arXiv subjects

Jonathan J. Heckman

Publications and source records attributed to Jonathan J. Heckman.

At least 55 records · Page 3Linked to original sources

arXiv2023

Junctions, Edge Modes, and $G_2$-Holonomy Orbifolds

One of the general strategies for realizing a wide class of interacting QFTs is via junctions and intersections of higher-dimensional bulk theories. In the context of string/M-theory, this includes many $D > 4$ superconformal field theories (SCFTs) coupled to an IR free bulk. Gauging the flavor symmetries of these theories and allowing position dependent gauge couplings provides a general strategy for realizing novel higher-dimensional junctions of theories coupled to localized edge modes. Here, we show that M-theory on singular, asymptotically conical $G_2$-holonomy orbifolds provides a general template for realizing strongly coupled 5D bulk theories with 4D $\mathcal{N} = 1$ edge modes. This geometric approach also shows how bulk generalized symmetries are inherited in the boundary system.

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arXiv2023

The Chronicles of IIBordia: Dualities, Bordisms, and the Swampland

In this work we investigate the Swampland Cobordism Conjecture in the context of type IIB string theory geometries with non-trivial duality bundle. Quite remarkably, we find that many non-trivial bordism classes with duality bundles in Mp$(2,\mathbb{Z})$, a double cover of SL$(2,\mathbb{Z})$ related to fermions, correspond to asymptotic boundaries of well-known supersymmetric F-theory backgrounds. These include $[p,q]$-7-branes, non-Higgsable clusters, S-folds, as well as various lower-dimensional generalizations. These string theoretic objects break the global symmetries associated to the non-trivial bordism groups, providing a strong test of the Cobordism Conjecture. Further including worldsheet orientation reversal promotes the duality group to the Pin$^+$ cover of GL$(2,\mathbb{Z})$. The corresponding bordism groups require a new non-supersymmetric "reflection 7-brane" and its compactifications to ensure the absence of global symmetries, thus providing an interesting prediction of the Cobordism Conjecture for non-supersymmetric type IIB backgrounds. A major component of the present work is the explicit derivation of the involved bordism groups as well as their generators, which correspond to asymptotic boundaries of explicit string theory backgrounds. The main tool is the Adams spectral sequence, to which we provide a detailed introduction. We anticipate that the same techniques can be applied in a wide variety of settings.

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arXiv2022

Exploring $\boldsymbol{2+2}$ Answers to $\boldsymbol{3+1}$ Questions

We explore potential uses of physics formulated in Kleinian (i.e., $2+2$) signature spacetimes as a tool for understanding properties of physics in Lorentzian (i.e., $3+1$) signature. Much as Euclidean (i.e., $4+0$) signature quantities can be used to formally construct the ground state wavefunction of a Lorentzian signature quantum field theory, a similar analytic continuation to Kleinian signature constructs a state of low particle flux in the direction of analytic continuation. There is also a natural supersymmetry algebra available in $2+2$ signature, which serves to constrain the structure of correlation functions. Spontaneous breaking of Lorentz symmetry can produce various $\mathcal{N} = 1/2$ supersymmetry algebras that in $3 + 1$ signature correspond to non-supersymmetric systems. We speculate on the possible role of these structures in addressing the cosmological constant problem.

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arXiv2022

Snowmass White Paper on SCFTs

Superconformal field theories (SCFTs) occupy a central role in the study of many aspects of quantum field theory. In this white paper for the Snowmass process we give a brief overview of aspects of SCFTs in $3\leq D \leq 6$ space-time dimensions, including classification efforts and some of the vast current research trends on the physical and mathematical structures generated by this rich class of physical theories.

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arXiv2022

6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6d gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible non-trivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4d $\mathcal{N} = 2$ SCFTs obtained by compactifying on a $T^2$ in the presence of a topologically non-trivial flat flavor bundle characterized by a 't Hooft magnetic flux. The resulting "Stiefel--Whitney twisted" compactifications realize several new infinite families of 4d $\mathcal{N} = 2$ SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d $\mathcal{N} = 2$ SCFTs.

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arXiv2022

6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains

Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these theories on a $T^2$ leads to 4D $\mathcal{N} = 2$ SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sectors of the theory in which operator mixing is captured by a 1D spin chain Hamiltonian with operator scaling dimensions controlled by a perturbation series in inverse powers of the R-charge. We regulate the inherent divergences present in the 6D computations with the associated 5D Kaluza--Klein theory. In the case of 6D SCFTs obtained from M5-branes probing a $\mathbb{C}^{2}/\mathbb{Z}_{K}$ singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg $XXX_{s=1/2}$ spin chain with open boundary conditions, and similar considerations hold for its $T^2$ reduction to a 4D $\mathcal{N}=2$ SCFT. In the case of M5-branes probing more general D- and E-type singularities where generalized quivers have conformal matter, we argue that similar mixing effects are captured by an integrable $XXX_{s}$ spin chain with $s>1/2$. We also briefly discuss some generalizations to other operator sectors as well as little string theories.

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arXiv2022

Extra $W$-Boson Mass from a D3-Brane

Motivated by the recent CDF measurement of the $W$-boson mass, we study string-based particle physics models which can accommodate this deviation from the Standard Model. We consider an F-theory GUT in which the visible sector is realized on intersecting 7-branes, and extra sector states arise from a probe D3-brane near an E-type Yukawa point. The D3-brane worldvolume naturally realizes a strongly coupled sector which mixes with the Higgs. In the limit where some extra sector states get their mass solely from Higgs vevs, this leads to a contribution to the $ρ$ parameter which is too large, but as the D3-brane is separated from the 7-brane stack, this effect is suppressed, leading to O(1) - O(10) TeV scale extra sector states and a correction to $ρ$ which would be in accord with the CDF result. We also estimate the contribution to the oblique electroweak parameter $S$, and find that it is compatible with existing constraints. This also leads to additional signatures, including diphoton resonances (as well as other diboson final states) in the O(1) - O(10) TeV range.

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arXiv2022

CFTs Blueshift Tensor Fluctuations Universally

The strong constraints of conformal symmetry cause any nearly-conformal sector to blueshift tensor fluctuations in cosmology. Hidden sectors with approximate conformal symmetry, which may be quite large, are a well-motivated extension of physics beyond the Standard Models of particle physics and cosmology. They can therefore lead to a detectable shift in the tensor tilt for next-generation CMB and gravitational wave experiments. We compute the leading-order contribution to the in-in graviton two-point function from virtual loops in such sectors to demonstrate this universal effect. In units where a single conformally-coupled scalar is 1, limits from Stage-IV CMB experiments could bound the size of this extra sector to be smaller than about 10^15. This would be sufficient to rule out N-Naturalness as a complete resolution of the hierarchy problem.

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arXiv2022

Misanthropic Entropy and Renormalization as a Communication Channel

A central physical question is the extent to which infrared (IR) observations are sufficient to reconstruct a candidate ultraviolet (UV) completion. We recast this question as a problem of communication, with messages encoded in field configurations of the UV being transmitted to the IR degrees of freedom via a noisy channel specified by renormalization group (RG) flow, with noise generated by coarse graining / decimation. We present an explicit formulation of these considerations in terms of lattice field theory, where we show that the "misanthropic entropy" -- the mutual information obtained from decimating neighbors -- encodes the extent to which information is lost in marginalizing over / tracing out UV degrees of freedom. Our considerations apply both to statistical field theories as well as density matrix renormalization of quantum systems, where in the quantum case, the statistical field theory analysis amounts to a leading order approximation. As a concrete example, we focus on the case of the 2D Ising model, where we show that the misanthropic entropy detects the onset of the phase transition at the Ising model critical point.

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arXiv2022

Higher Symmetries of 5d Orbifold SCFTs

We determine the higher symmetries of 5d SCFTs engineered from M-theory on a $\mathbb{C}^3 / Γ$ background for $Γ$ a finite subgroup of $SU(3)$. This resolves a longstanding question as to how to extract this data when the resulting singularity is non-toric (when $Γ$ is non-abelian) and/or not isolated (when the action of $Γ$ has fixed loci). The BPS states of the theory are encoded in a 1d quiver quantum mechanics gauge theory which determines the possible 1-form and 2-form symmetries. We also show that this same data can also be extracted by a direct computation of the corresponding defect group associated with the orbifold singularity. Both methods agree, and these computations do not rely on the existence of a resolution of the singularity. We also observe that when the geometry faithfully captures the global 0-form symmetry, the abelianization of $Γ$ detects a 2-group structure (when present). As such, this establishes that all of this data is indeed intrinsic to the superconformal fixed point rather than being an emergent property of an IR gauge theory phase.

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arXiv2022

On the Dynamics of Inference and Learning

Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of Bayes' theorem. We present a treatment of this Bayesian updating process as a continuous dynamical system. Statistical inference is then governed by a first order differential equation describing a trajectory or flow in the information geometry determined by a parametric family of models. We solve this equation for some simple models and show that when the Cramér-Rao bound is saturated the learning rate is governed by a simple $1/T$ power-law, with $T$ a time-like variable denoting the quantity of data. The presence of hidden variables can be incorporated in this setting, leading to an additional driving term in the resulting flow equation. We illustrate this with both analytic and numerical examples based on Gaussians and Gaussian Random Processes and inference of the coupling constant in the 1D Ising model. Finally we compare the qualitative behaviour exhibited by Bayesian flows to the training of various neural networks on benchmarked data sets such as MNIST and CIFAR10 and show how that for networks exhibiting small final losses the simple power-law is also satisfied.

cond-mat.dis-nn↗

arXiv2021

Reflections on the Matter of 3d $\mathcal{N} = 1$ Vacua and Local $Spin(7)$ Compactifications

We use Higgs bundles to study the 3d $\mathcal{N} = 1$ vacua obtained from M-theory compactified on a local $Spin(7)$ space given as a four-manifold $M_4$ of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. There can be strong quantum corrections to the massless degrees of freedom in the low energy effective field theory, but topologically robust quantities such as "parity" anomalies are still calculable. We show how geometric reflections of the compactification space descend to 3d reflections and discrete symmetries. The "parity" anomalies of the effective field theory descend from topological data of the compactification. The geometric perspective also allows us to track various perturbative and non-perturbative corrections to the 3d effective field theory. We also provide some explicit constructions of well-known 3d theories, including those which arise as edge modes of 4d topological insulators, and 3d $\mathcal{N} = 1$ analogs of grand unified theories. An additional result of our analysis is that we are able to track the spectrum of extended objects and their transformations under higher-form symmetries.

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arXiv2021

Disorder Averaging and its UV (Dis)Contents

We present a stringy realization of quantum field theory ensembles in $D \le 4$ spacetime dimensions, thus realizing a disorder averaging over coupling constants. When each member of the ensemble is a conformal field theory with a standard semi-classical holographic dual of the same radius, the resulting bulk can be interpreted as a single asymptotically Anti-de Sitter space geometry with a distribution of boundary components joined by wormhole configurations, as dictated by the Hartle-Hawking wave function. This provides a UV completion of a recent proposal by Marolf and Maxfield that there is a high-dimensional Hilbert space for baby universes, but one that is compatible with the proposed Swampland constraints of McNamara and Vafa. This is possible because our construction is really an approximation that breaks down both at short distances, but also at low energies for objects with a large number of microstates. The construction thus provides an explicit set of counterexamples to various claims in the literature that holographic and effective field theory considerations can be reliably developed without reference to any UV completion.

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arXiv2021

The anomaly that was not meant IIB

Type IIB supergravity enjoys a discrete non-Abelian duality group, which has potential quantum anomalies. In this paper we explicitly compute these, and present the bordism group that controls them, modulo some physically motivated assumptions. Quite surprisingly, we find that they do not vanish, which naively would signal an inconsistency of F-theory. Remarkably, a subtle modification of the standard 10d Chern-Simons term cancels these anomalies, a fact which relies on the ***specific*** field content of type IIB supergravity. We also discover other ways to cancel this anomaly, via a topological analog of the Green-Schwarz mechanism. These alternative type IIB theories have the same low energy supergravity limit as ordinary type IIB, but a different spectrum of extended objects. They could either be part of the Swampland, or connect to the standard theory via domain walls.

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arXiv2021

EFT of 6D SUSY RG Flows

Motivated by its potential use in constraining the structure of 6D renormalization group flows, we determine the low energy dilaton-axion effective field theory of conformal and global symmetry breaking in 6D conformal field theories (CFTs). While our analysis is largely independent of supersymmetry, we also investigate the case of 6D superconformal field theories (SCFTs), where we use the effective action to present a streamlined proof of the 6D a-theorem for tensor branch flows, as well as to constrain properties of Higgs branch and mixed branch flows. An analysis of Higgs branch flows in some examples leads us to conjecture that in 6D SCFTs, an interacting dilaton effective theory may be possible even when certain 4-dilaton 4-derivative interaction terms vanish, because of large momentum modifications to 4-point dilaton scattering amplitudes. This possibility is due to the fact that in all known $D > 4$ CFTs, the approach to a conformal fixed point involves effective strings which are becoming tensionless.

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arXiv2021

Statistical coupling constants from hidden sector entanglement

String theory predicts that the couplings of Nature descend from dynamical fields. All known string-motivated particle physics models also come with a wide range of possible extra sectors. It is common to posit that such moduli are frozen to a background value, and that extra sectors can be nearly completely decoupled. Performing a partial trace over all sectors other than the visible sector generically puts the visible sector in a mixed state, with coupling constants drawn from a quantum statistical ensemble. An observable consequence of this entanglement between visible and extra sectors is that the reported values of couplings will appear to have an irreducible variance. Including this variance in fits to experimental data gives an important additional parameter that can be used to distinguish this scenario from the case where couplings are treated as fixed parameters. There is a consequent interplay between energy range and precision of an experiment that allows an extended reach for new physics.

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arXiv2021

On the Swampland Cobordism Conjecture and Non-Abelian Duality Groups

We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial. In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes. On the other hand, the non-Abelian structure of the IIB duality group $SL(2,\mathbb{Z})$ implies the existence of additional $[p,q]$ 7-branes. We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton. This description allows to recover the full structure of non-Abelian braid statistics for 7-branes. Combining the cobordism conjecture with an earlier Swampland conjecture by Ooguri and Vafa, we argue that only certain congruence subgroups $Γ\subset SL(2,\mathbb{Z})$ specifying genus zero modular curves can appear in 8D F-theory vacua. This leads to a successful prediction for the allowed Mordell-Weil torsion groups for 8D F-theory vacua.

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arXiv2020

Qubit Construction in 6D SCFTs

We consider a class of 6D superconformal field theories (SCFTs) which have a large $N$ limit and a semi-classical gravity dual description. Using the quiver-like structure of 6D SCFTs we study a subsector of operators protected from large operator mixing. These operators are characterized by degrees of freedom in a one-dimensional spin chain, and the associated states are generically highly entangled. This provides a concrete realization of qubit-like states in a strongly coupled quantum field theory. Renormalization group flows triggered by deformations of 6D UV fixed points translate to specific deformations of these one-dimensional spin chains. We also present a conjectural spin chain Hamiltonian which tracks the evolution of these states as a function of renormalization group flow, and study qubit manipulation in this setting. Similar considerations hold for theories without $AdS$ duals, such as 6D little string theories and 4D SCFTs obtained from compactification of the partial tensor branch theory on a $T^2$.

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