arXiv subjects

Horacio Casini

Publications and source records attributed to Horacio Casini.

At least 19 recordsLinked to original sources

arXiv2026

Exact Mutual Information Difference: Scalar vs. Maxwell Fields

We compute, for any Rényi index $n$, the exact difference between the mutual Rényi informations of a pair of free massless scalars and that of a Maxwell field in $d=4$ dimensions. Using the standard dimensional reduction method in polar coordinates, the problem is mapped to that of a single scalar field in $d=2$ with Dirichlet boundary conditions, which in turn can be conveniently related to the algebra of a chiral current on the full line. This latter identification, which maps algebras on an interval to two-interval algebras, yields exact results that clarify the structure of the long-distance OPE perturbative expansion of the mutual information. We find that this series has a finite radius of convergence only for integer $n>1$, while it becomes only asymptotical for $n=1$ and general non-integer values of $n$.

hep-th↗

arXiv2025

Holographic Rényi $n\to 0$ entropy and Euclidean fluids

We explore the holographic prescription for computing the refined Rényi entropies $\tilde S_n$ in the $n \to 0$ limit within the AdS$_{d+1}$/CFT$_d$ framework. This limit can be interpreted as a high-temperature regime with respect to the energy defined by the modular Hamiltonian of the state reduced to a subregion. To leading order in $n$, we find that the system attains local equilibrium and admits a CFT description in terms of a Euclidean, irrotational perfect fluid. This fluid exhibits vortex-like boundary conditions at the entangling surface. Guided by this physical picture, we construct an ansatz for the dual geometry in terms of the boundary fluid variables. We show that our anzats solves Einstein's equations coupled to a cosmic brane at leading order in $n$, in agreement with Dong's proposal for the holographic dual to the refined Rényi entropy. The resulting conical singularity, signaling the brane's location, can be understood from this perspective as the bulk extension of the boundary fluid vortices.

hep-th↗

arXiv2025

A generalization of the DHR theorem for higher form symmetries

The Doplicher-Haag-Roberts (DHR) reconstruction theorem shows that standard ($0$-form) internal symmetries are associated to groups in relativistic quantum field theory in spacetime dimension $D>2$. In particular, non-invertible symmetry structures in $D>2$ correspond to the choice of a subtheory of a unique parent one, where the symmetry is a compact group. We present a theorem that generalizes this result to higher form symmetries. We first re-formulate the DHR theorem in terms of Haag duality violations (HDV) for regions with non-trivial homotopy group $π_0$ in the finite index case. In this light, the theorem states that the category associated with such HDV is the dual of a group, and it can be extended to spontaneous symmetry breaking scenarios. Then, after eliminating $π_0$ sectors via DHR reconstruction, we show that the HDV corresponding to regions with non-trivial $π_i$, $0 2$ are labeled by such groups, in agreement with the case of confinement order parameters in Yang-Mills theories (Wilson and 't Hooft loops). For the special case of $D=4n$ and loops of dimension $k=2 n-1$, the group is further required to have a Hermitian character table. This does not rule out the possibility of an extra $\mathbb{Z}_2$ factor that is not achievable by Lagrangian gauge models. In the way we find a new proof of the group-like origin of internal symmetries, and analyze the sectors for more general regions, e.g., direct sums, knots, and links. In particular, we find that generalized knot order parameters are classified by the unknot order parameters, and the commutator of knot non-local operators is determined by the linking number.

hep-th↗

arXiv2025

Mutual information from modular flow in CFTs

The operator product expansion (OPE) of twist operators in the replica trick framework enables a long-distance expansion of the mutual information (MI) in conformal field theories (CFTs). In this expansion, the terms are labeled by primary operators, as contributions from descendant operators can be resummed into conformal blocks. However, for the MI, the expansion involves primaries from the multi-replica theory, which includes far more operators than those in the original theory. In this work, we develop a method to resum this series, yielding an expansion in terms of the primaries of the original theory, specifically restricted to the two-copy sector. This is achieved by expressing the twist operators in a non-local manner across different replicas and using a modular flow representation to obtain the n -> 1 limit of the Rényi index. We explicitly compute the resulting "enhanced conformal blocks", which, surprisingly, provide excellent approximations to the MI of generalized free fields across the full range of cross ratios. Remarkably, this approximation appears to be exact in the limit of large spacetime dimensions.

hep-th↗

arXiv2025

Selection rules for RG flows of minimal models

Minimal d=2 CFTs are usually classified through modular invariant partition functions. There is a finer classification of ``non complete'' models when S-duality is not imposed. We approach this classification by starting with the local chiral algebra and adding primaries sequentially. At each step, we only impose locality (T-duality) and closure of the operator algebra. For each chiral algebra, this produces a tree-like graph. Each tree node corresponds to a local d=2 CFT, with an intrinsic Jones index measuring the size of Haag duality violation. This index can be computed with the partition function and is related to the total quantum dimension of the category of superselection sectors of the node, and to the relative size between the node and a modular invariant completion. In this way, we find in a very explicit manner a classification of local minimal (c<1) d=2 CFTs. When appropriate, this matches Kawahigashi-Longo's previous results. We use this finer classification to constrain RG flows. For a relevant perturbation, the flow can be restricted to the subalgebra associated with it, typically corresponding to a non-modular invariant node in the tree. The structure of the graph above such node needs to be preserved by the RG flow. In particular, the superselection sector category for the node must be preserved. This gives selection rules that recover in a unified fashion several known facts while unraveling new ones.

hep-th↗

arXiv2025

ABJ anomaly as a U(1) symmetry and Noether's theorem

The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In its seminal paper, Adler noticed that a modified chiral U(1) symmetry could still be defined, at the expense of being generated by a non-gauge-invariant conserved current. We show this internal U(1) symmetry has the special feature that it transforms the Haag duality violating sectors (or non-local operator classes). This provides a simple unifying perspective on the origin of anomaly quantization, anomaly matching, applicability of Goldstone theorem, and the absence of a Noether current. We comment on recent literature where this symmetry is considered to be either absent or non-invertible. We end by recalling the DHR reconstruction theorem, which states 0-form symmetries cannot be non-invertible for d>2, and argue for a higher-form symmetry reconstruction theorem.

hep-th↗

arXiv2024

Modular invariance as completeness

We review the physical meaning of modular invariance for unitary conformal quantum field theories in d=2. For QFT models, while T invariance is necessary for locality, S invariance is not mandatory. S invariance is a form of completeness of the theory that has a precise meaning as Haag duality for arbitrary multi-interval regions. We present a mathematical proof as well as derive this result from a physical standpoint using Renyi entropies and the replica trick. For rational CFT's, the failure of modular invariance or Haag duality can be measured by an index, related to the quantum dimensions of the model. We show how to compute this index from the modular transformation matrices. The index also appears in a limit of the Renyi mutual informations. Cases of infinite index are briefly discussed. Part of the argument can be extended to higher dimensions, where the lack of completeness can also be diagnosed using the CFT data through the thermal partition function and measured by an index.

hep-th↗

arXiv2024

Modular Hamiltonians on the null plane and the Markov property of the vacuum state

We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non locally outside the null plane. We regain this result in greater generality using more abstract tools on algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.

hep-th↗

arXiv2023

Standard translation twists and an operator-bounded energy inequality

Twist operators implement symmetries in bounder regions of the space. Standard twists are a special class of twists constructed using modular tools. The twists corresponding to translations have interesting special properties. They can move continuously an operator from a region to a disjoint one without ever passing through the gap separating the two. In addition, they have generators satisfying the spectrum condition. We compute explicitly these twists for the two dimensional chiral fermion field. The twist generator gives place to a new type of energy inequality where the smeared energy density is bounded below by an operator.

hep-th↗

arXiv2023

Rényi entropies in the $n\to0$ limit and entanglement temperatures

Entanglement temperatures (ET) are a generalization of Unruh temperatures valid for states reduced to any region of space. They encode in a thermal fashion the high energy behavior of the state around a point. These temperatures are determined by an eikonal equation in Euclidean space. We show that the real-time continuation of these equations implies ballistic propagation. For theories with a free UV fixed point, the ET determines the state at a large modular temperature. In particular, we show that the $n \to 0$ limit of Rényi entropies $S_n$, can be computed from the ET. This establishes a formula for these Rényi entropies for any region in terms of solutions of the eikonal equations. In the $n\to 0$ limit, the relevant high-temperature state propagation is determined by a free relativistic Boltzmann equation, with an infinite tower of conserved currents. For the special case of states and regions with a conformal Killing symmetry, these equations coincide with the ones of a perfect fluid.

hep-th↗

arXiv2023

Conformal bounds in three dimensions from entanglement entropy

The entanglement entropy of an arbitrary spacetime region $A$ in a three-dimensional conformal field theory (CFT) contains a constant universal coefficient, $F(A)$. For general theories, the value of $F(A)$ is minimized when $A$ is a round disk, $F_0$, and in that case it coincides with the Euclidean free energy on the sphere. We conjecture that, for general CFTs, the quantity $F(A)/F_0$ is bounded above by the free scalar field result and below by the Maxwell field one. We provide strong evidence in favor of this claim and argue that an analogous conjecture in the four-dimensional case is equivalent to the Hofman-Maldacena bounds. In three dimensions, our conjecture gives rise to similar bounds on the quotients of various constants characterizing the CFT. In particular, it implies that the quotient of the stress-tensor two-point function coefficient and the sphere free energy satisfies $C_{ \scriptscriptstyle T} / F_0 \leq 3/ (4π^2 \log 2 - 6ζ[3]) \simeq 0.14887$ for general CFTs. We verify the validity of this bound for free scalars and fermions, general $O(N)$ and Gross-Neveu models, holographic theories, $\mathcal{N}=2$ Wess-Zumino models and general ABJM theories.

hep-th↗

arXiv2023

Irreversibility, QNEC, and defects

We first present an analysis of infinitesimal null deformations for the entanglement entropy, which leads to a major simplification of the proof of the $C$, $F$ and $A$-theorems in quantum field theory. Next, we study the quantum null energy condition (QNEC) on the light-cone for a CFT. Finally, we combine these tools in order to establish the irreversibility of renormalization group flows on planar $d$-dimensional defects, embedded in $D$-dimensional conformal field theories. This proof completes and unifies all known defect irreversibility theorems for defect dimensions $d\le 4$. The F-theorem on defects ($d=3$) is a new result using information-theoretic methods. For $d \ge 4$ we also establish the monotonicity of the relative entropy coefficient proportional to $R^{d-4}$. The geometric construction connects the proof of irreversibility with and without defects through the QNEC inequality in the bulk, and makes contact with the proof of strong subadditivity of holographic entropy taking into account quantum corrections.

hep-th↗

arXiv2023

Lectures on entanglement in quantum field theory

These notes grew from a series of lectures given by the authors during the last decade. They will be published in the proceedings of TASI 2021. After a brief introduction to quantum information theory tools, they are organized in four chapters covering the following subjects: Entanglement in quantum field theory, Irreversibility theorems, Energy-entropy bounds, Entanglement and symmetries.

hep-th↗

arXiv2023

The entropic $g$-theorem in general spacetime dimension

We establish the irreversibility of renormalization group flows on a pointlike defect inserted in a $d$-dimensional Lorentzian conformal field theory. We identify the impurity entropy $g$ with the quantum relative entropy in two equivalent ways. One involves a null deformation of the Cauchy surface, and the other is given in terms of a local quench protocol. Positivity and monotonicity of the relative entropy imply that $g$ decreases monotonically along renormalization group flows, and provides a clear information-theoretic meaning for this irreversibility.

hep-th↗

arXiv2023

Charges in the UV completion of neutral electrodynamics

A theory with a non-compact form-symmetry is described by two closed form fields of degrees k and d-k. Effective theory examples are non-linear electrodynamics, a photon field coupled to a neutron field, and a low energy Goldstone boson. We show these models cannot be completed in the UV without breaking the non-compact form-symmetry down to a compact one. This amounts to the existence of electric or magnetic charges. A theory with an unbroken non-compact k-form symmetry is massless and free.

hep-th↗

arXiv2023

Reflected entropy, symmetries and free fermions

Exploiting the split property of quantum field theories (QFTs), a notion of von Neumann entropy associated to pairs of spatial subregions has been recently proposed both in the holographic context -- where it has been argued to be related to the entanglement wedge cross section -- and for general QFTs. We argue that the definition of this "reflected entropy" can be canonically generalized in a way which is particularly suitable for orbifold theories -- those obtained by restricting the full algebra of operators to those which are neutral under a global symmetry group. This turns out to be given by the full-theory reflected entropy minus an entropy associated to the expectation value of the "twist" operator implementing the symmetry operation. Then we show that the reflected entropy for Gaussian fermion systems can be simply written in terms of correlation functions and we evaluate it numerically for two intervals in the case of a two-dimensional Dirac field as a function of the conformal cross-ratio. Finally, we explain how the aforementioned twist operators can be constructed and we compute the corresponding expectation value and reflected entropy numerically in the case of the $\mathbb{Z}_2$ bosonic subalgebra of the Dirac field.

hep-th↗

arXiv2022

Mutual Information of Generalized Free Fields

We study generalized free fields (GFF) from the point of view of information measures. We first review conformal GFF, their holographic representation, and the ambiguities in the assignation of algebras to regions that arise in these theories. Then we study the mutual information (MI) in several geometric configurations. The MI displays unusual features at the short distance limit: a leading volume term rather than an area term, and a logarithmic term in any dimensions rather than only for even dimensions as in ordinary CFT's. We find the dependence of some subleading terms on the conformal dimension $Δ$ of the GFF. We study the long distance limit of the MI for regions with boundary in the null cone. The pinching limit of these surfaces show the GFF behaves as an interacting model from the MI point of view. The pinching exponents depend on the choice of algebra. The entanglement wedge algebra choice allows these models to ``fake'' causality, giving results consistent with its role in the description of large $N$ models.

hep-th↗

arXiv2022

Generalized symmetries and Noether's theorem in QFT

We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether's theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). We use these results to rederive Weinberg-Witten's theorem within local QFT, generalizing it to massless particles in arbitrary dimensions and representations of the Lorentz group. Several examples with local twists but without Noether currents are described. We end up discussing the conditions for the strong version to hold, dynamical aspects of QFT's with non-compact generalized symmetries, scale vs conformal invariance in QFT, connections with the Coleman-Mandula theorem and aspects of global symmetries in quantum gravity.

hep-th↗