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DOE OSTI2022

Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated su(2) Spin Systems

The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Here, our proof of principle results for XXZ and J1-J2 Heisenberg (in 1D and 2D) indicate that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams, and provides a better starting point for addressing challenging spin problems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Non-invertible duality interfaces in field theories with exotic symmetries

In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse according to a group law. Only recently has the interplay between these two been examined. In this paper, we provide further examples of the interplay in the XY plaquette model, XY cube model, 1+1 d theory with global dipole symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of the momentum symmetry on half of spacetime and then performing a duality transformation. We analyze the fusion rules of the symmetries and find that they are condensation defects from an analog of higher gauging exotic symmetries. We also address their dependence on the UV cutoff when relevant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Celestial holography meets twisted holography: 4d amplitudes from chiral correlators

We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the form factor integrand, starting from 6d holomorphic theories on twistor space. We show that the form factor integrands can be expressed as sums of products of 1.) correlators of a 2d chiral algebra, related to the algebra of asymptotic symmetries uncovered recently in the celestial holography program, and 2.) OPE coefficients of a 4d non-unitary CFT. We prove that conformal blocks of the chiral algebras are in one-to-one correspondence with local operators in 4d. We use this bijection to recover the Parke-Taylor formula, the CSW formula, and certain one-loop scattering amplitudes. Along the way, we explain and derive various aspects of celestial holography, incorporating techniques from the twisted holography program such as Koszul duality. This perspective allows us to easily and efficiently recover the infinite-dimensional chiral algebras of asymptotic symmetries recently extracted from scattering amplitudes of massless gluons and gravitons in the celestial basis. We also compute some simple one-loop corrections to the chiral algebras and derive the three-dimensional bulk theories for which these 2d algebras furnish an algebra of boundary local operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

String correlators on $\text{AdS}_3$: Analytic structure and dual CFT

We continue our study of string correlators on Euclidean \text{AdS}_3 AdS 3 with pure NS-NS flux. The worldsheet and spacetime correlators have a rich analytic structure, which we analyse completely for genus 0 four-point functions. We show that correlators exhibit a simple behaviour near their singularities. The spacetime correlators are meromorphic functions in the \mathrm{SL}(2,\mathbb{R}) S L ( 2 , ℝ ) -spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual \text{CFT}_2 CFT 2 . Moreover, we also compute the residues of the spacetime correlators for some of the poles exactly and find again a perfect match with the proposal for the dual \text{CFT}_2 CFT 2 , thereby checking the duality for some non-trivial four-point functions exactly. Our computations simplify drastically in the tensionless limit of \mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4 A d S 3 × S 3 × 𝕋 4 where the behaviour near the poles gives in fact the exact answer. This paper is the third in a series with several installments.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Remarks on geometric engineering, symmetry TFTs and anomalies

Abstract Geometric engineering is a collection of tools developed to establish dictionaries between local singularities in string theory and (supersymmetric) quantum fields. Extended operators and defects, as well as their higher quantum numbers captured by topological symmetries, can be encoded within geometric engineering dictionaries. In this paper we revisit and clarify aspects of these techniques, with special emphasis on ’t Hooft anomalies, interpreted from the SymTFT perspective as obstructions to the existence of Neumann boundary conditions. These obstructions to gauging higher symmetries are captured via higher link correlators for the SymTFT on spheres. In this work, we give the geometric engineering counterpart of this construction in terms of higher links of topological membranes. We provide a consistency check in the context of 5D SCFTs with anomalous 1-form symmetries, where we give two independent derivations of the anomaly in terms of higher links, one purely field theoretical and the other purely geometrical. Along the way, we also recover the construction of non-invertible duality defects in 4D$$ \mathcal{N} $$ N = 4 SYM from a geometric engineering perspective.

Physics↗
DOE OSTI2024

Parametrization of Generalized Parton Distributions from 𝑡-Channel String Exchange in AdS Spaces

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) that is valid for all skewness. Our approach leverages conformal moments, representing them as the sum of spin-𝑗 nucleon 𝐴-form factor and skewness-dependent spin-𝑗 nucleon 𝐷-form factor, derived from 𝑡-channel string exchange in AdS spaces consistent with Lorentz invariance and unitarity. This model-independent framework, satisfying the polynomiality condition due to Lorentz invariance, uses Mellin moments from empirical data to estimate these form factors. With just five Regge slope parameters, our method accurately produces various nucleon quark GPD types and symmetric nucleon gluon GPDs through pertinent Mellin-Barnes integrals. Our isovector nucleon quark GPD is in agreement with existing lattice data, promising to improve the empirical extraction and global analysis of nucleon GPDs in exclusive processes, by avoiding the deconvolution problem at any skewness, for the first time.

QCD phenomenology↗
DOE OSTI2026

Rapidity-dependent spin decomposition of the nucleon

We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At 𝜂 = 0 it reduces to the standard impact-parameter density, while at 𝜂 ≠ 0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point 𝑡 =−𝑐 𝜂 =−4⁢𝜂 2 ⁢𝑚$^{2}_{𝑁}$/(1 − 𝜂 2 ) and decreases monotonically with the rapidity gap Δ⁢𝑦 = ln⁡[(1+𝜂)/(1−𝜂)] = 2 artanh⁡(𝜂). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (𝑥,𝜂,𝑡) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet 𝑥-space channels at 𝜇 = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and 𝑡-slope systematics).

Gauge-gravity dualities↗
DOE OSTI2022

The Page curve for reflected entropy

We study the reflected entropy $S_{R}$ in the West Coast Model, a toy model of black hole evaporation consisting of JT gravity coupled to end-of-the-world branes. We demonstrate the validity of the holographic duality relating it to the entanglement wedge cross section away from phase transitions. Further, we analyze the important non-perturbative effects that smooth out the discontinuity in the phase transition. By performing the gravitational path integral, we obtain the reflected entanglement spectrum analytically. The spectrum takes a simple form consisting of superselection sectors, which we interpret as a direct sum of geometries, a disconnected one and a connected one involving a closed universe. We find that area fluctuations of $\textit{O}$$\sqrt{G_N}$ spread out the $S_{R}$ phase transition in the canonical ensemble, analogous to the entanglement entropy phase transition. We also consider a Renyi generalization of the reflected entropy and show that the location of the phase transition varies as a function of the Renyi parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

String-based axial and helicity-flip GPDs: A comparison to lattice QCD

We construct an analytic, string-based representation of the nucleon’s axial and helicity-flip conformal moments of generalized parton distributions (GPDs) that holds for skewness and for both the quark and gluon channels. The starting point is the Mellin-Barnes resummation of the conformal partial-wave expansion, where the moments are parametrized by open- (Reggeon) and closed-string (Pomeron) trajectories with slopes determined by experimental form factors and meson/glueball spectroscopy. The forward limits are fixed by the empirical unpolarized and polarized parton distributions. Polynomiality, crossing symmetry, and support are satisfied by construction. After next-to-leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi/Efremov-Radyushkin-Brodsky-Lepage evolution to μ = 2 GeV our analytic framework (i) reproduces some of the currently available lattice moments of E and H˜ in the nonsinglet sector, (ii) predicts sea-quark and gluon polarized moments that will be testable by forthcoming simulations and experiments at Jefferson Lab and the future Electron-Ion Collider, and (iii) yields axial and helicity-flip GPDs in x-space in reasonable agreement with lattice QCD.

Gauge-gravity dualities↗
DOE OSTI2026

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗
DOE OSTI2022

Dynamical evolution in the D1D5 CFT

It is interesting to ask: how does the radial space direction emerge from the CFT in gauge-gravity duality? In this context we resolve a long-standing puzzle with the gravity duals of two classes of states in the D1D5 CFT. For each class the CFT states are in the untwisted sector, suggesting that the energy gap should be 1/R y where R y is the radius of the circle on which the D1D5 CFT is compactified. For one class of states, the gravity dual indeed has exactly this gap, while for the other class, the gravity dual has a very deep throat, leading to an energy gap much smaller than 1/R y . We resolve this puzzle by showing that for the latter class of states, perturbing the CFT off its free point leads to the formation of a band structure in the CFT. We also explain why such a band structure does not arise for the first class of states. Thus for the case where a deep throat emerges in the gravity description, the dynamics of falling down this throat is described in the CFT as a sequential ‘hopping’ between states all of which have the same energy at the free point; this hopping amplitude converts an integer spaced spectrum into a closely spaced band of energy levels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗