We present a Group Field Theory (GFT) quantization of the Husain-Kuchav{r} (HK) model formulated as a non-interacting GFT. We demonstrate that the path-integral formulation of this HK-GFT provides a completion of a corresponding spinfoam model developed earlier
It has been recently realized that the bulk dual of the double-scaled SYK (DSSYK) model has both positive and negative Ricci curvature and is described by a dilaton-gravity theory with a $sin(Phi)$ potential arXiv:2404.03535. We study T$^2$-deformations in the DSSYK model after performing the ensemble averaging to probe regions of positive and approximately constant curvature. The dual finite cutoff interpretation of the deformation allows us to place the DSSYK model in the stretched horizon of the bulk geometry, partially realizing a conjecture of Susskind arXix:2109.14104. We show that the energy spectrum and thermodynamic entropy are well-defined for a contour reaching these regions. Importantly, the system displays a phase transition from a thermodynamically stable to an unstable configuration by varying its microcanonical temperature; unless it is located on any of the stretched horizons, which is always unstable. The thermodynamic properties in this model display an enhanced growth as the system approaches the stretched horizon, and it scrambles information at a (hyper)-fast rate.
We revisit the formalism of $text{T}overline{text{T}}$ deformations for quantum theories that are holographically dual to two-dimensional dilaton-gravity theories with Dirichlet boundary conditions. To better understand the microscopics of de Sitter space, we focus on deformations for which the dual bulk geometry flows from Anti-de Sitter to de Sitter space. We explore two distinct ways to achieve this: either through so-called centaur geometries that interpolate between AdS$_2$ and dS$_2$, or by a spherical dimensional reduction of $text{T}overline{text{T}} + Lambda_2$ theories that were proposed to give a microscopic interpretation of three-dimensional de Sitter entropy. We derive the microscopic energy spectrum, heat capacities, and deformed Cardy expressions for the thermodynamic entropy in the canonical and microcanonical ensembles for these two setups. In both setups a signature of the change from AdS to dS is that the heat capacity at a fixed deformation parameter of the boundary system changes sign, indicating the existence of a thermodynamically unstable de Sitter patch. Our findings provide important consistency conditions for holographic models of the dS$_2$ static patch.
Boundaries in gauge theory and gravity give rise to symmetries and charges at both finite and asymptotic distance. Due to their structural similarities, it is often held that soft modes are some kind of asymptotic limit of edge modes. Here, we show in Maxwell theory that there is an arguably more interesting relationship between the emph{asymptotic} symmetries and their charges, on one hand, and their emph{finite-distance} counterparts, on the other, without the need of a limit. Key to this observation is to embed the finite region in the global spacetime and identify edge modes as dynamical $rm{U}(1)$-reference frames for dressing subregion variables. Distinguishing emph{intrinsic} and emph{extrinsic} frames, according to whether they are built from field content in- or outside the region, we find that non-trivial corner symmetries arise only for extrinsic frames. Further, the asymptotic-to-finite relation requires asymptotically charged ones (like Wilson lines). Such frames, called emph{soft edges}, extend to asymptotia and realize the corner charge algebra by “pulling in” the asymptotic one from infinity. Realizing an infinite-dimensional algebra requires a new set of emph{soft boundary conditions}, relying on the distinction between extrinsic and intrinsic data. We identify the subregion Goldstone mode as the relational observable between extrinsic and intrinsic frames and clarify the meaning of vacuum degeneracy. We also connect the asymptotic memory effect with a more operational emph{quasi-local} one. A main conclusion is that the relationship between asymptotia and finite distance is emph{frame-dependent}; each choice of soft edge mode probes distinct cross-boundary data of the global theory. Our work combines the study of boundary symmetries with the program of dynamical reference frames and we anticipate that core insights extend to Yang-Mills theory and gravity.
In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information. In a quantum error correcting code (QECC), a collection of computational degrees of freedom that make up a device’s physical layer is used to redundantly encode a smaller amount of logical information. We elaborate this clear parallel in terms of quantum reference frames (QRFs), which are a universal toolkit for quantization in the presence of symmetries. The result is a precise dictionary between QECCs and QRFs within the perspective-neutral framework for constrained systems. Concepts from quantum error correction like error sets and correctability translate to novel insights into the informational architecture of gauge theories. Conversely, the dictionary provides a systematic procedure for constructing symmetry-based QECCs and characterizing their error correcting properties. In this initial work, we scrutinize the dictionary between Pauli stabilizer codes and their corresponding QRF setups, which possess symmetry groups that are isomorphic to the stabilizer group. We show that there is a one-to-one correspondence between maximal correctable error sets and tensor factorizations splitting system from frame degrees of freedom, relative to which errors corrupt only redundant frame data. When passed through the dictionary, standard Pauli errors from the code essentially behave as electric excitations that are exactly dual, via Pontryagin duality, to magnetic excitations related to gauge-fixing. We comprehensively illustrate our findings in surface codes, which themselves manifestly connect quantum error correction with gauge systems. The exploratory investigations in this article pave the way for deeper foundational applications to quantum gauge theories and for eventual practical applications to quantum simulation.
Two of us recently proposed an entanglement-based witness of non-classicality, which can be applied to testing quantum effects in gravity in what is known as the Bose-Marletto-Vedral (BMV) effect. The witness is based on this idea: if a system can create entanglement between two quantum probes by local means only, then it must be non-classical. In this note we discuss the role of locality as an assumption for the theorem supporting the witness; we also discuss other related notions of locality and comment on their mutual relations.
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of being connected or not, and be allowed to merge, split and reconnect coherently in a superposition. Second, tensors and traceouts are generalized, so that systems can be partitioned according to almost arbitrary logical predicates in a robust manner. The hereby presented mathematical framework is anchored on solid grounds through numerous lemmas. Indeed, one might have feared that the familiar interrelations between the notions of unitarity, complete positivity, trace-preservation, non-signalling causality, locality and localizability that are standard in quantum theory be jeopardized as the neighbourhood and partitioning between systems become both quantum, dynamical, and logical. Such interrelations in fact carry through, albeit two new notions become instrumental: consistency and comprehension.
The ER=EPR conjecture states that quantum entanglement between boundary degrees of freedom leads to the emergence of bulk spacetime itself. Although this has been tested extensively in String Theory for asymptotically anti-de Sitter spacetimes, its implications for an accelerating universe, such as our own, remain less explored. Assuming a cosmic version of ER=EPR for de Sitter space, we explore computational complexity corresponding to long-range entanglement responsible for bulk states on spacelike hypersurfaces. Rather remarkably, we find that the complexity (per unit volume) of the Euclidean vacuum, as an entangled state over two boundary CFT vacua, is finite both in the UV and the IR, which provides additional evidence for cosmic ER=EPR. Our result seems to be a universal feature of spacetimes with horizons and is explicitly independent of the details of the model under consideration.
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension of the quantum reference frame formalism to address this question for the Klein-Gordon field residing on a superposition of conformally equivalent metrics. Based on the group structure of “quantum conformal transformations”, we construct an explicit quantum operator that can map states describing a quantum field on a superposition of spacetimes to states representing a quantum field with a superposition of masses on a Minkowski background. This constitutes an extended symmetry principle, namely invariance under quantum conformal transformations. The latter allows to build an understanding of superpositions of diffeomorphically non-equivalent spacetimes by relating them to a more intuitive superposition of quantum fields on curved spacetime. Furthermore, it can be used to import the phenomenon of particle production in curved spacetime to its conformally equivalent counterpart, thus revealing new features in modified Minkowski spacetime.
Analyzing the geometry of correlation sets constrained by general causal structures is of paramount importance for foundational and quantum technology research. Addressing this task is generally challenging, prompting the development of diverse theoretical techniques for distinct scenarios. Recently, novel hybrid scenarios combining different causal assumptions within different parts of the causal structure have emerged. In this work, we extend a graph theoretical technique to explore classical, quantum, and no-signaling distributions in hybrid scenarios, where classical causal constraints and weaker no-signaling ones are used for different nodes of the causal structure. By mapping such causal relationships into an undirected graph we are able to characterize the associated sets of compatible distributions and analyze their relationships. In particular we show how with our method we can construct minimal Bell-like inequalities capable of simultaneously distinguishing classical, quantum, and no-signaling behaviors, and efficiently estimate the corresponding bounds. The demonstrated method will represent a powerful tool to study quantum networks and for applications in quantum information tasks.
