arXiv subjects

Jonathan J. Heckman

Publications and source records attributed to Jonathan J. Heckman.

At least 19 recordsLinked to original sources

arXiv2026

Learning to Trace Seiberg Dualities

Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems. In practice, though, it can often be computationally challenging to establish when two systems are dual, even when all of the "rules of the game" are well-known. Said differently, when confronted with two systems, how can one efficiently establish that they are in fact dual? In this paper we use machine learning methods to address this question for Seiberg dualities of supersymmetric quiver gauge theories. Mathematically, this involves establishing mutations of quivers, which is in turn a variation on the theme of "learning to unknot". On the one hand, this leads us to a practical tool for establishing the computational complexity of different dualities. On the other hand, it also allows us to study how different network architectures learn how to trace Seiberg dualities. We find that for quivers with a modest number of quiver nodes (of order $10$), different network architectures consisting of transformers and multi-layer perceptrons tend to outperform deterministic algorithms. Supplementing the network by well-established pathfinder algorithms (essentially "Google Maps for quivers") leads to an additional improvement in the efficiency and accuracy of the search strategy. We anticipate that this class of questions can serve as a useful benchmark for frontier AI models applied to theoretical physics.

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arXiv2026

Gravitational Background of Alice-Vortices and R7-Branes

Codimension-two vortex solutions are important solitonic objects in both quantum field theory and gravity. In this paper, we construct a class of codimension-two Alice-vortex solutions in axio-dilaton gravity, in which monodromy around the vortex enacts the axion transformation $C_0 \mapsto -C_0$. In IIB supergravity, this furnishes a class of R7-brane backgrounds of the sort predicted by the Swampland Cobordism Conjecture. Such configurations generically carry an intrinsic dipole moment. We extract additional properties of such branes from scattering probes. These results provide further evidence that the worldvolume theory of an R7-brane is an 8D non-supersymmetric interacting quantum field theory.

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arXiv2026

Controlled Chaos in 4D SCFTs

Chaotic dynamics play an important role in a number of physical systems. One of the qualitative hallmarks of this behavior is the appearance of a sufficiently "complex" spectrum of energy levels. This also makes it challenging to directly verify the onset of chaos in interacting quantum field theories. We present a class of 4D superconformal field theories (SCFTs) given by orbifolds of 4D $\mathcal{N} = 4$ Super Yang--Mills theory in which operator mixing in a controlled subsector is described by an effective spin chain in one spatial dimension with nearest neighbor interactions tuned by the marginal couplings of the SCFT. Tuning the marginal couplings results in a chaotic spectrum, while generically the spin chain exhibits Anderson localization. We diagnose the onset of chaos by analyzing the statistical distribution of eigenvalues of the dilatation operator, in particular properties such as eigenvalue level repulsion, spectral rigidity, and the spectral form factor. We also show that other diagnostics such as Krylov complexity sometimes do not faithfully capture this information. This structure defines a chaotic billiard in the target space of the stringy realization. We also comment on the large $N$ holographic dual description, where the controlled single spin chain approximation must be supplemented by multi-trace dynamics, i.e., the splitting and joining of multiple spin chains.

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arXiv2026

Quiver Approach to Symmetry Theories

Global symmetry anomalies of a quantum field theory (QFT) can be packaged as specific couplings of a higher-dimensional symmetry theory (SymTh). In this work we show that for 5D superconformal field theories (SCFTs) engineered from M-theory backgrounds $X$ a Calabi-Yau cone, this data can be extracted from the path algebra of branes probing $X$. This provides a complementary algebraic approach compared with more geometric computations based on the explicit calculation of triple intersection numbers in a resolved geometry and / or $η$-invariants extracted from the boundary geometry $\partial X$. Our method applies in situations where the counterpart geometric computation is either unknown or combinatorially unwieldy. We illustrate with several toric threefold examples, including orbifolds $\mathbb{C}^{3} / Γ$ and more general non-orbifold Calabi-Yau cones of Sasaki-Einstein five-manifolds.

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arXiv2026

Generalized Complexity Distances and Non-Invertible Symmetries

Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states define a collection of quantum gates for a parallel quantum computation scheme that includes post-selection / projection as a gate. Structures such as gate complexity and more geometric complexity measures generalize to this setting. We provide a class of distance / distinguishability measures that extend the standard notion of distance for Lie groups to both continuous and discrete non-invertible symmetries, as well as more general linear combinations of unitary quantum gates. We illustrate these considerations by computing the distance between non-invertible symmetries in some 4D and 2D QFTs. We find that the simple objects of a symmetry category can be highly complex computationally.

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arXiv2026

On the SymTFTs of Finite Non-Abelian Symmetries

The $(D+1)$-dimensional symmetry topological field theory (SymTFT$_{D+1}$) of a $D$-dimensional absolute quantum field theory (QFT$_D$) provides a topological characterization of symmetry data. In this framework, the SymTFT comes equipped with a physical boundary specifying a relative QFT, and a topological boundary which specifies the global form of symmetries. In general, there need not be a unique bulk theory which encodes this information but it is often helpful to have a more manifest presentation of symmetries in terms of bulk degrees of freedom. For the case of a finite non-Abelian symmetry group $G$, the bulk SymTFT may be described by a Dijkgraaf-Witten TFT with gauge group $G$. This makes manifest the ``electric'' presentation of the symmetry data but can obscure some of the magnetic data as well as non-Abelian structure present in the absolute QFT$_D$ such as symmetry operators which cannot fully detach from the topological boundary. We address these issues for 3D SymTFTs by constructing discrete BF-like theory Lagrangians for finite groups which admit a presentation as an extension by a finite Abelian group and a finite (possibly non-Abelian) group. This enables us to give a streamlined approach to reconstructing the fusion rules of the accompanying Drinfeld center, but also allows us to construct surface-attaching non-genuine line operators associated directly with non-Abelian group elements rather than just their conjugacy classes. We also sketch how our treatment generalizes to higher-dimensional SymTFTs.

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arXiv2026

Extra-Dimensional η-Invariants and Anomaly Theories

Anomalies of a quantum field theory (QFT) constitute fundamental non-perturbatively robust data. In this paper we extract anomalies of 5D superconformal field theories (SCFTs) directly from the underlying extra-dimensional geometry. We show that all of this information can be efficiently extracted from extra-dimensional $η$-invariants, bypassing previously established approaches based on computationally cumbersome blowup / resolution techniques. We illustrate these considerations for 5D SCFTs engineered in M-theory by non-compact geometries $X=\mathbb{C}^3/Γ$ with finite subgroup $Γ\subset SU(3)$, where the anomalies are determined by the $η$-invariants of the asymptotic boundary $\partial X=S^5/Γ$. Our results apply equally to Abelian and non-Abelian $Γ$, as well as isolated and non-isolated singularities. In the setting of non-isolated singularities we further analyze the interplay of anomaly structures across different strata of the singular locus. Our considerations extend readily to backgrounds which are not global orbifolds, as well as those which do not preserve supersymmetry.

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arXiv2026

Exploring Pintopia: Reflection Branes, Bordisms, and U-Dualities

The U-dualities of maximally supersymmetric non-chiral supergravity (SUGRA) theories lead to strong constraints on the non-perturbative structure of quantum gravity. In this paper we determine Spin- and Pin-lifts of these dualities, which extend this action to fermionic degrees of freedom. Among other things, this allows us to access non-supersymmetric sectors of these low energy effective field theories in which bosonic and fermionic degrees of freedom are treated differently. We use this refinement of the duality groups, in tandem with the Swampland Cobordism Conjecture, to predict new codimension-two branes. These are a natural generalization of the recently discovered R7-branes of type II string theories. The first bordism groups for Spin-twisted duality bundles follow directly from the Abelianization of the duality groups. Viewing the SUGRA theory as the low energy limit of a toroidal compactification of M-theory, winding around these codimension-two defects enacts a reflection around one of the torus directions, which in the effective field theory appears as a charge conjugation symmetry. We establish some basic properties of such branes, including determining BPS objects which can end on it, as well as braiding rules and bound states realized by multiple reflection branes.

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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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arXiv2026

GSO Defects: IIA/IIB Walls and the Surprisingly Stable $\mathrm{R}7$-Brane

The recently proposed Swampland Cobordism Conjecture predicts the existence of new non-supersymmetric objects which supplement the spectrum of low-energy gravitational effective field theories. In this paper, we study a subset of these defects related to the GSO projection on the string worldsheet. These include the predicted domain wall between Type IIA and IIB superstring theories and the newly-discovered $\mathrm{R}7$-brane. We study these defects in two different ways: via long-string probes and target-space effective field theory. We find that the $\mathrm{R}7$-brane can be identified with a collapsed cylindrical configuration of the IIA/IIB wall, and further, that the $\mathrm{R}7$-brane is stable, in contrast to previous expectations. Moreover, we argue that BPS D-branes pulled across the IIA/IIB wall become non-BPS D-branes, which we identify with fluxbrane configurations. We show that the non-BPS D-branes of either Type II theory are charged under a $\mathbb{Z}_2$ remnant of the Ramond-Ramond potentials of the other, which we identify with the mod 2 reduction of the Ramond-Ramond fluxes. Similar considerations provide a complementary perspective on the Heterotic ${\mathfrak{so}(32)}$ S-duals of known non-BPS 7- and 8-branes in Type I string theory.

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arXiv2025

Symmetry Theories, Wigner's Function, Compactification, and Holography

The global symmetry data of a $D$-dimensional absolute quantum field theory can sometimes be packaged in terms of a $(D+1)$-dimensional bulk system obtained by extending along an interval, with a relative QFT$_D$ at one end and suitable gapped / free boundary conditions at the other end. The partition function of the QFT$_D$ can then be interpreted as a wavefunction depending on background fields. However, in some cases, it is not possible or simply cumbersome to fix an absolute form of the symmetry data. Additionally, it is also of interest to consider entangled and mixed states of relative QFTs as well as entangled and mixed states of gapped / free boundary conditions. We argue that Wigner's quasi-probabilistic function on phase space provides a physical interpretation of the symmetry data in all such situations. We illustrate these considerations in the case of string compactifications and holographic systems.

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arXiv2025

On the Holographic Dual of a Symmetry Operator at Finite Temperature

Topological symmetry operators of holographic large $N$ CFT$_D$'s are dual to dynamical branes in the gravity dual AdS$_{D+1}$. We use this correspondence to establish a dictionary between thermal expectation values of symmetry operators in the Euclidean CFT$_D$ and the evaluation of gravitational saddles in the presence of a dynamical brane. Expectation values of $0$-form symmetry operators in the CFT$_D$ are then related to branes wrapped on volume minimizing cycles in the bulk, i.e., the Euclidean continuation of a black hole horizon. We illustrate with some representative examples, including gravity in AdS$_3$, duality / triality defects in 4D $\mathcal{N} = 4$ Super Yang-Mills theory, and the dual of R-symmetry operators probing 5D BPS black holes.

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arXiv2025

Top Down Approach to 6D SCFTs

Six-dimensional superconformal field theories (6D SCFTs) occupy a central place in the study of quantum field theories encountered in high energy theory. This article reviews the top down construction and study of this rich class of quantum field theories, in particular, how they are realized by suitable backgrounds in string / M- / F-theory. We review the recent F-theoretic classification of 6D SCFTs, explain how to calculate physical quantities of interest such as the anomaly polynomial of 6D SCFTs, and also explain recent progress in understanding renormalization group flows for deformations of such theories. Additional topics covered by this review include some discussion on the (weighted and signed) counting of states in these theories via superconformal indices. We also include several previously unpublished results as well as a new variant on the swampland conjecture for general quantum field theories decoupled from gravity. The aim of the article is to provide a point of entry into this growing literature rather than an exhaustive overview.

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arXiv2025

Cobordism Utopia: U-Dualities, Bordisms, and the Swampland

The U-dualities of maximally supersymmetric supergravity theories lead to celebrated non-perturbative constraints on the structure of quantum gravity. They can also lead to the presence of global symmetries since manifolds equipped with non-trivial duality bundles can carry topological charges captured by non-trivial elements of bordism groups. The recently proposed Swampland Cobordism Conjecture thus predicts the existence of new singular objects absent in the low-energy supergravity theory, which break these global symmetries. We investigate this expectation in two directions, involving the different choices of U-duality groups $G_U$, as well as $k$, the dimension of the closed manifold carrying the topological charge. First, we compute for all supergravity theories in dimension $3 \leq D \leq 11$ the bordism groups $Ω_1^{\text{Spin}}(BG_U)$. Second, we treat in detail the case of $D = 8$, computing all relevant bordism groups $Ω_k^{\text{Spin}}(BG_U)$ for $1 \leq k \leq 7$. In all cases, we identify corresponding string, M-, or F-theory backgrounds which implement the required U-duality defects. In particular, we find that in some cases there is no purely geometric background available which implements the required symmetry-breaking defect. This includes non-geometric twists as well as non-geometric strings and instantons. This computation involves several novel computations of the bordism groups for $G_U = \mathrm{SL}(2,\mathbb{Z}) \times \mathrm{SL}(3,\mathbb{Z})$, which localizes at primes $p=2,3$. Whereas an amalgamated product structure greatly simplifies the calculation of purely $\mathrm{SL}(2,\mathbb{Z})$ bundles, this does not extend to $\mathrm{SL}(3,\mathbb{Z})$. Rather, we leverage the appearance of product / ring structures induced from cyclic subgroups of $G_U$ which naturally act on the relevant bordism groups.

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arXiv2025

Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds

String / M-theory backgrounds with degrees of freedom at a localized singularity provide a general template for generating strongly correlated systems decoupled from lower-dimensional gravity. There are by now several complementary procedures for extracting the associated generalized symmetry data from orbifolds of the form $\mathbb{R}^6 / Γ$, including methods based on the boundary topology of the asymptotic geometry, as well as the adjacency matrix for fermionic degrees of freedom in the quiver gauge theory of probe branes. In this paper we show that this match between the two methods also works in non-supersymmetric and discrete torsion backgrounds. In particular, a refinement of geometric boundary data based on Chen-Ruan cohomology matches the expected answer based on quiver data. Additionally, we also show that free (i.e., non-torsion) factors count the number of higher-dimensional branes which couple to the localized singularity. We use this to also extract quadratic pairing terms in the associated symmetry theory (SymTh) for these systems, and explain how these considerations generalize to a broader class of backgrounds.

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arXiv2025

How to Falsify String Theory at a Collider

The string landscape accommodates a broad range of possible effective field theories. This poses a challenge for extracting verifiable predictions as well as falsifiable signatures of string theory. Motivated by these considerations, in this work we observe that all known stringy Standard Models support only low-dimensional representations of the gauge group. While it is in principle possible to produce contrived models with higher-dimensional representations, these generically appear in a tower of states with lighter ones in lower-dimensional representations, i.e., not in isolation. With this in mind, we consider the phenomenologically well-motivated scenario given by adding a single Majorana field in a real, $n$-dimensional representation of $SU(2)_L$ with $n \geq 5$ \textit{and nothing else}. This scenario is not realized in any known string construction, and we conjecture that this is true of string theory in general. Detection of this scenario would thus amount to falsifying the (known) string landscape. We recast existing LHC searches for new electroweak states to extract updated bounds on this class of scenarios. Improved limits from future colliders and dark matter detection experiments provide additional routes to potentially falsifying string theory.

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arXiv2025

Metric Isometries, Holography, and Continuous Symmetry Operators

In the AdS/CFT correspondence, a topological symmetry operator of the boundary CFT is dual to a dynamical brane in the gravitational bulk. Said differently, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the "internal" factor $X$ of $\text{AdS}\times X$. In the extra-dimensional geometry, these branes are associated with various metric singularities and do not arise from wrapped D-branes. Boosts relate configurations interpreted as topological symmetry operators and heavy defects in the CFT. From the perspective of the AdS factor, with gravity and bulk gauge fields, these are codimension two Gukov-Witten-like vortex configurations which are the gravity duals of 0-form symmetry operators. These effective branes come with an asymptotic tension and size which is also fully fixed by bulk dynamics. We use this higher-dimensional perspective to determine properties of the worldvolume theory for these branes. We also discuss how these considerations generalize to more general QFTs engineered via string theory which need not possess a semi-classical gravity dual.

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arXiv2025

Generalized Symmetries of Non-Supersymmetric Orbifolds

We determine generalized symmetries for 4D theories engineered via type II strings on non-supersymmetric orbifold backgrounds $\mathbb{R}^{3,1} \times \mathbb{R}^6 / Γ$. Probe branes detect generalized symmetries via the adjacency matrix for fermionic degrees of freedom in an associated quiver gauge theory. In situations where the tachyons are sequestered away from the boundary $S^5 / Γ$, this exactly matches the result extracted from singular homology. In situations with an unsequestered tachyon which stretches out to the boundary, the presence of tachyonic pulses partitions up the space into several distinct sectors, and the net contribution again matches with the answer expected via quiver methods. For IIA backgrounds, the presence of a localized closed string tachyon leads to transitions in the spectrum of states, generalized symmetries, higher-group symmetries, as well as the level matrix of the associated symmetry topological field theory (SymTFT). For IIB backgrounds with a stack of spacetime filling probe D3-branes, the onset of a radiatively generated potential leads to similar considerations involving scale dependent transitions in the symmetries of the theory, including structures such as duality defects / interfaces.

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