arXiv subjects

Javier M. Magan

Publications and source records attributed to Javier M. Magan.

At least 19 recordsLinked to original sources

arXiv2026

Non-invertible symmetries and selection rules for RG flows of coset models

We analyze superselection sectors, non-invertible symmetries and selection rules for RG flows triggered via perturbations of a UV two-dimensional conformal field theory (CFT$_2$). To this end we describe a method whose input is the local data, and whose output is the set of submodels of the modular invariant completions. We explain how this output set provides a classification of superselection sectors (DHR categories and Q-systems) and of topological defect lines, leading to a unified and potentially complete approach to selection rules for RG flows. This method is applied to scenarios in which the UV is a coset or a parafermion model. For these CFT$_2$ we explicitly find all submodels of the diagonal modular invariants. Our results gives selection rules that unify several known facts about such RG flows, while also allowing us to find new aspects.

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arXiv2025

Quantum microstate counting from Brownian motion: from many-body systems to black holes

We introduce a new way to produce infinite families of bases of a quantum system's Hilbert space, as well as methods to find its dimension. These families are constructed via Brownian motions in the Hilbert space, defined using disordered, time-dependent couplings. The dimension spanned by them has zero variance over the ensemble of disordered couplings, and it is determined by certain replica partition functions. We apply these methods to finite dimensional $q$-local systems (spin clusters and SYK) and black holes. For $q$-local systems we find exact expressions at finite $q$, $N$, and $t$, for replica partition functions, together with universal behavior at large times and a semiclassical analysis at large-$N$ in appropriate master field variables. The right Hilbert space dimension is obtained for any time $t>0$, $q>1$ and $N>0$. For black holes, the Brownian motions prepare quantitatively generic ensembles of black hole microstates, and the Bekenstein-Hawking entropy is universally reproduced by counting those. There the $n$-replica partition functions are constructed by gluing $n$-traversable womrholes at their future and past. This method demonstrates the robustness of black hole microstate counting methods, avoiding several limitations of previous constructions, including the non-genericity of the microstates and associated interiors, implicit statistics of heavy operators, limited microscopic control over overlaps, and the need for specific limits in the calculation.

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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.

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arXiv2025

ER for typical EPR

What do the typical entangled states of two black holes look like? Do they contain semiclassical interiors? We approach these questions constructively, providing ensembles of states which densely explore the black hole Hilbert space. The states contain very long Einstein-Rosen (ER) caterpillars: semiclassical wormholes with large numbers of matter inhomogeneities. Distinguishing these ensembles from the typical entangled states of the black holes is hard. We quantify this by deriving the correspondence between a microscopic notion of quantum randomness and the geometric length of the wormhole. This formalizes a ``complexity = geometry'' relation.

hep-th↗

arXiv2025

Random Circuits in the Black Hole Interior

In this paper, we present a quantitative holographic relation between a microscopic measure of randomness and the geometric length of the wormhole in the black hole interior. To this end, we perturb an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. We use the random circuit to prepare ensembles of states of the black hole whose semiclassical duals contain Einstein-Rosen (ER) caterpillars: long cylindrical wormholes with large numbers of matter inhomogeneities, of linearly growing length with the circuit time. In this setup, we show semiclassically that the ensemble of ER caterpillars of average length $k\ell_Δ$ and matter correlation scale $\ell_Δ$ forms an approximate quantum state $k$-design of the black hole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. We comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.

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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.

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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.

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arXiv2024

Spread complexity and the saturation of wormhole size

Recent proposals equate the size of Einstein-Rosen bridges in JT gravity to spread complexity of a dual, double-scaled SYK theory (DSSYK). We show that the auxiliary ``chord basis'' of these proposals is an extrapolation from a sub-exponential part of the finite-dimensional physical Krylov basis of a spreading thermofield double state. The physical tridiagonal Hamiltonian coincides with the DSSYK approximation on the initial Krylov basis, but deviates markedly over an exponentially large part of the state space. We non-perturbatively extend the identification of ER bridge size and spread complexity to the complete Hilbert space, and show that it saturates at late times. We use methods for tridiagonalizing random Hamiltonians to study all universality classes to which large N SYK theories and JT gravities can belong. The saturation dynamics depends on the universality class, and displays ``white hole'' physics at late times where the ER bridge shrinks from maximum size to a plateau. We describe extensions of our results to higher dimensions.

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arXiv2024

Two types of quantum chaos: testing the limits of the Bohigas-Giannoni-Schmit conjecture

There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The first type controls the early-time physics, e.g. the thermal relaxation and the sensitivity of the system to initial conditions. It can be traced back to the Eigenstate Thermalization Hypothesis (ETH), a statistical hypothesis about the eigenvectors of the Hamiltonian. The second type concerns very late-time physics, e.g. the ramp of the Spectral Form Factor. It can be traced back to Random Matrix Universality (RMU), a statistical hypothesis about the eigenvalues of the Hamiltonian. The Bohigas-Giannoni-Schmit (BGS) conjecture asserts a direct relationship between the two types of chaos for quantum systems with a chaotic semiclassical limit. The BGS conjecture is challenged by the Poissonian Hamiltonian ensembles, which can be used to model any quantum system displaying RMU. In this paper, we start by analyzing further aspects of such ensembles. On general and numerical grounds, we argue that these ensembles can have chaotic semiclassical limits. We then study the Poissonian ensemble associated with the Sachdev-Ye-Kitaev (SYK) model. While the distribution of couplings peaks around the original SYK model, the Poissonian ensemble is not $k$-local. This suggests that the link between ETH and RMU requires of physical $k$-locality as an assumption. We test this hypothesis by modifying the couplings of the SYK Hamiltonian via the Metropolis algorithm, rewarding directions in the space of couplings that do not display RMU. The numerics converge to a $k$-local Hamiltonian with eigenbasis chaos but without spectral chaos. We finally comment on ways out and corollaries of our results.

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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.

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arXiv2024

Tearing down spacetime with quantum disentanglement

A longstanding enigma within AdS/CFT concerns the entanglement entropy of holographic quantum fields in Rindler space. The vacuum of a quantum field in Minkowski spacetime can be viewed as an entangled thermofield double of two Rindler wedges at a temperature $T=1/2π$. We can gradually disentangle the state by lowering this temperature, and the entanglement entropy should vanish in the limit $T\to 0$ to the Boulware vacuum. However, holography yields a non-zero entanglement entropy at arbitrarily low $T$, since the bridge in the bulk between the two wedges retains a finite width. We show how this is resolved by bulk quantum effects of the same kind that affect the entropy of near-extremal black holes. Specifically, a Weyl transformation maps the holographic Boulware states to near-extremal hyperbolic black holes. A reduction to an effective two-dimensional theory captures the large quantum fluctuations in the geometry of the bridge, which bring down to zero the density of entangled states in the Boulware vacuum. Using another Weyl transformation, we construct unentangled Boulware states in de Sitter space.

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arXiv2024

Universal Construction of Black Hole Microstates

We refine and extend a recent construction of sets of black hole microstates with semiclassical interiors that span a Hilbert space of dimension $e^S$, where $S$ is the black hole entropy. We elaborate on the definition and properties of microstates in statistical and black hole mechanics. The gravitational description of microstates employs matter shells in the interior of the black hole, and we argue that in the limit where the shells are very heavy, the construction acquires universal validity. To this end, we show it for very wide classes of black holes: we first extend the construction to rotating and charged black holes, including extremal and near-extremal solutions, with or without supersymmetry, and we sketch how the construction of microstates can be embedded in String Theory. We then describe how the approach can include general quantum corrections, near or far from extremality. For supersymmetric black holes, the microstates we construct differ from other recent constructions in that the interior excitations are not confined within the near-extremal throat.

hep-th↗

arXiv2023

Quantum chaos, integrability, and late times in the Krylov basis

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum chaotic systems display a Lanczos spectrum whose local means and covariances are well described by RMT. To support this proposal, we first demonstrate its validity in examples of chaotic and integrable systems. We then show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffices to produce the full long time behavior of general survival probabilities including the spectral form factor, as well as the spread complexity. In addition, for initial states with continuous overlap with energy eigenstates, we analytically find the long time averages of the probabilities of Krylov basis elements in terms of the mean Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos. Finally, we clarify the relation between spread complexity and the universality classes of RMT by exploring various values of the Dyson index and Poisson distributed spectra.

hep-th↗

arXiv2023

Microscopic origin of the entropy of astrophysical black holes

We construct an infinite family of microstates for black holes in Minkowski spacetime which have effective semiclassical descriptions in terms of collapsing dust shells in the black hole interior. Quantum mechanical wormholes cause these states to have exponentially small, but universal, overlaps. We show that these overlaps imply that the microstates span a Hilbert space of log dimension equal to the event horizon area divided by four times the Newton constant, explaining the statistical origin of the Bekenstein-Hawking entropy.

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arXiv2023

Microscopic origin of the entropy of black holes in general relativity

We construct an infinite family of microstates with geometric interiors for eternal black holes in general relativity with negative cosmological constant in any dimension. Wormholes in the Euclidean path integral for gravity cause these states to have small, but non-zero, quantum mechanical overlaps that have a universal form. The overlaps have a dramatic consequence: the microstates span a Hilbert space of log dimension equal to the Bekenstein-Hawking entropy. The semiclassical microstates we construct contain Einstein-Rosen bridges of arbitrary size behind their horizons. Our results imply that all these bridges can be interpreted as quantum superpositions of wormholes of size at most exponential in the entropy.

hep-th↗

arXiv2023

Krylov complexity of modular Hamiltonian evolution

We investigate the complexity of states and operators evolved with the modular Hamiltonian by using the Krylov basis. In the first part, we formulate the problem for states and analyse different examples, including quantum mechanics, two-dimensional conformal field theories and random modular Hamiltonians, focusing on relations with the entanglement spectrum. We find that the modular Lanczos spectrum provides a different approach to quantum entanglement, opening new avenues in many-body systems and holography. In the second part, we focus on the modular evolution of operators and states excited by local operators in two-dimensional conformal field theories. We find that, at late modular time, the spread complexity is universally governed by the modular Lyapunov exponent $λ^{mod}_L=2π$ and is proportional to the local temperature of the modular Hamiltonian. Our analysis provides explicit examples where entanglement entropy is indeed not enough, however the entanglement spectrum is, and encodes the same information as complexity.

hep-th↗

arXiv2023

Generalized Symmetries For Generalized Gravitons

We construct generalized symmetries for linearized Einstein gravity in arbitrary dimensions. First-principle considerations in QFT force generalized symmetries to appear in dual pairs. Verifying this prediction helps us find the full set of non-trivial conserved charges -- associated, in equal parts, with 2-form and $(D-2)$-form currents. Their total number is $D(D+1)$. We compute the quantum commutators of pairs of dual charges, showing that they are non-vanishing for regions whose boundaries are non-trivially linked with each other and zero otherwise, as expected on general grounds. We also consider general linearized higher-curvature gravities. These propagate, in addition to the usual graviton, a spin-0 mode as well as a massive ghost-like spin-2 one. When the latter is absent, the theory is unitary and the dual-pairs principle is respected. In particular, we find that the number and types of charges remain the same as for Einstein gravity, and that they correspond to continuous generalizations of the Einsteinian ones.

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.

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