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DOE OSTI2020

Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD

We show that 2 2 d adjoint QCD, an SU(N) S U ( N ) gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 2 2 index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of N N , are matched by spontaneous chiral symmetry breaking. We find that massless 2 2 d adjoint QCD confines for N >2 N > 2 , except for test charges of N N -ality N/2 N / 2 , which are deconfined. In other words, \mathbb Z_N ℤ N center symmetry is unbroken for odd N N and spontaneously broken to \mathbb Z_{N/2} ℤ N / 2 for even N N . All of these results are confirmed by explicit calculations on small \mathbb{R}\times S^1 ℝ × S 1 . We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when N N is even. Furthermore, for most values of N N , 2 2 d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 8 8 . As a result, it fits into the classification of (1+1) ( 1 + 1 ) d SPT phases of interacting Majorana fermions in an interesting way.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

A Fast Algorithm for Computing Zigzag Representatives

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed $O(m^ω)$ in time, where $ω < 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.

Persistent homology↗

DOE OSTI2023

Manipulation of Scattering Spectra with Topology of Light and Matter

Structured lights, including beams carrying spin and orbital angular momenta, radially and azimuthally polarized vector beams, as well as spatiotemporal optical vortices, have attracted significant interest due to their unique amplitude, phase front, polarization, and temporal structures, enabling a variety of applications in optical and quantum communications, micromanipulation, and super-resolution imaging. In parallel, structured optical materials, metamaterials, and metasurfaces consisting of engineered unit cells—meta-atoms, opened new avenues for manipulating the flow of light and optical sensing. While several studies explored structured light effects on the individual meta-atoms, their shapes are largely limited to simple spherical geometries. However, the synergy of the structured light and complex-shaped meta-atoms has not been fully explored. Here, in this paper, the role of the helical wavefront of Laguerre–Gaussian beams in the excitation and suppression of higher-order resonant modes inside all-dielectric meta-atoms of various shapes, aspect ratios, and orientations, is demonstrated and the excitation of various multipolar moments that are not accessible via unstructured light illumination is predicted. The presented study elucidates the role of the complex phase distribution of the incident light in shape-dependent resonant scattering, which is of utmost importance in a wide spectrum of applications ranging from remote sensing to spectroscopy.

42 ENGINEERING↗