arXiv subjects

Jackson R. Fliss

Publications and source records attributed to Jackson R. Fliss.

At least 19 recordsLinked to original sources

arXiv2026

A spool for every quotient: One-loop partition functions in AdS$_3$ gravity

The Wilson spool is a prescription for expressing one-loop determinants as topological line operators in three-dimensional gravity. We extend this program to describe massive spinning fields on all smooth, cusp-free, solutions of Euclidean gravity with a negative cosmological constant. Our prescription makes use of the expression of such solutions as a quotients of hyperbolic space. The result is a gauge-invariant topological operator, which can be promoted to an off-shell operator in the gravitational path integral about a given saddle-point. When evaluated on-shell, the Wilson spool reproduces and extends the known results of one-loop determinants on hyperbolic quotients. We motivate our construction of the Wilson spool from multiple perspectives: the Selberg trace formula, worldline quantum mechanics, and the quasinormal mode method.

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arXiv2026

What's the Matter with 3D Gravity?

We revisit the problem of minimally coupling matter to Einstein gravity in three dimensions with negative cosmological constant. By working in the worldline formalism, we construct a classical phase space on an initial time surface $Σ$, which we quantize using geometric quantization. States in the Hilbert space correspond to Virasoro conformal blocks with operators of conformal weight $h<c/24$. As an application of our formalism, we compute the partition function on thermal $\text{AdS}_3$ through equivariant localization. Our answer reproduces the AdS$_3$ Wilson spool and agrees with the known one-loop result. It further serves as a conjecture for the value of the path integral of gravity minimally coupled to a massive scalar field in thermal $\text{AdS}_3$ to all orders in $G_N$.

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arXiv2026

Fortuity and Complexity in a Simple Quark Model

We observe and elaborate on a structural similarity between the categorization of monotone and fortuitous BPS operators in supersymmetric theories and gauge invariant quark operators in $SU(N_c)$ QCD. Our designation of fortuity does not rely on supersymmetry and instead uses the BRST cohomology. We argue that within this designation, baryon states are fortuitous while meson states are monotone. We illustrate that in the Veneziano limit of large number of flavors and colors, this designation displays features resembling the fortuitous vs. monotone categorization of BPS operators, e.g., an exponential vs. polynomial dichotomy in the counting of operators. We explore these ideas explicitly in a toy qubit model of quarks. We further investigate the stabilizer Rényi entropy of meson and baryon states as a proxy for the complexity of classical simulation for these states. We show that all mesons display power law complexity and present evidence that typical baryons display super-exponential complexity in the Veneziano limit.

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arXiv2026

Modave lectures on energy conditions in quantum field theory and semi-classical gravity

We review well known classical energy conditions and their implications for gravitational solutions, including the celebrated Hawking and Penrose singularity theorems. We then consider quantum fields coupled to gravity, where the topic becomes both richer and more subtle, as even the simplest quantum theories violate local energy conditions. We discuss directions for constraining energy densities in quantum field theories, including averaging over regions of spacetime and bounds relating energy and quantum information. We explore implications of these bounds for quantum field theory coupled to gravity as an effective theory and discuss how they guide our understanding of quantum gravity more broadly. These notes are based on a series of lectures given at the XXI Modave Summer School in Mathematical Sciences.

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arXiv2026

Medicine show: A Calogero model with principal series states

The Calogero model is an interacting, $N$-particle, $\mathfrak{sl}(2,\mathbb R)$-invariant quantum mechanics, whose Hilbert space is furnished by a tower of discrete series modules. The system enjoys both classical and quantum integrability at any $N$ and at any value of the coupling; this is guaranteed by the existence of $N$ mutually-commuting currents, one of them being the Hamiltonian. In this paper, we alter the Calogero model so that it may accommodate states in the unitary principal series irreducible representation of $\mathfrak{sl}(2,\mathbb R)$. Doing so requires changing the domain of the quantum operators--a procedure which succeeds in preserving unitarity and $\mathfrak{sl}(2,\mathbb R)$-invariance, but alters the integrability properties of the theory. We explicitly solve the deformed model for $N=2,3$ and outline a procedure for solving the model at general $N$. We expect this deformed model to provide us with general lessons that carry over to other systems with states in the principal series, for example, interacting massive quantum field theories on de Sitter space.

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arXiv2026

Curious QNEIs from QNEC: New Bounds on Null Energy in Quantum Field Theory

We derive new families of quantum null energy inequalities (QNEIs), i.e. bounds on integrated null energy, in quantum field theories in two and higher dimensions. These are universal, state-independent lower bounds on semi-local integrals of $\langle T_{vv} \rangle$, the energy-momentum flux in a null direction, and the first of this kind for interacting theories in higher dimensions. Our ingredients include the quantum null energy condition (QNEC), strong subadditivity of von Neumann entropies, defect operator expansions, and the vacuum modular Hamiltonians of null intervals and strips. These results are fundamental constraints on null energy in quantum field theories.

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arXiv2025

Matrix Quantum Mechanics and Entanglement Entropy: A Review

We review aspects of entanglement entropy in the quantum mechanics of $N\times N$ matrices, i.e. matrix quantum mechanics (MQM), at large $N$. In doing so we review standard models of MQM and their relation to string theory, D-brane physics, and emergent non-commutative geometries. We overview, in generality, definitions of subsystems and entanglement entropies in theories with gauge redundancy and discuss the additional structure required for definining subsystems in MQMs possessing a $U(N)$ gauge redundancy. In connecting these subsystems to non-commutative geometry, we review several works on `target space entanglement,' and entanglement in non-commutative field theories, highlighting the conditions in which target space entanglement entropy displays an `area law' at large $N$. We summarize several example calculations of entanglement entropy in non-commutative geometries and MQMs. We review recent work in connecting the area law entanglement of MQM to the Ryu-Takayanagi formula, highlighting the conditions in which $U(N)$ invariance implies a minimal area formula for the entanglement entropy at large $N$. Finally, we make comments on open questions and research directions.

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arXiv2025

Minimal Areas from Entangled Matrices

We define a relational notion of a subsystem in theories of matrix quantum mechanics and show how the corresponding entanglement entropy can be given as a minimisation, exhibiting many similarities to the Ryu-Takayanagi formula. Our construction brings together the physics of entanglement edge modes, noncommutative geometry and quantum internal reference frames, to define a subsystem whose reduced state is (approximately) an incoherent sum of density matrices, corresponding to distinct spatial subregions. We show that in states where geometry emerges from semiclassical matrices, this sum is dominated by the subregion with minimal boundary area. As in the Ryu-Takayanagi formula, it is the computation of the entanglement that determines the subregion. We find that coarse-graining is essential in our microscopic derivation, in order to control the proliferation of highly curved and disconnected non-geometric subregions in the sum.

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arXiv2025

Massive fields and Wilson spools in JT gravity

We give a prescription for minimally coupling massive matter to JT gravity with either sign of cosmological constant directly in its formulation as a topological BF theory. This coupling takes the form of a `Wilson spool,' originally introduced in the context of three-dimensional gravity. The Wilson spool expresses the exact one-loop partition function as the integral over a Wilson loop operator. We construct the spool by considering the partition function of a massive scalar field on Euclidean dS$_2$ and on Euclidean AdS$_2$. We discuss its extension to other geometries (including the `trumpet' and conical defect geometries) and its relation to the three-dimensional spool through dimensional reduction.

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arXiv2024

How negative can null energy be in large N CFTs?

Smeared null energy has been shown to be bounded from below for free minimally coupled quantum field theories. This is not the case for conformally coupled free bosonic theories where states of unbounded null energy can be constructed by increasing the particle number. Little is known for interacting conformal field theories (CFTs) in dimensions larger than two. In this work we consider states that are superpositions of scalar primary operators or the stress-energy tensor itself in large N CFTs. Within the large N approximation we present arguments that the negative smeared null energy of such states scales at worst as the central charge of theory, $C_T$. This provides evidence for a general bound for CFTs in d-dimensions proportional to the central charge.

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arXiv2024

Entanglement in BF theory I: Essential topological entanglement

We study the entanglement structure of Abelian topological order described by $p$-form BF theory in arbitrary dimensions. We do so directly in the low-energy topological quantum field theory by considering the algebra of topological surface operators. We define two appropriate notions of subregion operator algebras which are related by a form of electric-magnetic duality. To each subregion algebra we assign an entanglement entropy which we coin essential topological entanglement. This is a refinement to the traditional topological entanglement entropy. It is intrinsic to the theory, inherently finite, positive, and sensitive to more intricate topological features of the state and the entangling region. This paper is the first in a series of papers investigating entanglement and topological order in higher dimensions.

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arXiv2024

Entanglement in BF theory II: Edge-modes

We consider the entanglement entropy arising from edge-modes in Abelian $p$-form topological field theories in $d$ dimensions on arbitrary spatial topology and across arbitrary entangling surfaces. We find a series of descending area laws plus universal corrections proportional to the Betti numbers of the entangling surface, which can be taken as a higher-dimensional version of the "topological entanglement entropy." Our calculation comes in two flavors: firstly, through an induced edge-mode theory appearing on the regulated entangling surface in a replica path integral and secondly through a more rigorous definition of the entanglement entropy through an extended Hilbert space. Along the way we establish several key results that are of their own merit. We explain how the edge-mode theory is a novel combination of $(p-1)$-form and $(d-p-2)$-form Maxwell theories linked by a chirality condition, in what we coin a "chiral mixed Maxwell theory." We explicitly evaluate the thermal partition function of this theory. Additionally we show that the extended Hilbert space is completely organized into representations of an infinite-dimensional, centrally extended current algebra which naturally generalizes 2d Kac-Moody algebras to arbitrary dimension and topology. We construct the Verma modules and the representation characters of this algebra. Lastly, we connect the two approaches, showing that the thermal partition function of the chiral mixed Maxwell theory is precisely an extended representation character of our current algebra, establishing an exact correspondence of the edge-mode theory and the entanglement spectrum.

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arXiv2024

Keeping matter in the loop in dS$_3$ quantum gravity

We propose a mechanism that couples matter fields to three-dimensional de Sitter quantum gravity. Our construction is based on the Chern-Simons formulation of three-dimensional Euclidean gravity, and it centers on a collection of Wilson loops winding around Euclidean de Sitter space. We coin this object a Wilson spool. To construct the spool, we build novel representations of $\mathfrak{su}(2)$. To evaluate the spool, we adapt and exploit several known exact results in Chern-Simons theory. Our proposal correctly reproduces the one-loop determinant of a free massive scalar field on $S^3$ as $G_N\to 0$. Moreover, allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory.

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arXiv2024

Spinning up the spool: Massive spinning fields in 3d quantum gravity

We show how to incorporate massive spinning fields into the Euclidean path integral of three-dimensional quantum gravity via its Chern-Simons formulation. The coupling of the spinning fields to gravity is captured by a Wilson spool, a collection of Wilson loops winding around closed paths of the geometry, and generalizes the proposal of [1,2]. We present a robust derivation of the Wilson spool by providing a new group-theoretic perspective of the quasinormal mode method for one-loop determinants. We test our proposal on Euclidean BTZ and $S^3$ backgrounds. We also evaluate explicitly the quantum corrections to the path integral on $S^3$, and report on how $G_N$ and the mass are renormalized to leading order in perturbation theory.

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arXiv2023

Non-minimal coupling, negative null energy, and effective field theory

The non-minimal coupling of scalar fields to gravity has been claimed to violate energy conditions, leading to exotic phenomena such as traversable wormholes, even in classical theories. In this work we adopt the view that the non-minimal coupling can be viewed as part of an effective field theory (EFT) in which the field value is controlled by the theory's cutoff. Under this assumption, the average null energy condition, whose violation is necessary to allow traversable wormholes, is obeyed both classically and in the context of quantum field theory. In addition, we establish a type of "smeared" null energy condition in the non-minimally coupled theory, showing that the null energy averaged over a region of spacetime obeys a state dependent bound, in that it depends on the allowed field range. We finally motivate our EFT assumption by considering when the gravity plus matter path integral remains semi-classically controlled.

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arXiv2023

Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory

We propose a mechanism that couples matter fields to three-dimensional quantum gravity, which can be used for theories with a positive or negative cosmological constant. Our proposal is rooted in the Chern-Simons formulation of three-dimensional gravity and makes use of the Wilson spool, a collection of Wilson loops winding around closed paths of the background. We show that the Wilson spool correctly reproduces the one-loop determinant of a free massive scalar field on rotating black holes in AdS$_3$ and Euclidean dS$_3$ as $G_N\to 0$. Moreover, we describe how to incorporate quantum metric fluctuations into this formalism.

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arXiv2021

The double smeared null energy condition

The null energy condition (NEC), an important assumption of the Penrose singularity theorem, is violated by quantum fields. The natural generalization of the NEC in quantum field theory, the renormalized null energy averaged over a finite null segment, is known to be unbounded from below. Here, we propose an alternative, the double smeared null energy condition (DSNEC), stating that the null energy smeared over two null directions has a finite lower bound. We rigorously derive DSNEC from general worldvolume bounds for free quantum fields in Minkowski spacetime. Our method allows for future systematic inclusion of curvature corrections. As a further application of the techniques we develop, we prove additional lower bounds on the expectation values of various operators such as conserved higher spin currents. DSNEC provides a natural starting point for proving singularity theorems in semi-classical gravity.

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arXiv2021

Entanglement in the quantum Hall fluid of dipoles

We revisit a model for gapped fractonic order in (2+1) dimensions (a symmetric-traceless tensor gauge theory with conservation of dipole and trace-quadrupole moments described in \cite{Prem:2017kxc}) and compute its ground-state entanglement entropy on $\mathbb R^2$. Along the way, we quantize the theory on open subsets of $\mathbb R^2$ which gives rise to gapless edge excitations that are Lifshitz-type scalar theories. We additionally explore varieties of gauge-invariant extended operators and rephrase the fractonic physics in terms of the local deformability of these operators. We explore similarities of this model to the effective field theories describing quantum Hall fluids: in particular, quantization of dipole moments through a novel compact symmetry leads us to interpret the vacuum of this theory as a dipole condensate atop of which dipoles with fractionalized moments appear as quasi-particle excitations with Abelian anyonic statistics. This interpretation is reflected in the subleading "topological entanglement" correction to the entanglement entropy. We extend this result to a series of models with conserved multipole moments.

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