Quantum phase transition in a Dp-Dq system

TL;DR

This paper investigates quantum phase transitions in intersecting Dp-Dq brane systems in string theory, revealing conditions under which Berezinskii-Kosterlitz-Thouless (BKT) type transitions occur, including cases without charge density.

Contribution

It demonstrates the existence of BKT transitions in D3-D5 and D5-D5 systems under specific magnetic field configurations, expanding understanding of quantum phase transitions in string theory.

Findings

BKT transition occurs in D3-D5 with magnetic fields but no charge density.

BKT transition in D5-D5 requires both charge density and magnetic fields.

D3-D7 system does not exhibit BKT transition.

Abstract

Using the top-down approach, we study intersecting Dp-Dq brane configuration in string theory and find examples, where there can be a quantum phase transition at zero temperature induced by the violation of the Breitenlohner-Freedman (BF) bound at IR, which is done essentially by a combination of charge density and magnetic fields. In particular, there exists a Berezinskii-Kosterlitz-Thouless (BKT) type of transition for D3-D5 and D5-D5 systems. The study of the BKT type of transition is initiated by Jensen et al. [Phys. Rev. Lett. {\bf 105}, 041601 (2010) ] for a D3-D5 system with nonzero charge density and a magnetic field. Here, we show that one can have the BKT transition for a D3-D5 system even in the absence of charge density but requires multiple magnetic fields. In this case the field theory lives in 2+1 dimensions, whereas for the D5-D5 type, the transition requires the presence of both the charge density and magnetic fields and the dual field theory lives on a 3+1 dimensional spacetime. We also study the D3-D7 system but it does not show the BKT type of transition.