Black Hole Entropy, Quantum Corrections and EFT Transitions (2502.02655v1)

Abstract: We revisit and study quantum corrections to the supersymmetric entropy of BPS black holes in 4d $\mathcal{N}=2$ effective field theories (EFTs), which can be obtained from Type IIA string theory compactified on a Calabi-Yau threefold. Macroscopically, these corrections arise from an infinite series of higher-derivative F-terms that encode certain modifications to the two-derivative supergravity effective action. Within the large volume regime, we analyze in detail the moduli dependence of these semi-classical contributions and explore their implications for the black hole entropy. As a byproduct, we show that the entropy captures, in a rather intricate way, the transition between four- and five-dimensional dual EFT descriptions. In fact, the expansion parameter $\alpha$ controlling the relevant asymptotic series can be related to the ratio of the black hole horizon and the Kaluza-Klein scale, given here by the inverse D0-brane mass. Furthermore, we are able to resum the series into a well-behaved convergent expression for all values of $\alpha$. This demonstrates, in turn, that (stable) black holes can, indeed, probe scales besides the quantum gravity cutoff. More precisely, by examining two representative BPS systems -- the D0-D2-D4 and D2-D6 black hole solutions -- we explicitly illustrate how highly non-local (perturbative) quantum effects resolve the divergences, ultimately leading to a well-defined entropy function. Additionally, in certain cases, we show that one can take a suitable decompactification limit to 5d and verify that the corrected entropy function reproduces the exact microstate counting of the underlying five-dimensional black string. Our results also clarify the role of non-perturbative quantum corrections, which, remarkably, do not modify any of our prior conclusions.

• The paper quantitatively examines how higher-derivative F-term corrections modify the semiclassical entropy of BPS black holes.
• It employs resummation techniques to address divergence in the perturbative series and clarifies the transition from 4D to 5D effective descriptions.
• The research underscores the role of the expansion parameter and duality insights in deepening our understanding of quantum gravity and microstate counting.

Analysis of Quantum Corrections to Black Hole Entropy in $\mathcal{N}=2$ Supergravity

The paper explores the intricate topic of quantum corrections to the supersymmetric entropy of BPS black holes within four-dimensional $\mathcal{N}=2$ effective field theories (EFTs), which originate from compactifying Type IIA string theory over a Calabi-Yau threefold. By evaluating the macroscopic impact of an infinite series of higher-derivative F-terms, it provides insights into the intricate relationships between black hole entropy, effective field theory transitions, and the daunting quantum aspects of gravity.

Key concepts lie in how the semi-classical entropy of BPS black holes is modified by these higher-order corrections, which are encoded within the theory's F-term expansion. The analysis emphasizes the crucial role of the expansion parameter, denoted as $\alpha$, which correlates with the ratio of the black hole horizon scale to the Kaluza-Klein scale, manifested through the inverse mass of D0-branes. Such a detailed exploration is significant for understanding the transition between four-dimensional and five-dimensional effective theories in quantum gravity.

Perturbative and Non-Perturbative Corrections

Regarding perturbative expansions, the paper shows that quantum corrections to the black hole entropy manifest as an asymptotic series, particularly when these objects possess a physical size at the order of the extra dimension scale. This is especially apparent in the studied examples of D0-D2-D4 and D2-D6 black holes. In the large volume regime, dominant corrections derive from constant world-sheet maps into the internal Calabi-Yau space.

Asymptotic Series and Non-Local Effects

The work identifies how perturbative expansions could lead to divergence issues, interpreted physically as the breakdown of four-dimensional EFT when black holes are comparable to the fifth dimension characterized by the inverse D0-brane mass. However, the series can be resummed into non-local expressions - a critical step allowing exploration into regimes previously inaccessible. These non-local perturbative effects, including resumation of Schwinger contributions, signify black holes probing beyond typical quantum gravity cutoffs.

Symmetries and 5D Descriptions

A remarkably significant aspect is how the paper provides a bridge across dimensional descriptions. In scenarios translating to 5d, such as the D0-D2-D4 system, the entropic function recovers five-dimensional entropy predictions, specifically through M-theory duality scenarios.

The paper recognizes that every class of BPS black holes behaves under two regimes - large and comparable horizon-to-quantum scale - to test the fidelity of four-dimensional EFT. Such symmetry-breaking analysis allows for a clearer understanding of the compactification dynamics and gauge charge roles in thermodynamic behaviors.

Non-Perturbative Roles and Challenges

A highlight is the analytic approach towards non-perturbative effects, especially those initially suggested by the potential for Schwinger pair effects of Kaluza-Klein states. The paper intriguingly shows that some configurations present no significant non-perturbative modifications, underscoring the robustness of these BPS states' entropic properties.

Future Implications

This comprehensive evaluation opens multiple paths for continued exploration. First is the possibility of extending beyond large volume limits to include more worldsheet instanton effects, reflecting other singularities within moduli spaces in various compactifications. Second, by leveraging these resummed quantum corrections, future work could provide deeper insights into non-perturbative topological string dynamics, especially regarding duality roles in quantum states counting.

Overall, this investigation emphasizes a powerful methodology combining higher-derivative expansions, duality insights, and quantum gravity's non-local dynamics. The implications yield important progress towards resolving long-standing questions about the nature of entropy, microstates, and the dimensional transitions in the context of quantum black holes.