More Like this

1. QUANTUM TEICHMÜLLER SPACES AND QUANTUM TRACE MAP

   https://doi.org/10.1017/S1474748017000068  

   Lê, Thang T. ( March 2019 , Journal of the Institute of Mathematics of Jussieu)

   We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichmüller space of a marked surface, defined by Chekhov–Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra.
2. First law and quantum correction for holographic entanglement contour

   https://doi.org/10.21468/SciPostPhys.11.3.058  

   Han, Muxin ; Wen, Qiang ( January 2021 , SciPost Physics)

   Entanglement entropy satisfies a first law-like relation, whichequates the first order perturbation of the entanglement entropy for theregion A A to the first order perturbation of the expectation value of the modularHamiltonian, \delta S_{A}=\delta \langle K_A \rangle δ S A = δ ⟨ K A ⟩ .We propose that this relation has a finer version which states that, thefirst order perturbation of the entanglement contour equals to the firstorder perturbation of the contour of the modular Hamiltonian,i.e.  \delta s_{A}(\textbf{x})=\delta \langle k_{A}(\textbf{x})\rangle δ s A ( 𝐱 ) = δ ⟨ k A ( 𝐱 ) ⟩ .Here the contour functions s_{A}(\textbf{x}) s A ( 𝐱 ) and k_{A}(\textbf{x}) k A ( 𝐱 ) capture the contribution from the degrees of freedom at \textbf{x} 𝐱 to S_{A} S A and K_A K A respectively. In some simple cases k_{A}(\textbf{x}) k A ( 𝐱 ) is determined by the stress tensor. We also evaluate the quantumcorrection to the entanglement contour using the fine structure of theentanglement wedge and the additive linear combination (ALC) proposalfor partial entanglement entropy (PEE) respectively. The fine structurepicture shows that, the quantum correction to the boundary PEE can beidentified as a bulk PEE of certain bulk region. Whilemore »the shows thatthe quantum correction to the boundary PEE comes from the linearcombination of bulk entanglement entropy. We focus on holographictheories with local modular Hamiltonian and configurations of quantumfield theories where the applies.« less
3. Type 𝐼𝐼 quantum subgroups of 𝔰𝔩_{𝔑}. ℑ: Symmetries of local modules

   https://doi.org/10.1090/cams/19  

   Edie-Michell, Cain ( May 2023 , Communications of the American Mathematical Society)

   This paper is the first of a pair that aims to classify a large number of the type I I II quantum subgroups of the categories C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . In this work we classify the braided auto-equivalences of the categories of local modules for all known type I I quantum subgroups of C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . We find that the symmetries are all non-exceptional except for four cases (up to level-rank duality). These exceptional cases are the orbifolds C ( s l 2 , 16 ) Rep ⁡ ( Z 2 ) 0 \mathcal {C}(\mathfrak {sl}_{2}, 16)^0_{\operatorname {Rep}(\mathbb {Z}_{2})} , C ( s l 3 , 9 ) Rep ⁡ ( Z 3 ) 0 \mathcal {C}(\mathfrak {sl}_{3}, 9)^0_{\operatorname {Rep}(\mathbb {Z}_{3})} , C ( s l 4 , 8 ) Rep ⁡ ( Z 4 ) 0 \mathcal {C}(\mathfrak {sl}_{4}, 8)^0_{\operatorname {Rep}(\mathbb {Z}_{4})} , and C ( s l 5 , 5 ) Rep ⁡ ( Z 5 ) 0 \mathcal {C}(\mathfrak {sl}_{5}, 5)^0_{\operatorname {Rep}(\mathbb {Z}_{5})} . We develop several technical tools in this work. We givemore »a skein theoretic description of the orbifold quantum subgroups of C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . Our methods here are general, and the techniques developed will generalise to give skein theory for any orbifold of a braided tensor category. We also give a formulation of orthogonal level-rank duality in the type D D - D D case, which is used to construct one of the exceptionals. We uncover an unexpected connection between quadratic categories and exceptional braided auto-equivalences of the orbifolds. We use this connection to construct two of the four exceptionals. In the sequel to this paper we will use the classified braided auto-equivalences to construct the corresponding type I I II quantum subgroups of the categories C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) . This will essentially finish the type I I II classification for s l n \mathfrak {sl}_n modulo type I I classification. When paired with Gannon’s type I I classification for r ≤ 6 r\leq 6 , our results will complete the type I I II classification for these same ranks. This paper includes an appendix by Terry Gannon, which provides useful results on the dimensions of objects in the categories C ( s l r + 1 , k ) \mathcal {C}(\mathfrak {sl}_{r+1}, k) .« less
4. A computational examination of the zeta and eta phases in the hafnium nitrides

   https://doi.org/10.1111/jace.17405  

   Weinberger, Christopher R. ; Thompson, Gregory B. ( August 2020 , Journal of the American Ceramic Society)

   The hafnium‐rich portion of the of the hafnium‐nitrogen phase diagram is dominated by a substoichiometric rocksalt HfN_1‐x, the ζ‐Hf₄N_3−x, the η‐Hf₃N_2−x, and the elemental Hf phase. The zeta and eta nitride phases have a close packed metal atom stacking sequence but their nitrogen atom ordering has yet to be concretely identified. With respect to the composition of these phases, recent computational studies of their phase stability using density functional theory (DFT) are not in agreement with reported experimental observations. In this work, we re‐examine the phase stability of the zeta and eta phases using DFT combined with enumerated searches using the known metal atom stacking sequences of these phases but with variable carbon concentration and ordering. We have found new structures for the zeta and eta phases that are now in better agreement with experimental findings. Furthermore, we report a new eta phase,‐Hf₁₂N₇, which lies on the convex hull and has a nitrogen atom ordering that is substantially different from the zeta phase. This work also demonstrates the importance of configurational entropy in dictating the finite temperature phase diagrams in this system.
5. Wilson loop in general representation and RG flow in 1D defect QFT

   https://doi.org/10.1088/1751-8121/ac7018  

   Beccaria, M. ; Giombi, S. ; Tseytlin, A. A. ( June 2022 , Journal of Physics A: Mathematical and Theoretical)

   The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in$\mathcal{N}=4$SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameterζhas a non-trivial beta function and may be viewed as a running coupling constant in a 1D defect QFT. In this paper we continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and beyond the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rankksymmetric representation ofSU(N), we also consider a certain ‘semiclassical’ limit wherekis taken to infinity with the productkζ²fixed. This limit can be conveniently studied using a 1D defect QFT representation in terms ofNcommuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the largeklimit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1D RG flow and comment onmore »the consistency of the results with the 1D defect version of the F-theorem.

   « less