Strings with non-relativistic conformal symmetry and limits of the AdS/CFT correspondence

Abstract

We find a Polyakov-type action for strings moving in a torsional Newton-Cartan geometry. This is obtained by starting with the relativistic Polyakov action and fixing the momentum of the string along a non-compact null isometry. For a flat target space, we show that the world-sheet theory becomes the Gomis-Ooguri action. From a target space perspective these strings are non-relativistic but their world-sheet theories are still relativistic. We show that one can take a scaling limit in which also the world-sheet theory becomes non-relativistic with an infinite-dimensional symmetry algebra given by the Galilean conformal algebra. This scaling limit can be taken in the context of the AdS/CFT correspondence and we show that it is realized by the 'Spin Matrix Theory' limits of strings on AdS 5 × S 5 . Spin Matrix theory arises as non-relativistic limits of the AdS/CFT correspondence close to BPS bounds. The duality between non-relativistic strings and Spin Matrix theory provides a holographic duality of its own and points towards a framework for more tractable holographic dualities whereby non-relativistic strings are dual to near BPS limits of the dual field theory.2 As will be clear in Sec. 2.1 we find in this paper that the TNC geometry is extended with a periodic target space direction.3 This Nambu-Goto form was also obtained in [20]. 4 The GCA was also observed in earlier work on non-relativistic limits of AdS/CFT [21]. See also Ref. [22] for useful work on representations of the GCA and aspects of non-relativistic conformal two-dimensional field theories.

Nonrelativistic Corners of N=4 Supersymmetric Yang-Mills Theory

“…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.…”

Hirota-Satsuma dynamics as a non-relativistic limit of KdV equations

“…In the context of 2 + 1 gravity, this limit would yield a nonrelativistic version of the KdV boundary dynamics found in [4]. It would be interesting to see what 'gravity-like' theory has couplings satisfying the scalings (18): such a theory would have a well-defined non-relativistic limit, suggesting applications in non-relativistic AdS/CFT [13,22].…”

Nonrelativistic giant magnons from Newton Cartan strings

“…Here, ζ is the additional compact direction associated with the null reduced target space geometry along which the string winds [12]- [13]. On the other hand, ε 01 = −ε 01 = 1 is the 2D Levi-Civita symbol together with,…”

“…where, g = c 2 λ is the effective string tension [13] in the NR limit. Following NR sigma model/SMT duality [15] we understand g( 1) as the coupling constant on the dual gauge theory side such that the corresponding SYM coupling (λ) is considered to be weak.…”