The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
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q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
KZ connections with irregular singularities have monodromies that realize topological invariants of links and tangles.
In W3 CFTs, Lanczos coefficients b_N grow as N^2 for generalized Liouvillian with W generators, violating the universal linear growth bound and causing divergent Krylov complexity, with the same quadratic growth in the SL(3,R) subalgebra.
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.
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The von Neumann algebraic quantum group $\mathrm{SU}_q(1,1)\rtimes \mathbb{Z}_2$ and the DSSYK model
The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
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q-Askey Deformations of Double-Scaled SYK
q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
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Fermionic trace relations and supersymmetric indices at finite $N$
The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
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On the monodromy of KZ-connections with irregular singularities
KZ connections with irregular singularities have monodromies that realize topological invariants of links and tangles.
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Violation of Universal Operator Growth Hypothesis in $\mathcal{W}_3$Conformal Field Theories
In W3 CFTs, Lanczos coefficients b_N grow as N^2 for generalized Liouvillian with W generators, violating the universal linear growth bound and causing divergent Krylov complexity, with the same quadratic growth in the SL(3,R) subalgebra.
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Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
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Probing the Chaos to Integrability Transition in Double-Scaled SYK
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.