arXiv subjects

Charlie Cummings

Publications and source records attributed to Charlie Cummings.

7 recordsLinked to original sources

arXiv2026

Entanglement entropy in topological tensor networks

We derive an entropy formula for recently proposed tensor network models which prepare diffeomorphism invariant states of topological quantum field theories with non-compact and/or continuous gauge groups. We show that our entropy formula generalizes the notion of ``topological entanglement entropy'' to incorporate the infinite number of particle-like excitations in such theories. When our networks are endowed with gauge group $\mathrm{SL}(2,\mathbb{R})$, we can interpret them as models of three-dimensional gravity with small Newton's constant and possibly non-invertible metrics.

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arXiv2026

The Topological Equivalence Principle: On Decoupling TFTs from Gravity

Topological field theories (TFTs) play an important role in characterizing the deep infrared (IR) of many quantum systems with a mass gap, as well as the global symmetries of quantum field theories (QFTs) decoupled from gravity. In gravitational asymptotically AdS spacetimes, TFT sectors which are putatively decoupled from local metric data are nevertheless non-perturbatively sensitive to Newton's constant via a sum over topologically distinct saddle point configurations. Tracking the fate of this non-decoupling in the boundary dual, we argue that in spite of appearances, this dependence on Newton's constant extends to local metric fluctuations. Said differently, TFTs are in the Swampland. In tandem with earlier results on the absence of global symmetries in theories with subregion-subregion duality, this also establishes that topological operators of boundary systems with a gravity dual are always non-topological in the bulk.

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arXiv2025

Diffeomorphism invariant tensor networks for 3d gravity

Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of both problems were addressed in a tensor network discretization of topological field theories (TFT) with finite or compact gauge groups. Here, we extend this work towards gravity by generalizing to gauge groups that are discrete or continuous, compact or non-compact. Applied to $\text{SL}(2,\mathbb{R}) \times \text{SL}(2,\mathbb{R})$ Chern-Simons theory, our construction can be interpreted as building states of three dimensional gravity with a negative cosmological constant. Our tensor networks prepare states that satisfy the constraints of Chern-Simons theory. In metric variables, this implies that the states we construct satisfy the Wheeler-DeWitt equation and momentum constraints, and so are diffeomorphism invariant.

hep-th↗

arXiv2025

Purely GHZ-like entanglement is forbidden in holography

We provide evidence that three-party entanglement signals in holography obey a relation that is not satisfied by generalized Greenberger-Horne-Zeilinger (GHZ) states. Using proposed holographic duals for these entanglement signals, we provide a geometric argument establishing this relation. This is the first known inequality on the structure of pure three-party holographic states, and shows that time-symmetric holographic states can never have purely GHZ-like entanglement. We also discuss similar relations for four parties.

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arXiv2025

Entanglement in Typical States of Chern-Simons Theory

We compute various averages over bulk geometries of quantum states prepared by the Chern-Simons path integral, for any level $k$ and compact simple gauge group $G$. We do so by carefully summing over all topologically distinct bulk geometries which have $n$ disjoint boundary tori and a decomposition into space$\times$time of fixed spatial topology. We find that to leading order in the complexity of the state, the typical state contains many types of multiparty entanglement, proving a conjecture of Balasubramanian et al. Additionally, we compute an averaged wave function which captures the leading order statistics of boundary observables in the $n$ torus Chern-Simons Hilbert space.

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arXiv2025

Multipartite Entanglement Structure of Fibered Link States

We study the patterns of multipartite entanglement in Chern-Simons theory with compact simple gauge group $G$ and level $k$ for states defined by the path integral on ``link complements'', i.e., compact manifolds whose boundaries consist of $n$ topologically linked tori. We focus on link complements which can be described topologically as fibrations over a Seifert surface. We show that the entanglement structure of such fibered link complement states is controlled by a topological invariant, the monodromy of the fibration. Thus, the entanglement structure of a Chern-Simons link state is not simply a function of the link, but also of the background manifold in which the link is embedded. In particular, we show that any link possesses an embedding into some background that leads to Greenberger--Horne--Zeilinger state (GHZ)-like entanglement. Furthermore, we demonstrate that all fibered links with periodic monodromy have GHZ-like entanglement, i.e., a partial trace on any link component produces a separable state. These results generalize to any three dimensional topological field theory with a dual chiral rational conformal field theory.

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arXiv2023

The entropy of finite gravitating regions

We develop a formalism for calculating the entanglement entropy of an arbitrary spatial region of a gravitating spacetime at a moment of time symmetry. The crucial ingredient is a path integral over embeddings of the region into the overall spacetime, interpretable as a sum over the edge modes associated with the region. We find that the entanglement entropy of a gravitating region equals the minimal surface area among all regions that enclose it. This suggests a notion of "terrestrial holography" where regions of space can encode larger ones, in contrast to the standard form of holography, in which degrees of freedom on the celestial sphere at the boundary of the universe encode the interior.

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