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3D gauged supergravity from wrapped M5-branes with AdS/CMT applications

Eoin Ó Colgáin, Henning Samtleben

Abstract

By identifying a bosonic consistent truncation from the 1/4-BPS wrapped M5-brane geometry of Maldacena, Strominger and Witten in D = 11 supergravity and finding a supersymmetric extension, we recover an N = 2 D = 3 supergravity theory. Reductions of a large class of supersymmetric solutions corresponding to wrapped M2 and M5-branes lead to black strings and warped AdS3 solutions preserving supersymmetry. With a view to AdS/CMT applications, we also construct a numerical hairy BTZ black hole and, as a preliminary step in this direction, determine the conductivity of the dual CFT.

3D gauged supergravity from wrapped M5-branes with AdS/CMT applications

Abstract

By identifying a bosonic consistent truncation from the 1/4-BPS wrapped M5-brane geometry of Maldacena, Strominger and Witten in D = 11 supergravity and finding a supersymmetric extension, we recover an N = 2 D = 3 supergravity theory. Reductions of a large class of supersymmetric solutions corresponding to wrapped M2 and M5-branes lead to black strings and warped AdS3 solutions preserving supersymmetry. With a view to AdS/CMT applications, we also construct a numerical hairy BTZ black hole and, as a preliminary step in this direction, determine the conductivity of the dual CFT.

Paper Structure

This paper contains 14 sections, 81 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Consistent Truncation
  3. Effective $D=3$ supergravity
  4. Redualizing and scalar geometry
  5. Gauging and scalar potential
  6. Equations of motion
  7. Supersymmetric solutions
  8. Null-Warped $AdS_3$
  9. A supersymmetric domain wall solution
  10. Numerical Black Holes
  11. Conductivity
  12. Discussion
  13. Details of consistent truncation
  14. Coset space $SU(2,1)/U(2)$

Figures (2)

  • Figure 1: The left-hand figure captures the emerging conformal symmetry as $W$ approaches its $AdS_3$ value at the boundary from a set initial starting value of $w_0 = 0$ at horizon ($AdS_3$ radius $\ell =1$ i.e. $W_{AdS} = -\tfrac{1}{3} \ln 2$). From the right-hand figure we see clearly that $V$ approaches a constant at the boundary.
  • Figure 2: The left and right graphs here illustrate the results of calculating Re($\sigma$) and Im($\sigma$) at temperatures of $T=0.042$ (Red), $T=0.038$ (Blue), $T=0.033$ (Black), $T=0.028$ (Green) and $T=0.022$ (Orange).