We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does not admit such a graph realization, it must lie outside the cone, in which case the algorithm finds a graph whose corresponding entropy vector most nearly approximates the target and allows us to probe the location of the facets. For the N = 3 cone, we confirm that our algorithm successfully rediscovers monogamy of mutual information beginning with a target vector outside the holographic entropy cone. We then apply the algorithm to the N = 6 cone, analyzing the 6 mystery extreme rays of the subadditivity cone from [1] that satisfy all known holographic entropy inequalities yet lacked graph realizations. We found realizations for 3 of them, proving they are genuine extreme rays of the holographic entropy cone, while providing evidence that the remaining 3 are not realizable, implying unknown holographic inequalities exist for N = 6.
", "doi": "10.1007/jhep06(2026)267", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2026-06", "series_number": "6", "volume": "2026", "issue": "6", "pages": "267" }, { "id": "authors:wr2vt-6d751", "collection": "authors", "collection_id": "wr2vt-6d751", "cite_using_url": "https://authors.library.caltech.edu/records/wr2vt-6d751", "type": "article", "title": "Effective Density Matrix for Vacua in Asymptotically Flat Gravity", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Mitra", "given_name": "Prahar" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We explicitly construct the density matrix associated to the vacuum state of a large spherically symmetric causal diamond of area \ud835\udc34 in four-dimensional asymptotically flat gravity. We achieve this using the soft effective action, which characterizes the low-energy gravitational degrees of freedom that arise in the long-distance limit of the Einstein-Hilbert action and consists of both the soft graviton mode and the Goldstone mode arising from the spontaneous breaking of supertranslation symmetry. Integrating out the soft graviton mode, we obtain an effective action for purely the Goldstone mode, from which we extract the density matrix and therefore the modular Hamiltonian ^\ud835\udc3e\ud835\udc60 associated to the vacuum state. As a corollary, we explicitly compute the mean and variance of ^\ud835\udc3e\ud835\udc60, finding \u27e8Δ\u2062^\ud835\udc3e2\ud835\udc60\u27e9=\ud835\udc34/\ud835\udf002UV, with \ud835\udf00UV being a length-scale UV cutoff on the celestial sphere.
", "doi": "10.1103/n48t-3dr1", "issn": "0031-9007", "publisher": "American Physical Society", "publication": "Physical Review Letters", "publication_date": "2026-05-27", "series_number": "21", "volume": "136", "issue": "21", "pages": "211501" }, { "id": "authors:hspxm-f5s60", "collection": "authors", "collection_id": "hspxm-f5s60", "cite_using_url": "https://authors.library.caltech.edu/records/hspxm-f5s60", "type": "article", "title": "From Asymptotically Flat Gravity to Finite Causal Diamonds", "author": [ { "family_name": "Ciambelli", "given_name": "Luca" }, { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We demonstrate that the phase space of the soft sector of asymptotically flat gravity in four spacetime dimensions can be identified with that of a spherically symmetric finite casual diamond in Minkowski spacetime. The leading soft graviton mode is geometrically identified with the radial fluctuation of the causal diamond size, while the Goldstone mode involves both the radial fluctuation and its symplectic partner. This allows us to relate the radial fluctuations of the causal diamond with the asymptotic transverse fluctuations parametrized by the soft modes.
", "doi": "10.1103/lbm1-vkks", "issn": "0031-9007", "publisher": "American Physical Society", "publication": "Physical Review Letters", "publication_date": "2026-05-13", "series_number": "19", "volume": "136", "issue": "19", "pages": "191501" }, { "id": "authors:p5why-e8h82", "collection": "authors", "collection_id": "p5why-e8h82", "cite_using_url": "https://authors.library.caltech.edu/records/p5why-e8h82", "type": "article", "title": "Thermodynamics of a spherically symmetric causal diamond in Minkowski spacetime", "author": [ { "family_name": "Fransen", "given_name": "Kwinten", "orcid": "0000-0002-0919-9971", "clpid": "Fransen-Kwinten" }, { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We compute a gravitational on-shell action of a finite, spherically symmetric causal diamond in (d + 2)-dimensional Minkowski spacetime, finding it is proportional to the area of the bifurcate horizon A_B. We then identify the on-shell action with the saddle point of the Euclidean gravitational path integral, which is naturally interpreted as a partition function. This partition function is thermal with respect to a modular Hamiltonian K. Consequently, we determine, from the on-shell action using standard thermodynamic identities, both the mean and variance of the modular Hamiltonian, finding\u3008K\u3009=\u3008(\u2206K)2\u3009= A_B/4G_N. Finally, we show that modular fluctuations give rise to fluctuations in the geometry, and compute the associated phase shift of massless particles traversing the diamond under such fluctuations.
", "doi": "10.1007/jhep12(2025)125", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2025-12", "series_number": "12", "volume": "2025", "issue": "12", "pages": "125" }, { "id": "authors:1ya8r-k8p87", "collection": "authors", "collection_id": "1ya8r-k8p87", "cite_using_url": "https://authors.library.caltech.edu/records/1ya8r-k8p87", "type": "article", "title": "Quantum area fluctuations from gravitational phase space", "author": [ { "family_name": "Ciambelli", "given_name": "Luca", "orcid": "0000-0001-6631-836X" }, { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We study the gravitational phase space associated to a stretched horizon within a finite-sized causal diamond in (d + 2)-dimensional spacetimes. By imposing the Raychaudhuri equation, we obtain its constrained symplectic form using the covariant phase space formalism and derive the relevant quantum commutators by inverting the symplectic form and quantizing. Finally, we compute the area fluctuations of the causal diamond by taking a Carrollian limit of the stretched horizon in pure Minkowski spacetime, and derive the relationship\u3008(ΔA)² \u3009≥ 2πG/d\u3008A\u3009, showing that the variance of the area fluctuations is proportional to the area itself.
", "doi": "10.1007/jhep08(2025)199", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2025-08", "series_number": "8", "volume": "2025", "issue": "8", "pages": "199" }, { "id": "authors:0jeq5-qve44", "collection": "authors", "collection_id": "0jeq5-qve44", "cite_using_url": "https://authors.library.caltech.edu/records/0jeq5-qve44", "type": "article", "title": "Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the N = 6 solution", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Hubeny", "given_name": "Veronika E.", "orcid": "0000-0003-0268-5587" }, { "family_name": "Rota", "given_name": "Massimiliano", "orcid": "0000-0001-5097-8259" } ], "abstract": "We compute the set of all extreme rays of the 6-party subadditivity cone that are compatible with strong subadditivity. In total, we identify 208 new (genuine 6-party) orbits, 52 of which violate at least one known holographic entropy inequality. For the remaining 156 orbits, which do not violate any such inequalities, we construct holographic graph models for 150 of them. For the final 6 orbits, it remains an open question whether they are holographic. Consistent with the strong form of the conjecture in [1], 148 of these graph models are trees. However, 2 of the graphs contain a \"bulk cycle\", leaving open the question of whether equivalent models with tree topology exist, or if these extreme rays are counterexamples to the conjecture. The paper includes a detailed description of the algorithm used for the computation, which is presented in a general framework and can be applied to any situation involving a polyhedral cone defined by a set of linear inequalities and a partial order among them to find extreme rays corresponding to down-sets in this poset.
", "doi": "10.1007/jhep06(2025)055", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2025-06", "series_number": "6", "volume": "2025", "issue": "6", "pages": "55" }, { "id": "authors:1bjjz-q0g24", "collection": "authors", "collection_id": "1bjjz-q0g24", "cite_using_url": "https://authors.library.caltech.edu/records/1bjjz-q0g24", "type": "article", "title": "An infrared on-shell action and its implications for soft charge fluctuations in asymptotically flat spacetimes", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Raclariu", "given_name": "Ana-Maria", "orcid": "0000-0002-0606-7340" }, { "family_name": "Zurek", "given_name": "Kathryn M", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We study the infrared on-shell action of Einstein gravity in asymptotically flat spacetimes (AFSs), obtaining an effective, gauge-invariant boundary action for memory and shockwave spacetimes. We show that the phase space is in both cases parameterized by the leading soft variables in AFSs, thereby extending the equivalence between shockwave and soft commutators to spacetimes with non-vanishing Bondi mass. We then demonstrate that our on-shell action is equal to three quantities studied separately in the literature: (i) the soft supertranslation charge; (ii) the shockwave effective action, or equivalently the modular Hamiltonian; and (iii) the soft effective action. Finally, we compute the quantum fluctuations in the soft supertranslation charge and, assuming the supertranslation parameter may be promoted to an operator, we obtain an area law, consistent with earlier results showing that the modular Hamiltonian has such fluctuations.
", "doi": "10.1088/1751-8121/adc4a2", "issn": "1751-8113", "publisher": "IOP Publishing", "publication": "Journal of Physics A: Mathematical and Theoretical", "publication_date": "2025-04-21", "series_number": "16", "volume": "58", "issue": "16", "pages": "165402" }, { "id": "authors:pc4ds-dwb23", "collection": "authors", "collection_id": "pc4ds-dwb23", "cite_using_url": "https://authors.library.caltech.edu/records/pc4ds-dwb23", "type": "article", "title": "Quantum Mechanics of a Spherically Symmetric Causal Diamond in Minkowski Spacetime", "author": [ { "family_name": "Bub", "given_name": "Mathew W.", "orcid": "0000-0003-4251-0845", "clpid": "Bub-Mathew-W" }, { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Mitra", "given_name": "Prahar", "orcid": "0000-0001-8518-9399" }, { "family_name": "Zhang", "given_name": "Yiwen", "orcid": "0000-0003-2355-9416", "clpid": "Zhang-Yiwen" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We construct the phase space of a spherically symmetric causal diamond in (d+2)-dimensional Minkowski spacetime. Utilizing the covariant phase space formalism, we identify the relevant degrees of freedom that localize to the d-dimensional bifurcate horizon and, upon canonical quantization, determine their commutators. On this phase space, we find two Iyer-Wald charges. The first of these charges, proportional to the area of the causal diamond, is responsible for shifting the null time along the horizon and has been well documented in the literature. The second charge is much less understood, being integrable for d≥2 only if we allow for field-dependent diffeomorphisms and is responsible for changing the size of the causal diamond.
", "doi": "10.1103/physrevlett.134.121501", "issn": "0031-9007", "publisher": "American Physical Society", "publication": "Physical Review Letters", "publication_date": "2025-03-25", "series_number": "12", "volume": "134", "issue": "12", "pages": "121501" }, { "id": "authors:xpjpv-m7h61", "collection": "authors", "collection_id": "xpjpv-m7h61", "cite_using_url": "https://authors.library.caltech.edu/records/xpjpv-m7h61", "type": "article", "title": "Diamond of infrared equivalences in abelian gauge theories", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Mitra", "given_name": "Prahar", "orcid": "0000-0001-8518-9399" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We demonstrate a tree-level equivalence between four distinct infrared objects in (d+2)-dimensional Abelian gauge theories. These are (i) the large gauge charge Q\u03f5 where the function \u03f5 on the sphere parametrizing large gauge transformations is identified with the Goldstone mode θ of spontaneously broken large gauge symmetry; (ii) the soft effective action that captures the dynamics of the soft and Goldstone modes; (iii) the edge mode action with Neumann boundary conditions; and (iv) the Wilson line dressing of a scattering amplitude, including a novel dressing for soft photons, which have local charge distributions despite having vanishing global charge. The promotion of the large gauge parameter to the dynamical Goldstone and the novel dressing of soft gauge particles give rise to intriguing possibilities for the future study of infrared dynamics of gauge theories and gravity.
", "doi": "10.1103/physrevd.110.105018", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2024-11-25", "series_number": "10", "volume": "110", "issue": "10", "pages": "105018" }, { "id": "authors:jdmtj-jbn68", "collection": "authors", "collection_id": "jdmtj-jbn68", "cite_using_url": "https://authors.library.caltech.edu/records/jdmtj-jbn68", "type": "article", "title": "Beyond the Holographic Entropy Cone via Cycle Flows", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Hern\u00e1ndez-Cuenca", "given_name": "Sergio" }, { "family_name": "Keeler", "given_name": "Cynthia", "orcid": "0000-0002-4248-3704" } ], "abstract": "Motivated by bit threads, we introduce a new prescription for computing entropy vectors outside the holographic entropy cone. By utilizing cycle flows on directed graphs, we show that the maximum cycle flow associated to any subset of vertices, which corresponds to a subsystem, manifestly obeys purification symmetry. Furthermore, by restricting ourselves to a subclass of directed graphs, we prove that the maximum cycle flow obeys both subadditivity and strong subadditivity, thereby establishing it as a viable candidate for the entropy associated to the subsystem. Finally, we demonstrate how our model generalizes the entropy vectors obtainable via conventional flows in undirected graphs, as well as conjecture that our model similarly generalizes the entropy vectors arising from hypergraphs.
\nWe derive the soft effective action in (\ud835\udc51+2)-dimensional Abelian gauge theories from the on-shell action obeying Neumann boundary conditions at timelike and null infinity and Dirichlet boundary conditions at spatial infinity. This allows us to identify the on-shell degrees of freedom on the boundary with the soft modes living on the celestial sphere. Following the work of Donnelly and Wall, this suggests that we can interpret soft modes as entanglement edge modes on the celestial sphere and study entanglement properties of soft modes in Abelian gauge theories.
", "doi": "10.1103/physrevd.109.125016", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2024-06-15", "series_number": "12", "volume": "109", "issue": "12", "pages": "125016" }, { "id": "authors:rjthj-wzw94", "collection": "authors", "collection_id": "rjthj-wzw94", "cite_using_url": "https://authors.library.caltech.edu/records/rjthj-wzw94", "type": "article", "title": "Asymptotic structure of higher dimensional Yang-Mills theory", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Mitra", "given_name": "Prahar", "orcid": "0000-0001-8518-9399" } ], "abstract": "Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in (d+2)-dimensional Minkowski spacetime for any d \u2265 2, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in (d+2)-dimensional spacetime.", "doi": "10.21468/scipostphys.16.5.142", "issn": "2542-4653", "publisher": "Stichting SciPost", "publication": "SciPost Physics", "publication_date": "2024-05", "series_number": "5", "volume": "16", "issue": "5", "pages": "142" }, { "id": "authors:7f5rh-5af67", "collection": "authors", "collection_id": "7f5rh-5af67", "cite_using_url": "https://authors.library.caltech.edu/records/7f5rh-5af67", "type": "article", "title": "Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Hubeny", "given_name": "Veronika E.", "orcid": "0000-0003-0268-5587", "clpid": "Hubeny-Veronika-E" }, { "family_name": "Rota", "given_name": "Massimiliano", "orcid": "0000-0001-5097-8259", "clpid": "Rota-Massimiliano" } ], "abstract": "We show via explicit construction that all the extreme rays of both the three-party quantum entropy cone and the four-party stabilizer entropy cone can be obtained from subsystem coarse grainings of specific higher-party quantum states, namely, extreme states characterized by saturating a (nontrivial) maximal set of instances of subadditivity. This suggests that the study of the “subadditivity cone,” and the set of its extreme rays realizable in quantum mechanics, provides a powerful tool for deriving inner bounds for the quantum and stabilizer entropy cones, as well as constraints on new inequalities for the von Neumann entropy.
", "doi": "10.1103/physreva.109.052407", "issn": "2469-9926", "publisher": "American Physical Society", "publication": "Physical Review A", "publication_date": "2024-05", "series_number": "5", "volume": "109", "issue": "5", "pages": "052407" }, { "id": "authors:a9b3f-r2r87", "collection": "authors", "collection_id": "a9b3f-r2r87", "cite_using_url": "https://authors.library.caltech.edu/records/a9b3f-r2r87", "type": "article", "title": "Gap between holographic and quantum mechanical extreme rays of the subadditivity cone", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Hubeny", "given_name": "Veronika E.", "orcid": "0000-0003-0268-5587", "clpid": "Hubeny-Veronika-E" }, { "family_name": "Rota", "given_name": "Massimiliano", "orcid": "0000-0001-5097-8259", "clpid": "Rota-Massimiliano" } ], "abstract": "We show via explicit construction that for six or more parties, there exist extreme rays of the subadditivity cone that can be realized by quantum states, but not by holographic states. This is a counterexample to a conjecture first formulated in Hernández-Cuenca et al. [The holographic entropy cone from marginal independence, J. High Energy Phys. 09 (2022) 190.], and implies the existence of deep holographic constraints that restrict the allowed patterns of independence among various subsystems beyond the universal quantum mechanical restrictions.
", "doi": "10.1103/physrevd.109.l041901", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2024-02-15", "series_number": "4", "volume": "109", "issue": "4", "pages": "L041901" }, { "id": "authors:284fv-ps246", "collection": "authors", "collection_id": "284fv-ps246", "cite_using_url": "https://authors.library.caltech.edu/records/284fv-ps246", "type": "article", "title": "From shockwaves to the gravitational memory effect", "author": [ { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Raclariu", "given_name": "Ana-Maria", "orcid": "0000-0002-0606-7340" }, { "family_name": "Zurek", "given_name": "Kathryn M.", "orcid": "0000-0002-2629-337X", "clpid": "Zurek-K-M" } ], "abstract": "We study the relationship between shockwave geometries and the gravitational memory effect in four-dimensional asymptotically flat spacetime. In particular, we show the 't Hooft commutation relations of shockwave operators are equivalent to the commutation relation between soft and Goldstone modes parametrizing a sector of the gravitational phase space. We demonstrate this equivalence via a diffeomorphism that takes a shockwave metric to a metric whose transverse traceless component is the gravitational memory. The shockwave momentum in 't Hooft's analysis is related to the soft graviton mode, which is responsible for the memory effect, while the shift in the shockwave position is related to the Goldstone mode. This equivalence opens new directions to utilize the gravitational memory effect to explore the observational implications of shockwave geometries in flat space.
", "doi": "10.1007/jhep01(2024)006", "issn": "1029-8479", "publisher": "Springer Science and Business Media LLC", "publication": "Journal of High Energy Physics", "publication_date": "2024-01", "series_number": "1", "volume": "2024", "issue": "1", "pages": "6" }, { "id": "authors:qxnvf-96z92", "collection": "authors", "collection_id": "qxnvf-96z92", "cite_using_url": "https://authors.library.caltech.edu/records/qxnvf-96z92", "type": "article", "title": "Entropy growth in perturbative scattering", "author": [ { "family_name": "Cheung", "given_name": "Clifford", "orcid": "0000-0002-9983-9425", "clpid": "Cheung-Clifford" }, { "family_name": "He", "given_name": "Temple", "orcid": "0000-0002-2873-3746", "clpid": "He-Temple" }, { "family_name": "Sivaramakrishnan", "given_name": "Allic", "orcid": "0000-0002-0114-4909", "clpid": "Sivaramakrishnan-Allic" } ], "abstract": "Inspired by the second law of thermodynamics, we study the change in subsystem entropy generated by dynamical unitary evolution of a product state in a bipartite system. Working at leading order in perturbative interactions, we prove that the quantum n-Tsallis entropy of a subsystem never decreases, \u0394S\u2099 \u2265 0, provided that subsystem is initialized as a statistical mixture of states of equal probability. This is true for any choice of interactions and any initialization of the complementary subsystem. When this condition on the initial state is violated, it is always possible to explicitly construct a \"Maxwell's demon\" process that decreases the subsystem entropy, \u0394S\u2099 < 0. Remarkably, for the case of particle scattering, the circuit diagrams corresponding to n-Tsallis entropy are the same as the on shell diagrams that have appeared in the modern scattering amplitudes program, and \u0394S\u2099 \u2265 0 is intimately related to the nonnegativity of cross sections.
", "doi": "10.1103/physrevd.108.045013", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "2023-08-15", "series_number": "4", "volume": "108", "issue": "4", "pages": "045013" }, { "id": "authors:s45t1-jbk91", "collection": "authors", "collection_id": "s45t1-jbk91", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160622-112748138", "type": "monograph", "title": "Limitations on Dimensional Regularization in Renyi Entropy", "author": [ { "family_name": "Bao", "given_name": "Ning", "orcid": "0000-0002-3296-1039", "clpid": "Bao-Ning" }, { "family_name": "He", "given_name": "Temple", "clpid": "He-Temple" } ], "abstract": "Dimensional regularization is a common method used to regulate the UV divergence of field theoretic quantities. When it is used in the context of Renyi entropy, however, it is important to consider whether such a procedure eliminates the statistical interpretation thereof as a measure of entanglement of states living on a Hilbert space. We therefore examine the dimensionally regularized Renyi entropy of a 4d unitary CFT and show that it admits no underlying Hilbert space in the state-counting sense. This gives a concrete proof that dimensionally regularized Renyi entropy cannot always be obtained as a limit of the Renyi entropy of some finite-dimensional quantum system.", "doi": "10.48550/arXiv.1603.08531", "publisher": "N/A", "publication_date": "2016-03-28" } ]