An Introduction to String Newton-Cartan Holography and Integrability

Abstract

String Newton-Cartan holography is a new example of gauge/gravity duality relating non-relativistic string theory and gauge theories. We review how to construct a family of string and $p$-brane Newton-Cartan holographic dualities by consistently taking the non-relativistic limit of the AdS/CFT correspondence. We also review classical string solutions, quantisation, string coset action and integrability of the non-relativistic string theory appearing in the String Newton-Cartan limit of the AdS$_5$/CFT$_4$ correspondence.

Figures (3)

• Figure 1: The non-relativistic limit produces a codimension two singular foliation of the target space, where the relativistic vielbein $E_{\mu}{}^{\hat{A}}$ is replaced by the degenerate SNC vielbeine $(\tau_{\mu}{}^A, e_{\mu}{}^a)$, with $A=0,1$, $a=2, ..., 9$.
• Figure 2: Maldacena's construction of the AdS$_5$/CFT$_4$.
• Figure 3: In the gravity theory, there are two conceptually different symmetries: the symmetries acting in the bulk and the asymptotic symmetries acting at the boundary. Only the asymptotic symmetries need to holographically match the symmetries of the dual gauge theory.