thereby yields the NR sigma model,…”

A worldsheet supersymmetric Newton-Cartan string

“…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.…”

“…Surprise, of course, is a function of ignorance. An explanation for the surprise is that the worldsheet description of strings in certain Newton-Cartan backgrounds can be related to strings in relativistic backgrounds with a null isometry using a sort of T-duality transformation [1,3,5]. From the relativistic side, this appears to be ill-defined (recall the Buscher rule inverts the metric component in the isometry direction,g zz = 1…”

Remark about non-relativistic p-brane

“…The stringy limit of the superstring in Ad S 5 × S 5 was also formulated in [20] and it was argued here that it provides another soluble sector of the AdS/CFT correspondence; for related work, see [25,26]. The non-relativistic 1 For a recent very nice proposal of non-relativistic string, see lso [29]. a e-mail: klu@physics.muni.cz limit was further extended to the case of higher dimensional objects in string theory, as for example p-branes [21][22][23][24].…”