[Paper Review] Non-BPS Black Branes in M-theory over Calabi-Yau Threefolds

Alessio Marrani, Anshul Mishra+1 more|arXiv (Cornell University)|Feb 14, 2022

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates non-BPS black branes in M-theory compactified on Calabi-Yau threefolds, using the attractor mechanism and effective black hole potential formalism to compute moduli, entropy, and tension. It finds that non-BPS black holes are always unstable and decay into BPS/anti-BPS pairs, confirming the Weak Gravity Conjecture, while non-BPS black strings exhibit multiple stable attractors in two-moduli THCY models, indicating recombination and volume-minimizing representatives with distinct local volumes.

ABSTRACT

[abridged version] We study extremal solutions arising in M-theory compactifications on Calabi-Yau threefolds, focussing on non-BPS attractors for their importance in relation to the Weak Gravity Conjecture. In the low-energy/field theory limit one obtains minimal N=2, D=5 supergravity coupled to Abelian vector multiplets. By making use of the effective black hole potential formalism with Lagrange multipliers and of the Attractor Mechanism, and focussing on two-moduli complete intersection (CICY) or toric hypersurface (THCY) Calabi-Yau threefolds, we investigate the possible non-uniqueness of the attractor solutions, as well as the stability of non-BPS black holes and black strings. In all models taken into consideration, we find that both BPS and non-BPS extremal black hole attractors are always unique for a given, supporting electric charge configuration; moreover, non-BPS black holes are always unstable, and thus they decay into constituent BPS/anti-BPS pairs. For what concerns extremal black strings, we confirm uniqueness also for non-BPS strings in two-moduli CICY models. On the other hand, we discover multiple non-BPS extremal black string attractors (with different tensions) in most of the two-moduli THCY models, and we determine the corresponding magnetic configurations supporting them; this indicates the existence of volume-minimizing representatives in the same homology class having different values of their local minimal volume. Moreover, we find that non-BPS black strings, both for single and multiple solutions, are stable and thus enjoy recombination of their constituent BPS/anti-BPS pairs.

Motivation & Objective

• To investigate the attractor mechanism for extremal non-BPS black holes and black strings in M-theory compactifications on Calabi-Yau threefolds.
• To determine the uniqueness and stability of non-BPS attractor solutions in two-moduli complete intersection (CICY) and toric hypersurface (THCY) Calabi-Yau models.
• To test the Weak Gravity Conjecture by analyzing decay and recombination of non-BPS states into BPS constituents.
• To explore the existence of multiple volume-minimizing representatives in the same homology class for non-BPS black strings.

Proposed method

• Employing the effective black hole potential formalism with Lagrange multipliers to derive attractor moduli for BPS and non-BPS solutions.
• Applying the attractor mechanism to compute Bekenstein-Hawking entropy and black string tension in five-dimensional $N=2$ supergravity.
• Using the 5D electric and magnetic 'new attractor' approaches to analyze extremal solutions in two-moduli models.
• Performing analytical and numerical evaluation of the recombination factor $R$ to assess stability of non-BPS black holes and strings.
• Classifying non-BPS attractor solutions via triple intersection numbers and charge configurations in CICY and THCY models.
• Analyzing the Kähler cone constraints and moduli space geometry to determine existence and stability of attractor solutions.

Experimental results

Research questions

• RQ1 Are non-BPS black hole attractors unique for a given electric charge configuration in two-moduli Calabi-Yau compactifications?
• RQ2 Do non-BPS black strings in THCY models admit multiple attractor solutions with different tensions and local volumes?
• RQ3 Is the recombination factor $R$ less than 1 for non-BPS black strings, indicating stability and potential recombination?
• RQ4 Can non-BPS black holes decay into BPS/anti-BPS pairs, thereby supporting the Weak Gravity Conjecture?
• RQ5 Do multiple non-BPS black string attractors in THCY models correspond to distinct volume-minimizing representatives in the same homology class?

Key findings

• Non-BPS black holes are always unstable and decay into BPS/anti-BPS pairs, with recombination factor $R < 1$, confirming the Weak Gravity Conjecture.
• In all CICY and THCY models studied, non-BPS black hole attractors are unique for a given electric charge configuration.
• Multiple non-BPS black string attractors with different tensions exist in most two-moduli THCY models, indicating distinct local minimal volumes in the same homology class.
• Non-BPS black strings in THCY models are stable for certain ranges of the magnetic charge ratio $p$, with $R < 1$ observed numerically across all models.
• The model $(3,1)_{-144}^{2,74}$ was excluded from analysis due to a negative eigenvalue in the metric $G_{IJ}$, rendering it physically inconsistent.
• In THCY models, the existence of multiple stable non-BPS black string attractors implies that the volume of the representative can be less than that of the minimal piecewise-holomorphic cycle, supporting recombination.