ICTS

As the 2020 Nobel Prize in Physics made manifest, black hole formation and singularities play a central role in our current understanding of classical gravity in the framework of general relativity. One of the most important open questions in this area is whether, in general, singularities are hidden inside black holes. This question goes under the name of  the Weak Cosmic Censorship Conjecture. In this talk, I will review the current status of this conjecture, both in asymptotically flat spaces and in AdS. Determining whether singularities can be accessible to external far away observers is important for the perdictivity of general relativity as a classical theory of gravity and for the possibility of observing Planck scale physics.

Study Materials:

• D. Christodoulou, “On the global initial value problem and the issue of singularities”, Class. Quantum Gravity  16 (1999) A23-A35
• L. Lehner and F. Pretorius, ``Final state of Gregory\textendash{}Laflamme instability,’' [arXiv:1106.5184 [gr-qc]].
• P. Figueras, M. Kunesch and S. Tunyasuvunakool, ``End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture,’' Phys. Rev. Lett. \textbf{116} (2016) no.7, 071102 [arXiv:1512.04532 [hep-th]].
• P. Figueras, M. Kunesch, L. Lehner and S. Tunyasuvunakool, ``End Point of the Ultraspinning Instability and Violation of Cosmic Censorship,’' Phys. Rev. Lett. \textbf{118} (2017) no.15, 151103 [arXiv:1702.01755 [hep-th]].
• T. Crisford and J. E. Santos, ``Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti\textendash{}de Sitter Space,'' Phys. Rev. Lett. \textbf{118} (2017) no.18, 181101 [arXiv:1702.05490 [hep-th]].
• T. Crisford, G. T. Horowitz and J. E. Santos, ``Testing the Weak Gravity - Cosmic Censorship Connection,’' Phys. Rev. D \textbf{97} (2018) no.6, 066005 [arXiv:1709.07880 [hep-th]].
• P. Bizon and A. Rostworowski, ``On weakly turbulent instability of anti-de Sitter space,’' Phys. Rev. Lett. \textbf{107} (2011), 031102 [arXiv:1104.3702 [gr-qc]].
• P. M. Chesler and D. A. Lowe, ``Nonlinear Evolution of the AdS$_4$ Superradiant Instability,’' Phys. Rev. Lett. \textbf{122} (2019) no.18, 181101 [arXiv:1801.09711 [gr-qc]].
   

We study a class of gauge theories   whose gauge group is semi-direct product of a continuous abelian  $U(1)^{N-1}$ and discrete non-abelian gauge groups, such as permutation group $S_N$.  We call this class as semi-abelian theories.  Unlike other known calculable models, such as Polyakov model on $R^3$, Seiberg-Witten theory on $R^4$ and QCD(adj) $R^3 \times S^1$ where $S_N$ part of gauge structure is Higgsed,  and this pervades the physics of the theory, in the  semi-abelian theory, $S_N$ is not Higgsed. Mass gaps and string tensions are calculable in the monopole-gas description, and  receive equal contributions from monopoles associated with the entire $SU(N)$ root system,  unlike theories like the Polyakov model where only simple roots contribute at leading order.

Even though the center symmetry of the semi-Abelian gauge theory is given by $Z_N$, we observe that the string tensions do not obey the $N$-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant  of $U(1)^{N-1}$ one-form symmetry in the original Abelian lattice theory.

When adding charged particles corresponding to $W$-bosons, such non-invertible symmetries are explicitly broken so that the $N$-ality rule should emerge in the deep infrared regime. We expect that non-invertible symmetry plays a prominent role  both in  Yang-Mills theory and QCD with fundamental fermions.

Reference Material: LINK