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We develop finite-dimensional versions of the quantum error-correcting codes proposed by Albert, Covey, and Preskill (ACP) for continuous-variable quantum computation on configuration spaces with non-Abelian symmetry groups. Our codes can be realized by a charged particle in a Landau level on a spherical geometry, in contrast to the planar Landau level realization of the qudit codes of Gottesman, Kitaev, and Preskill (GKP), or more generally by spin coherent states. Our quantum error-correction scheme is inherently approximate, and the encoded states may be easier to prepare than those of GKP or ACP. 

A bstract We develop the gauge theory formulation of $$ \mathcal{N} $$ N = 1 Jackiw-Teitelboim supergravity in terms of the underlying OSp(1|2 , ℝ) supergroup, focusing on boundary dynamics and the exact structure of gravitational amplitudes. We prove that the BF description reduces to a super-Schwarzian quantum mechanics on the holographic boundary, where boundary-anchored Wilson lines map to bilocal operators in the super-Schwarzian theory. A classification of defects in terms of monodromies of OSp(1|2 , ℝ) is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of OSp(1|2 , ℝ) and show that whereas the corresponding Plancherel measure does not match the density of states of $$ \mathcal{N} $$ N = 1 JT supergravity, a restriction to the positive subsemigroup OSp + (1|2 , ℝ) yields the correct density of states, mirroring the analogous results for bosonic JT gravity. We illustrate these results with several gravitational applications, in particular computing the late-time complexity growth in JT supergravity. 

A bstract We investigate the underlying quantum group symmetry of 2d Liouville and dilaton gravity models, both consolidating known results and extending them to the cases with $$ \mathcal{N} $$ N = 1 supersymmetry. We first calculate the mixed parabolic representation matrix element (or Whittaker function) of U q ( $$ \mathfrak{sl} $$ sl (2 , ℝ)) and review its applications to Liouville gravity. We then derive the corresponding matrix element for U q ( $$ \mathfrak{osp} $$ osp (1 | 2 , ℝ)) and apply it to explain structural features of $$ \mathcal{N} $$ N = 1 Liouville supergravity. We show that this matrix element has the following properties: (1) its q → 1 limit is the classical OSp + (1 | 2 , ℝ) Whittaker function, (2) it yields the Plancherel measure as the density of black hole states in $$ \mathcal{N} $$ N = 1 Liouville supergravity, and (3) it leads to 3 j -symbols that match with the coupling of boundary vertex operators to the gravitational states as appropriate for $$ \mathcal{N} $$ N = 1 Liouville supergravity. This object should likewise be of interest in the context of integrability of supersymmetric relativistic Toda chains. We furthermore relate Liouville (super)gravity to dilaton (super)gravity with a hyperbolic sine (pre)potential. We do so by showing that the quantization of the target space Poisson structure in the (graded) Poisson sigma model description leads directly to the quantum group U q ( $$ \mathfrak{sl} $$ sl (2 , ℝ)) or the quantum supergroup U q ( $$ \mathfrak{osp} $$ osp (1 | 2 , ℝ)). 

Abstract Quantum circuit complexity has played a central role in recent advances in holography and many‐body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real‐time) framework. In a departure from standard treatments, we aim to quantify the complexity of the Euclidean path integral. In this setting, there is no clear separation between space and time, and the notion of unitary evolution on a fixed Hilbert space no longer applies. As a proof of concept, we argue that the pants decomposition provides a natural notion of circuit complexity within the category of 2‐dimensional bordisms and use it to formulate the circuit complexity of states and operators in 2‐dimensional topological quantum field theory. We comment on analogies between our formalism and others in quantum mechanics, such as tensor networks and second quantization. 

A bstract We develop an approach to the study of Coulomb branch operators in 3D $$ \mathcal{N} $$ N = 4 gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For “good” and “ugly” theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.