The mild form of the Weak Gravity Conjecture states that quantum or higher-derivative corrections should decrease the mass of large extremal charged black holes at fixed charge. This allows extremal black holes to decay, unless protected by a symmetry (such as supersymmetry). We reformulate this conjecture as an integrated condition on the effective stress tensor capturing the effect of quantum or higher-derivative corrections. In addition to charged black holes, we also consider rotating BTZ black holes and show that this condition is satisfied as a consequence of the c-theorem, proving a spinning version of the Weak Gravity Conjecture. We also apply our results to a five-dimensional boosted black string with higher-derivative corrections. The boosted black string has a BTZ×S 2 near-horizon geometry and, after Kaluza-Klein reduction, describes a four-dimensional charged black hole. Combining the spinning and charged Weak Gravity Conjecture we obtain positivity bounds on the five-dimensional Wilson coefficients that are stronger than those obtained from charged black holes alone.

United States

Lars Aalsma

Netherlands

Alex Cole

Gregory Loges

Gary Shiu

A new spin on the Weak Gravity Conjecture

In recent literature, it has been argued that a mild form of the Weak Gravity Conjecture (WGC) is satisfied by wide classes of effective field theories in which higher-derivative corrections can be shown to shift the charge-to-mass ratios of extremal black holes to larger values. However, this mild form does not directly constrain low-energy physics because the black holes satisfying the WGC have masses above the cutoff of the effective theory. In this note, we point out that in string theory modular invariance can connect a light superextremal state to heavy superextremal states; the latter collapse into black holes at small string coupling. In the context of heterotic string theory, we show that these states are black holes that have α′-exact charge-to-mass ratios exceeding the classical extremality bound. This suggests that modular invariance of the string partition function can be used to relate the existence of a light superextremal particle to the positive shift in charge-to-mass ratio of extremal black holes.

Weak gravity conjecture, black hole entropy, and modular invariance

In this paper, we employ genetic algorithms to explore the landscape of type IIB flux vacua. We show that genetic algorithms can efficiently scan the landscape for viable solutions satisfying various criteria. More specifically, we consider a symmetric T 6 as well as the conifold region of a Calabi-Yau hypersurface. We argue that in both cases genetic algorithms are powerful tools for finding flux vacua with interesting phenomenological properties. We also compare genetic algorithms to algorithms based on different breeding mechanisms as well as random walk approaches.

Andreas Schachner

Searching the landscape of flux vacua with genetic algorithms

Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string vacua. As a scaled-down version of the program, we use persistent homology to characterize distributions of Type IIB flux vacua on moduli space for three examples: the rigid Calabi-Yau, a hypersurface in weighted projective space, and the symmetric six-torus T 6 = (T 2)3. These examples suggest that persistence pairing and multiparameter persistence contain useful information for characterization of the landscape in addition to the usual information contained in standard persistent homology. We also study how restricting to special vacua with phenomenologically interesting low-energy properties affects the topology of a distribution.

Topological data analysis for the string landscape

In this work, we consider tunneling between nonmetastable states in gravitational theories. Such processes arise in various contexts, e.g., in inflationary scenarios where the inflaton potential involves multiple fields or multiple branches. They are also relevant for bubble wall nucleation in some cosmological settings. However, we show that the transition amplitudes computed using the Euclidean method generally do not approach the corresponding field theory limit as <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>→</mo><mi>∞</mi></mrow></math>. This implies that in the Euclidean framework, there is no systematic expansion in powers of <math><msub><mi>G</mi><mi>N</mi></msub></math> for such processes. Such considerations also carry over directly to no-boundary scenarios involving Hawking-Turok instantons. In this note, we illustrate this failure of decoupling in the Euclidean approach with a simple model of axion monodromy and then argue that the situation can be remedied with a Lorentzian prescription such as the Picard-Lefschetz theory. As a proof of concept, we illustrate with a simple model how tunneling transition amplitudes can be calculated using the Picard-Lefschetz approach.