11/12 12:30 Dr. Kaberi Goswami (NTHU) Genuine Multi-Entropy in Abelian Chern–Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States. (R521, 5F, General Building II, Nat'l Tsing Hua Univ.)
******** CTCD/NTHU HEP Seminar ********
Speaker : Dr. Kaberi Goswami (NTHU)
Title : Genuine Multi-Entropy in Abelian Chern–Simons Theory: Exact Key-Ring Collapse
and Its Breakdown for Generic Link States.
Time ：12:30-13:30, Thursday, 2026/11/12
Place ：R521, 5F, General Building II, Nat'l Tsing Hua Univ.
Host ： Prof. Kingman Cheung (NTHU) & Prof. Norihiro Iizuka (NTHU)
Abstract:
I will discuss our recent work https://arxiv.org/abs/2608.29627 on the study of genuine multi-entropy in Abelian U (1)_k Chern-Simons theory. For key-ring link states, where only the linking numbers between one distinguished component K and the remaining q − 1 components are nonzero, we derive an exact closed-form expression for the q-partite Rényi multi-entropy for general q, level k, and Rényi index n. For q = 4, this shows that the genuine multi-entropy GM_{n}^4 collapses exactly onto the tripartite information I_{3,n} for all n, while for q = 5 it is likewise completely determined, for all n, by a linear combination of tripartite and bipartite Rényi multi-entropies. We then go beyond the key-ring class and study general four-component link states with arbitrary pairwise linking numbers. A numerical scan over Chern–Simons levels 2 ≤ k ≤ 24 shows that the all-n collapse found analytically for key-ring states does not survive for generic link states. Remarkably, the collapse remains exact at n = 2 for every level examined. At n = 3, violations occur, within the scanned range, only when 3 | k, with a further dependence on the 3-adic valuation of k.
At n = 4 and n = 5, violations occur for every level examined, with rates that vary strongly with k. These results show that the breakdown is not controlled simply by the zero-divisor _structure of composite Z_k, but instead exhibits a nontrivial joint dependence on the Rényi index and the arithmetic structure of the Chern–Simons level.
Speaker : Dr. Kaberi Goswami (NTHU)
Title : Genuine Multi-Entropy in Abelian Chern–Simons Theory: Exact Key-Ring Collapse
and Its Breakdown for Generic Link States.
Time ：12:30-13:30, Thursday, 2026/11/12
Place ：R521, 5F, General Building II, Nat'l Tsing Hua Univ.
Host ： Prof. Kingman Cheung (NTHU) & Prof. Norihiro Iizuka (NTHU)
Abstract:
I will discuss our recent work https://arxiv.org/abs/2608.29627 on the study of genuine multi-entropy in Abelian U (1)_k Chern-Simons theory. For key-ring link states, where only the linking numbers between one distinguished component K and the remaining q − 1 components are nonzero, we derive an exact closed-form expression for the q-partite Rényi multi-entropy for general q, level k, and Rényi index n. For q = 4, this shows that the genuine multi-entropy GM_{n}^4 collapses exactly onto the tripartite information I_{3,n} for all n, while for q = 5 it is likewise completely determined, for all n, by a linear combination of tripartite and bipartite Rényi multi-entropies. We then go beyond the key-ring class and study general four-component link states with arbitrary pairwise linking numbers. A numerical scan over Chern–Simons levels 2 ≤ k ≤ 24 shows that the all-n collapse found analytically for key-ring states does not survive for generic link states. Remarkably, the collapse remains exact at n = 2 for every level examined. At n = 3, violations occur, within the scanned range, only when 3 | k, with a further dependence on the 3-adic valuation of k.
At n = 4 and n = 5, violations occur for every level examined, with rates that vary strongly with k. These results show that the breakdown is not controlled simply by the zero-divisor _structure of composite Z_k, but instead exhibits a nontrivial joint dependence on the Rényi index and the arithmetic structure of the Chern–Simons level.