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Can black holes preserve $N > 4$ supersymmetry?

Matthew Heydeman, Xiaoyi Shi, Gustavo J. Turiaci

Abstract

The dynamics of near-BPS black holes are governed by the breaking of the conformal symmetry that emerges near their horizons. Using the classification of superconformal symmetries, we systematically classify and quantize all effective theories that can arise in the near-BPS limit of black holes. Using these results, we argue, under certain physical assumptions, that BPS black holes cannot preserve more than four supercharges. This conclusion is consistent with existing constructions in string theory.

Can black holes preserve $N > 4$ supersymmetry?

Abstract

The dynamics of near-BPS black holes are governed by the breaking of the conformal symmetry that emerges near their horizons. Using the classification of superconformal symmetries, we systematically classify and quantize all effective theories that can arise in the near-BPS limit of black holes. Using these results, we argue, under certain physical assumptions, that BPS black holes cannot preserve more than four supercharges. This conclusion is consistent with existing constructions in string theory.
Paper Structure (27 sections, 158 equations, 6 figures)

This paper contains 27 sections, 158 equations, 6 figures.

Table of Contents

  1. Introduction and motivation
  2. Effective theories for near-BPS horizons
  3. The general approach
  4. The action and the partition function
  5. Some examples
  6. Large $\mathcal{N}=4$
  7. Orthosymplectic groups
  8. Other cases:
  9. Black holes with $\mathcal{N}=3$
  10. Two theories with $\text{SO}(3)$ $R$-symmetry and their solution
  11. Commutation relations of conserved charges
  12. The index for $\mathcal{N}=3$
  13. Linearization of the model, its solution, and the index
  14. Black holes with large $\mathcal{N}=4$
  15. Solution of the model
  16. ...and 12 more sections

Figures (6)

  • Figure 1: Global superconformal groups, together with the $R$-symmetry $G_R$, the representation $\rho$ of the fermionic generators, and the number of generators. To each of these supergroups there is an associated local superconformal group Knizhnik:1986wc.
  • Figure 2: The microcanonical density of states for the non-anomalous $\mathcal{N}=3$ Schwarzian theory at fixed $j=0$. There is a degenerate set of BPS states at $E_{\text{BPS}}=0$ which are short multiplets. The apparent BPS bound at $E_0$ in this figure results from a $j=1$ long multiplet which has a $j=0$ state, but this bound is not actually saturated by any BPS state. Instead, we see the inverse square root edge behavior.
  • Figure 3: The microcanonical density of states for the non-anomalous $\mathcal{N}=3$ Schwarzian theory at fixed $j=1$. In contrast to the previous figure, there are no BPS states in this sector (they all have $j=0$). Instead, we see two apparent BPS bounds at $E_0(j=1,2)$ which comes from long multiplets containing $j=1$. Each apparent bound exhibits an inverse square root edge. To emphasize, there are no BPS states in this figure, only BPS bounds.
  • Figure 4:
  • Figure 5: The microcanonical density of states for the large $\mathcal{N}=4$ Schwarzian theory at fixed $(j_+,j_-)=(1,1)$ and $\upalpha = \frac{4}{3}$. As in the previous figure, the blue curve represents the contribution of different long multiplets which have these R-charges. In contrast, the edge $E_0$ is now colliding with a BPS bound (there remains a small gap which is not visible). The yellow delta function indicates that there is still a short multiplet with $(1,1)$ BPS states, but for this value of $\upalpha$, the second set of BPS states (green curve above) is absent. These would-be BPS states are instead replaced by long multipets approaching the BPS bound.
  • ...and 1 more figures