Special limits and non-relativistic solutions

TL;DR

This work constructs a controlled, zero-temperature (condensation) limit of boosted D3-branes with a compact light-cone, yielding a non-relativistic Lifshitz geometry with dynamical exponent $a=3$ in a DLCQ framework. The key technical move is the simultaneous limit $r_0\to0$ and $\lambda\to\infty$ with $r_0^4\lambda^2=\beta^2$ fixed, which preserves a finite lightlike circle and produces a Galilean AdS$_5$ background that, after diagonalization, reveals Lifshitz scaling. The authors also explore Type IIA duals via T-duality and an M-theory uplift, and extend the analysis to boosted black M2-branes, where a fractional dynamical exponent $a=5/2$ emerges, corresponding to non-relativistic dynamics along a wire. UV issues arise due to the shrinking light-cone circle and growing string coupling, motivating UV completions in IIA/M-theory and prompting further study of zero-temperature limits for other D$p$-branes.

Abstract

We study special vanishing horizon limit of `boosted' black D3-branes having a compact light-cone direction. The type IIB solution obtained by taking such a zero temperature limit is found to describe a nonrelativistic system with dynamical exponent 3. We discuss about such limits in M2-branes case also.