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Register a new userA Euclidean Perspective on Completeness and Weak Gravity
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In this paper we use Euclidean gravity methods to show that charged black holes which are sufficiently close to extremality must be able to decay. The argument proceeds by showing that Euclidean gravity would otherwise imply a violation of charge quantization. As this is the assumption which leads to the weak gravity conjecture, our argument gives a derivation of that conjecture. We use a small negative cosmological constant as an infrared regulator, but our argument applies to near-extremal black holes which are arbitrarily small compared to the $AdS$ curvature scale. We also give a universal formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero fraction, this gives a new proof of the completeness hypothesis for finite gauge fields. Based on these observations we make two conjectures about many-body quantum physics: we propose a lower bound on the critical temperature for the instability of a semi-local quantum liquid, and we propose that our formula for the density of black hole microstates in each representation of a finite gauge group also applies at high energy to any quantum field theory with a finite group global symmetry.
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In a gravitational theory with a massless photon the maximum charge-to-mass ratio of black holes approaches the prediction of the Einstein-Maxwell theory as black hole mass increases: $Q_{rm ext}/M =1+ alpha/M^2$ for some constant $alpha$. We will show that $alpha>0$ if below the quantum gravity scale $Lambda$ there are many degrees of freedom with a hierarchically small mass gap $log(Lambda/m_{rm gap})gg 1$. In this regime one can treat gravity as a non-dynamical background field and derive field-theoretic sum-rules for the coefficients of the leading corrections to the Einstein-Maxwell theory. The positivity of $alpha$ follows from the sum-rules. As a consequence, gravitational attraction gets weaker than the electric force among maximally charged black holes as they become lighter, and large extremal black holes can decay into smaller black holes.
We study holographic shear sum rules in Einstein gravity with curvature squared corrections. Sum rules relate weighted integral over spectral densities of retarded correlators in the shear channel to the one point functions of the CFTs. The proportionality constant can be written in terms of the data of three point functions of the stress tenors of the CFT ($t_2$ and $t_4$). For CFTs dual to two derivative Einstein gravity, this proportionality constant is just $frac{d}{2(d+1)}$. This has been verified by a direct holographic computation of the retarded correlator for Einstein gravity in $AdS_{d+1}$ black hole background. We compute corrections to the holographic shear sum rule in presence of higher derivative corrections to the Einstein-Hilbert action. We find agreement between the sum rule obtained from a general CFT analysis and holographic computation for Gauss Bonnet theories in $AdS_5$ black hole background. We then generalize the sum rule for arbitrary curvature squared corrections to Einstein-Hilbert action in $dgeq 4$. Evaluating the parameters $t_2$ and $t_4$ for the possible dual CFT in presence of such curvature corrections, we find an agreement with the general field theory derivation to leading order in coupling constants of the higher derivative terms.
We investigate the emergence of ${cal N}=1$ supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, and use it to prove that supersymmetry-breaking operators are irrelevant, thus proving that such operators are suppressed in the infrared. All our findings are illustrated with the aid of the $epsilon$-expansion and a functional variant of perturbation theory, but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group.
The Weak Gravity Conjecture (WGC) was proposed to constrain Effective Field Theories (EFTs) with Abelian gauge symmetry coupled to gravity. In this article, I study the WGC from low energy observers perspective, and revisit the issue of to what extent the WGC actually constrains EFTs. For this purpose, for a given EFT, I introduce associated idealized low energy observers who only have access to the energy scale below the UV cut-off scale of the EFT. In the framework of EFT, there is a clear difference between the particles lighter than the UV cut-off scale and the particles which are heavier than the UV cut-off scale, as the lighter particles can be created below the UV cut-off scale while the heavier particles are not. This difference implies that the knowledge of the low energy observers on the stable heavy particles can be limited, as the availability of the stable heavy particles is determined by the environment prepared by some UV theory unknown to the low energy observers. The limitation of the knowledge of the low energy observers regarding the stable heavy particles whose mass is above the UV cut-off scale of the EFT leads to the limitation of the WGC for constraining EFTs. To illustrate these points in an example, I analyze a model proposed by Saraswat arXiv:1608.06951 which respects the WGC at high energy, but which may appear to violate the WGC for the low energy observers. Implications of the analysis to the bottom-up model buildings using EFTs are discussed.
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