Attractor mechanism and nonrenormalization theorem in 6D (1, 0) supergravity

Yi Pang

doi:10.1103/physrevd.103.026018

Abstract

We compute the macroscopic entropy of the supersymmetric rotating dyonic strings carrying linear momentum in 6D (1, 0) supergravity with curvature squared corrections. Our calculation is based on Sen's entropy function formalism applied to the near-horizon geometry of the string solution taking the form of an extremal Ban\ifmmode \tilde{}\else \~{}\fi{}ados-Teitelboim-Zanelli $\ifmmode\times\else\texttimes\fi{}{S}^{3}$. The final entropy formula states that the two independent supersymmetric completions of Riemann tensor squared contribute equally to the entropy. A further ${S}^{3}$ compactification of the 6D theory results in a matter coupled 3D supergravity model in which the quantization condition of the ${\mathrm{SU}(2)}_{R}$ Chern-Simons level implies the horizon value of the dilaton is not modified by higher derivative interactions beyond supersymmetric curvature squared terms.

Highlights

The most striking feature hidden in the black hole thermodynamics is the area law of the entropy instead of the usual volume law observed in most local physical systems
Upon solving the attractor equations whose solution extremizes the entropy function, we observed that inclusion of the higher derivative interactions does not modify the AdS3 radius of the BTZ black hole but does shrink the size of the extremal horizon
There are two independent supersymmetric completions of the Riemann tensor squared, the entropy is insensitive to their detailed structures but depends only on the coefficient of the Riemann squared term fixed to be α0=8 upon embedding the 6D supergravity model in the K3 compactification of IIA string

Summary

INTRODUCTION

The most striking feature hidden in the black hole thermodynamics is the area law of the entropy instead of the usual volume law observed in most local physical systems. In the 6D setup, we will explore whether different supersymmetric completions of the Riemann tensor squared give the same contribution to the black hole entropy, by virtue of the fact that there is a unique off-shell formulation of 6D (1, 0) supergravity allowing for well-defined two- and higher derivative superinvariants [15,16,17] V with discussions emphasizing the nonrenormalization of the horizon value of the dilaton beyond the leading α0 correction

THE MODEL

MACROSCOPIC ENTROPY FROM EXTREMIZING ENTROPY FUNCTION

THE RENORMALIZED HORIZON VALUE OF DILATON

CONCLUSION AND DISCUSSIONS