Description
Andrea Antinucci
Duality defects in two and four dimensional theories, anomalies and gauging
Abstract:
Duality defects are ubiquitous in two and four dimensions, where they generate a 0-form symmetry, which is often non-invertible. However, sometimes it becomes invertible in specific global variants. In such cases, the duality is a non-intrinsic non-invertible symmetry. By employing the powerful tool of symmetry TFT, we study and classify obstructions to gauging the duality symmetries. We show that in the intrinsic non-invertible case, they are necessarily anomalous, hence implying a strong constraint on the IR of duality-preserving RG flows. In the non-intrinsic case, we found that the anomaly is not uniquely determined, depending on further data, namely the choice of an equivariantization of a Lagrangian algebra of the Drinfeld center. We propose and verify in several examples that the boundary counterpart of this ambiguity is a choice of symmetry fractionalization of the duality symmetry on the global variant where it becomes invertible.
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Weiguang Cao
Subsystem Kramars-Wannier duality and non-invertible symmetry
Abstract:
Recently, the notion of symmetry has been generalized by relaxing the dimensions, invertibility and topologicalness of the symmetry operators. In this poster, I will introduce a new generalization, subsystem non-invertible symmetry, by lifting both the invertibility and topologicalness of the ordinary global symmetry. I will first review the simplest non-invertible symmetry in (1+1)d from the ordinary Kramers-Wannier transformation. Then I will explore non-invertible symmetries in two-dimensional lattice models with subsystem Z_2 symmetry by introduce a subsystem Z_2-gauging procedure, called the subsystem Kramers-Wannier transformation. For both case, the corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. I will derive the fusion rules, check the mobility of the defects and comment on the anomaly. Finally, I will comment on generalizing the results to subsystem Z_n symmetry in (2+1)d and further to subsystems in arbitrary dimensions. I will also give examples in continuum field theory.
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Saki Koizumi
Anomaly Inflow of Rarita-Schwinger Field in 3 Dimensions
Abstract: We study the anomaly inflow of the Rarita-Schwinger field with gauge symmetry in $3$ dimensions. We find that global anomalies of the Rarita-Schwinger field are obtained by the spectral flow, which is similar to Witten's $SU(2)$ global anomaly for a Weyl fermion. The Rarita-Schwinger operator is shown to be a self-adjoint Fredholm operator, and its spectral flow is determined by a path on the set of self-adjoint Fredholm operators with the gap topology. From the spectral equivalence of the spectral flow, we find that the spectral flow of the Rarita-Schwinger operator is equivalent to that of the spin-$3/2$ Dirac operator. From this fact, we confirm that the anomaly of the $3$-dimensional Rarita-Schwinger field is captured by the anomaly inflow.
Finally, we find that there are no global anomalies of gauge-diffeomorphism transformations on spin manifolds with any gauge group. We also confirm that the anomalous phase of the partition function which corresponds to the generator of $\Omega_4^{{\rm Pin}^+}(pt)=\mathbb{Z}_{16}$ is $\exp(3i\pi /8)$ for the Rarita-Schwinger theory on unorientable ${\rm Pin}^+$ manifolds without gauge symmetry.
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Enoch Leung
Brane Fusion Frenzy: Non-Invertible Defect Fusion and Tachyon Condensation
Abstract: It has been recently appreciated in the literature that non-invertible symmetry defects in QFTs can be realized holographically as certain D-brane configurations. The hallmark of non-invertible defects is two-fold: 1) the fusion “coefficients” are generally decoupled TQFTs, 2) the fusion of a defect with its dual gives rise to a “condensation defect” comprising localized lower-dimensional defects. We show that both of these field-theoretic features are fully characterized by brane kinematics/dynamics, namely, the former corresponds to the relative motion of two stacks of D-branes, and the latter corresponds to tachyon condensation on a brane-antibrane pair.
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Linhao Li
Non-Invertible Kennedy-Tasaki Transformation and Applications to Gapless-SPT
Abstract: In this poster, I propose a way to define it on a closed chain, by sacrificing unitarity. The operator realizing such a non-unitary transformation satisfies non-invertible fusion rule, and implements a generalized gauging of the Z_2×Z_2 global symmetry. By choosing free boundary on the open chain, this generalization will reduce to the original KT transformation. Besides, we further apply the KT transformation to systematically construct gapless symmetry protected topological phases. This construction reproduces the known examples of (intrinsically) gapless SPT where the non-trivial topological features come from the gapped sectors by means of decorated defect constructions. We also construct new (intrinsically) purely gapless SPTs where there are no gapped sectors, hence are beyond the decorated defect construction.
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Veronica Pasquarella
Drinfeld Centers from Magnetic Quivers
The present work shows that magnetic quivers encode the necessary information for determining the Drinfeld center in the symmetry topological field theory constructions (SymTFT) associated to a given absolute theory. The crucial argument resides in their common aim of generalising homological mirror symmetry.
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Giovanni Rizi
Symmetries and topological operators, on average.
Abstract: We study Ward identities and selection rules for local correlators in disordered theories where a 0-form global symmetry of a QFT is explicitly broken by a random coupling hh but it re-emerges after quenched average. We consider hh space-dependent or constant. In both cases we construct the symmetry operator implementing the group action, topological after average. In the first case, relevant in statistical systems with random impurities, such symmetries can be coupled to external backgrounds and can be gauged, like ordinary symmetries in QFTs. We also determine exotic selection rules arising when symmetries emerge after average in the IR, explaining the origin of LogCFTs from symmetry considerations. In the second case, relevant in AdS/CFT to describe the dual boundary theory of certain bulk gravitational theories, the charge operator is not purely codimension-1, it can be defined only on homologically trivial cycles and on connected spaces. Selection rules for average correlators exist, yet such symmetries cannot be coupled to background gauge fields in ordinary ways and cannot be gauged. When the space is disconnected, in each connected component charge violation occurs, as expected from Euclidean wormholes in the bulk theory. Our findings show the obstruction to interpret symmetries emergent after average as gauged in the bulk.
