Weak Gravity Conjecture, Central Charges and $\eta/s$

Shesansu Sekhar Pal

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Weak Gravity Conjecture, Central Charges and $\eta/s$

Shesansu Sekhar Pal

High Energy Physics - Theory · Submitted 3 Mar 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The result that follows from this example suggests that WGC makes the KSS conjecture to hold in the extremal limit but only when one of the coefficient vanishes ($c_1=0, c_2\neq 0$ or $c_2=0, c_1\neq 0$) and when both the coefficients are non zero it can respect and/or violate the KSS conjecture depending on the choice to $c_1$ at extremality, even though $\eta/s$ do not depend on $c_1$ at extremality.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.87 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.32 · compares with prior results 0.34 · mentions code or data availability 0.01.

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We correlate the weak gravity conjecture (WGC), the KSS conjecture with chemical potential at extremality and the central charges by going through a particular example in five dimensional AdS spacetime with two unknown coefficients $c_1, c_2$, assuming WGC exists in AdS spacetime. The result that follows from this example suggests that WGC makes the KSS conjecture to hold in the extremal limit but only when one of the coefficient vanishes ($c_1=0, c_2\neq 0$ or $c_2=0, c_1\neq 0$) and when both the coefficients are non zero it can respect and/or violate the KSS conjecture depending on the choice to $c_1$ at extremality, even though $\eta/s$ do not depend on $c_1$ at extremality. Moreover, WGC is not fully compatible with the calculation of central charges even though the bounds on coefficient $c_1$ that follows from demanding WGC stays within the bounds that central charges predict. As usual, the KSS conjecture is violated, of course, in the non-extremal limit.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We correlate the weak gravity conjecture (WGC), the KSS conjecture with chemical potential at extremality and the central charges by going through a particular example in five dimensional AdS spacetime with two unknown coefficients $c_1, c_2$, assuming WGC exists in AdS spacetime.	contribution 0.68	0.87	0.08	asserted 0.91
s1	The result that follows from this example suggests that WGC makes the KSS conjecture to hold in the extremal limit but only when one of the coefficient vanishes ($c_1=0, c_2\neq 0$ or $c_2=0, c_1\neq 0$) and when both the coefficients are non zero it can respect and/or violate the KSS conjecture depending on the choice to $c_1$ at extremality, even though $\eta/s$ do not depend on $c_1$ at extremality.	result 0.97	0.89	0.76	hedged possibility 0.99
s2	Moreover, WGC is not fully compatible with the calculation of central charges even though the bounds on coefficient $c_1$ that follows from demanding WGC stays within the bounds that central charges predict.	result 0.96	0.81	0.15	asserted 0.99
s3	As usual, the KSS conjecture is violated, of course, in the non-extremal limit.	result 0.46	0.25	0.06	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.89.

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Original abstract

We correlate the weak gravity conjecture (WGC), the KSS conjecture with chemical potential at extremality and the central charges by going through a particular example in five dimensional AdS spacetime with two unknown coefficients $c_1, c_2$, assuming WGC exists in AdS spacetime. The result that follows from this example suggests that WGC makes the KSS conjecture to hold in the extremal limit but only when one of the coefficient vanishes ($c_1=0, c_2\neq 0$ or $c_2=0, c_1\neq 0$) and when both the coefficients are non zero it can respect and/or violate the KSS conjecture depending on the choice to $c_1$ at extremality, even though $\eta/s$ do not depend on $c_1$ at extremality. Moreover, WGC is not fully compatible with the calculation of central charges even though the bounds on coefficient $c_1$ that follows from demanding WGC stays within the bounds that central charges predict. As usual, the KSS conjecture is violated, of course, in the non-extremal limit.

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4 arXiv papers cite this in 8 sentences

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Papers citing it · 4 sentences without a confident label

Compares with it 2 papers

These results are consistent with the results of other black branes [ref] , which could mean the universal behavior of corrections in these conjectures.

The correlation of WGC and Hydrodynamics bound with $R^4$ correction in the charged AdS$_{d+2}$ black brane · Conclusions · 0.85
A similar behavior was observed for the $R_μνρσ F^μν F^ρσ$ term in four-derivative actions [ref] .

The Weak Gravity Conjecture and the Viscosity Bound with Six-Derivative Corrections · Conclusions · 0.91

Cites it as background 2 papers

Another factor that characterizes the universal relaxation properties of perturbation fluids is the lower limit of $η/s≥1/4π$ or KSS bound (Kovtun-Starinets-Son) [ref] .

The correlation of WGC and Hydrodynamics bound with $R^4$ correction in the charged AdS$_{d+2}$ black brane · Introduction · 0.83
Researchers have explored the WGC's implications across diverse cosmological contexts, including black hole thermodynamics, black branes, and inflationary models [ref] .

Reconciling the Weak Gravity and Weak Cosmic Censorship Conjectures in Einstein-Euler-Heisenberg-AdS Black Holes · Introduction · 0.92

What it cites · 20 sentences without a confident label

Builds on 1 paper

Let us consider an effective action of the following type S=12κ^2∫√(-g)[R+12-14F^MNF_MN+c_1R_MNKLR^MNKL+c_2 R^MNKL F_MNF_KL], this action is a special case to the action considered in [ref] , but for our purpose this is good enough.

Holographic Hydrodynamics with a Chemical Potential · A gravitational system · 0.86

Uses the method or tool of 5 papers

The coefficient of shear viscosity can be very easily computed using the prescription given in [ref] and the result is same as in [ref] η=r^3_02κ^2(1-24 c_1 q^2r^6_0) and the entropy density in terms of $q/r^3_0$, can be calculated using the Wald's entropy formula [ref] s=4πr^3_02κ^2[1+8 c_1-q^2r^6_0(28 c_1+24 c_2)]

Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm · shear viscosity and $η/s$ · 0.91
The coefficient of shear viscosity can be very easily computed using the prescription given in [ref] and the result is same as in [ref] η=r^3_02κ^2(1-24 c_1 q^2r^6_0) and the entropy density in terms of $q/r^3_0$, can be calculated using the Wald's entropy formula [ref] s=4πr^3_02κ^2[1+8 c_1-q^2r^6_0(28 c_1+24 c_2)]

Holographic Hydrodynamics with a Chemical Potential · shear viscosity and $η/s$ · 0.91
The coefficient of shear viscosity can be very easily computed using the prescription given in [ref] and the result is same as in [ref] η=r^3_02κ^2(1-24 c_1 q^2r^6_0) and the entropy density in terms of $q/r^3_0$, can be calculated using the Wald's entropy formula [ref] s=4πr^3_02κ^2[1+8 c_1-q^2r^6_0(28 c_1+24 c_2)]

Black Hole Entropy is Noether Charge · shear viscosity and $η/s$ · 0.91

Compares with 1 paper

In particular, when $c_2=0$, WGC imply $c_1$ should always be positive but central charge calculation [ref] suggests $c_1$ can take negative values.

Conformal collider physics: Energy and charge correlations · Conclusion and discussion · 0.95

Cites as background 4 papers

The KSS conjecture [ref] suggests that the ratio of coefficient of shear viscosity $η$ to entropy density $s$ must have a minimum value of $1/4π$ at zero chemical potential for theories that admits gravity dual.

Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics · Conjectures: WGC and KSS · 0.99
The WGC [ref] , came out of the fact that gravity is the weakest force and says that a stable charged particle minimizes the ratio of energy density to charge density and is less than unity in some units[Here we are using the terminology, energy density for mass and charge density for charge.].

The String Landscape, Black Holes and Gravity as the Weakest Force · Conjectures: WGC and KSS · 0.97
The application of the holographic correspondence [ref] to systems which is described by that kind of action yields interesting connections between WGC and holography.

The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 0.85

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