arXiv subjects

Jonathan J. Heckman

Publications and source records attributed to Jonathan J. Heckman.

At least 37 records · Page 2Linked to original sources

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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arXiv2025

Celestial Topology, Symmetry Theories, and Evidence for a Non-SUSY D3-Brane CFT

Symmetry Theories (SymThs) provide a flexible framework for analyzing the global categorical symmetries of a $D$-dimensional QFT$_{D}$ in terms of a $(D+1)$-dimensional bulk system SymTh$_{D+1}$. In QFTs realized via local string backgrounds, these SymThs naturally arise from dimensional reduction of the linking boundary geometry. To track possible time dependent effects we introduce a celestial generalization of the standard "boundary at infinity" of a SymTh. As an application of these considerations we revisit large $N$ quiver gauge theories realized by spacetime filling D3-branes probing a non-supersymmetric orbifold $\mathbb{R}^6 / Γ$. Comparing the imprint of symmetry breaking on the celestial geometry at small and large 't Hooft coupling we find evidence for an intermediate symmetry preserving conformal fixed point.

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arXiv2025

6d Large Charge and 2d Virasoro Blocks

We compute observables in the interacting rank-one 6d $\mathcal{N}=(2,0)$ SCFT at large R-charge. We focus on correlators involving $Φ^n$, namely symmetric products of the bottom component of the supermultiplet containing the stress-tensor. By using the moduli space effective action and methods from the large-charge expansion, we compute the OPE coefficients $\langleΦ^nΦ^mΦ^{n+m}\rangle$ in an expansion in 1/n. The coefficients of the expansion are only partially determined from the 6d perspective, but we manage to fix them order-by-order in 1/n numerically by utilizing the 6d/2d correspondence. This is made possible by the fact that this $6d$ observable can be extracted in 2d from a specific double-scaling limit of the vacuum Virasoro block, which can be efficiently computed numerically. We also extend the computation to higher-rank SCFTs, and discuss various applications of our results to 6d as well as 2d.

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arXiv2024

First Constraints on a Pixelated Universe in Light of DESI

Pixelated dark energy is a string theory scenario with a quantum mechanically stable cosmological constant. The number of pixels that make up the universe slowly increases, manifesting as a time-dependent source of dark energy. DESI has recently reported evidence for dynamical dark energy that fits within this framework. In light of this, we perform the first cosmological analysis of the pixelated model. We find that the simplest model where the pixel growth rate is constant is able to accommodate the data, providing a marginally better fit than $Λ$CDM; and we show that models where the pixel growth rate is increasing and of order the Hubble constant today could provide better fits. Our analysis helps to clarify the features of UV constructions of dark energy necessary to accommodate the data.

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arXiv2024

On the Holographic Dual of a Topological Symmetry Operator

We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction we argue that the bulk counterpart has a non-topological worldvolume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global $p$-form symmetries for $p \geq 0$ in asymptotically AdS spacetimes, which includes the case of non-invertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, $(-m)$-form symmetries for $m \geq 2$.

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arXiv2024

The Dark Dimension and the Grand Unification of Forces

The dark dimension scenario, predicting one extra mesoscopic dimension in the micron range, has emerged by applying various Swampland principles to the dark energy. In this note we find that realizing the grand unification of gauge forces is highly constraining in this context. Without actually constructing any GUT models, we argue that the mere assumption of grand unification of forces in this scenario, together with the experimental bounds on massive replicas of the Standard Model gauge bosons, predicts an upper bound for the GUT scale, $M_{GUT}\lesssim 10^{16}\ {\rm GeV}$. Combined with the experimental bound on the proton lifetime, this predicts that the $X$ gauge boson mediating proton decay is a 5d solitonic string of Planckian tension stretched across a length scale $L\sim ({\rm 1-10\ TeV})^{-1}$ ending on gauge branes of the same diameter $\sim L$. This leads to a mass of $M_X\sim 10^{15}-10^{16}\ {\rm GeV}$. In particular assuming grand unification in the dark dimension scenario results in a tower of Kaluza-Klein excitations of Standard Model gauge bosons on the gauge branes in the 1-10 TeV range. This suggests that the diameter/separation $L$ of the gauge branes correlates with both the weak scale $\sim 1/L$ near a TeV {\it and} the GUT scale $\sim M_5^2 L$ at $10^{16}\ {\rm GeV}$.

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arXiv2024

Cornering Relative Symmetry Theories

The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated $(d+1)$-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in $D = d+m$ dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, with the original QFT degrees of freedom localized at a corner of this $D$-dimensional bulk system. We present a bottom up characterization of this structure and also show how it naturally arises in a number of string-based constructions of QFTs with both finite and continuous symmetries.

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arXiv2024

Top Down Approach to Topological Duality Defects

Topological duality defects arise as codimension one generalized symmetry operators in quantum field theories (QFTs) with a duality symmetry. Recent investigations have shown that in the case of 4D $\mathcal{N} = 4$ Super Yang-Mills (SYM) theory, an appropriate choice of (complexified) gauge coupling and global form of the gauge group can lead to a rather rich fusion algebra for the associated defects, leading to examples of non-invertible symmetries. In this work we present a top down construction of these duality defects which generalizes to QFTs with lower supersymmetry, where other 0-form symmetries are often present. We realize the QFTs of interest via D3-branes probing $X$ a Calabi-Yau threefold cone with an isolated singularity at the tip of the cone. The IIB duality group descends to dualities of the 4D worldvolume theory. Non-trivial codimension one topological interfaces arise from configurations of 7-branes "at infinity" which implement a suitable $SL(2, \mathbb{Z})$ transformation when they are crossed. Reduction on the boundary topology $\partial X$ results in a 5D symmetry TFT. Different realizations of duality defects, such as the gauging of 1-form symmetries with certain mixed anomalies and half-space gauging constructions, simply amount to distinct choices of where to place the branch cuts in the 5D bulk.

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arXiv2024

R7-Branes as Charge Conjugation Operators

R7-branes are a class of recently discovered non-supersymmetric real codimension-two duality defects in type IIB string theory predicted by the Swampland Cobordism Conjecture. For type IIB realizations of 6D SCFTs with $\mathcal{N} = (2,0)$ supersymmetry, wrapping an R7-brane "at infinity" leads to a topological operator associated with a zero-form charge conjugation symmetry that squares to the identity. Similar considerations hold for those theories obtained from further toroidal compactification, but this can be obstructed by bundle curvature effects. Using some minimal data on the topological sector of the R7-branes, we extract the associated fusion rules for these charge conjugation operators. More broadly, we sketch a top down realization of various topological operators / interfaces associated with $\mathsf{C}$, $\mathsf{R}$, and $\mathsf{T}$ transformations. We also use holography to provide strong evidence for the existence of the R7-brane which is complementary to the Cobordism Conjecture. Similar considerations apply to other string-realized QFTs with symmetry operators constructed via non-supersymmetric branes which carry a conserved charge.

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arXiv2024

On the Fate of Stringy Non-Invertible Symmetries

Non-invertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of non-invertible gauge symmetries? In theories with gravity we find a new form of non-invertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy non-invertible gauge symmetries appear in standard examples such as non-abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of non-invertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate non-invertible symmetries have implications for Swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the Distance Conjecture, and can sometimes explain the existence of slightly sub-extremal states which fill in the gaps in the sublattice Weak Gravity Conjecture.

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arXiv2024

SymTrees and Multi-Sector QFTs

The global symmetries of a $D$-dimensional QFT can, in many cases, be captured in terms of a $(D+1)$-dimensional symmetry topological field theory (SymTFT). In this work we construct a $(D+1)$-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly non-topological junctions. In string-realized multi-sector QFTs, these junctions are smoothed out in the extra-dimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large $M$ averaging where the topological sectors of different large $M$ replicas become dressed by additional extended operators associated with the SymTree.

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arXiv2023

The Branes Behind Generalized Symmetry Operators

The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry $X$, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary $\partial X$. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in $\partial X$. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

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arXiv2023

Generalized Symmetries, Gravity, and the Swampland

Generalized global symmetries are a common feature of many quantum field theories decoupled from gravity. By contrast, in quantum gravity / the Swampland program, it is widely expected that all global symmetries are either gauged or broken, and this breaking is in turn related to the expected completeness of the spectrum of charged states in quantum gravity. We investigate the fate of such symmetries in the context of 7D and 5D vacua realized by compact Calabi-Yau spaces with localized singularities in M-theory. We explicitly show how gravitational backgrounds support additional dynamical degrees of freedom which trivialize (i.e.,"break") the higher symmetries of the local geometric models. Local compatability conditions across these different sectors lead to gluing conditions for gauging higher-form and (in the 5D case) higher-group symmetries. This also leads to a preferred global structure of the gauge group and higher-form gauge symmetries. In cases based on a genus-one fibered Calabi-Yau space, we also get an F-theory model in one higher dimension with corresponding constraints on the global form of the gauge group.

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arXiv2023

Super-Spin Chains for 6D SCFTs

Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to extract a protected large R-charge subsector of operators, with operator mixing controlled at leading order in an inverse large R-charge expansion by an integrable spin $s$ Heisenberg spin chain, where $s$ is determined by the $\mathfrak{su}(2)_{R}$ R-symmetry representation of the conformal matter operator. In this work, we show that this same structure extends to the full superconformal algebra $\mathfrak{osp}(6,2|1)$. In particular, we determine the corresponding Bethe ansatz equations which govern this super-spin chain, as well as distinguished subsectors which close under operator mixing. Similar considerations extend to 6D little string theories (LSTs) and 4D $\mathcal{N} = 2$ SCFTs with the same generalized quiver structures.

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arXiv2023

IIB Explored: Reflection 7-Branes

The Swampland Cobordism Conjecture successfully predicts the supersymmetric spectrum of 7-branes of IIB / F-theory. Including reflections on the F-theory torus, it also predicts the existence of new non-supersymmetric objects, which we dub reflection 7-branes (R7-branes). We present evidence that these R7-branes only exist at strong coupling. R7-branes serve as end of the world branes for 9D theories obtained from type IIB asymmetric orbifold and Dabholkar-Park orientifold backgrounds, and an anomaly inflow analysis suggests the existence of a gapless Weyl fermion, which would have the quantum numbers of a goldstino. Using general arguments, we conclude that different kinds of branes are able to end on the R7, and accounting for their charge requires exotic localized degrees of freedom, for which the simplest possibility is a massless 3-form field on the R7-brane worldvolume. We also show how to generalize the standard F-theory formalism to account for reflections.

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arXiv2023

0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds

Orbifold singularities of M-theory constitute the building blocks of a broad class of supersymmetric quantum field theories (SQFTs). In this paper we show how the local data of these geometries determines global data on the resulting higher symmetries of these systems. In particular, via a process of cutting and gluing, we show how local orbifold singularities encode the 0-form, 1-form and 2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from the possible singularities which extend to the boundary of the non-compact geometry. The resulting category of boundary conditions then captures these symmetries, and is equivalently specified by the orbifold homology of the boundary geometry. We illustrate these general points in the context of a number of examples, including 5D superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as 4D SQCD-like theories engineered via M-theory on non-compact $G_2$ spaces.

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arXiv2023

Fluxbranes, Generalized Symmetries, and Verlinde's Metastable Monopole

The stringy realization of generalized symmetry operators involves wrapping "branes at infinity". We argue that in the case of continuous (as opposed to discrete) symmetries, the appropriate objects are fluxbranes. We use this perspective to revisit the phase structure of Verlinde's monopole, a proposed particle which is BPS when gravity is decoupled, but is non-BPS and metastable when gravity is switched on. Geometrically, this monopole is obtained from branes wrapped on locally stable but globally trivial cycles of a compactification geometry. The fluxbrane picture allows us to characterize electric (resp. magnetic) confinement (resp. screening) in the 4D theory as a result of monopole decay. In the presence of the fluxbrane, this decay also creates lower-dimensional fluxbranes, which in the field theory is interpreted as the creation of an additional topological field theory sector.

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