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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 conformal field theory 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 nontopological world volume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global $p$ -form symmetries for $p\ge 0$ in asymptotically anti–de Sitter spacetimes, which includes the case of noninvertible 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 $m\ge 2$ . Published by the American Physical Society 2024

The global symmetries of a $D$ -dimensional quantum field theory (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 nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional 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. Published by the American Physical Society 2024

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 satisfies the Bogomol’nyi-Prasad-Sommerfield (BPS) condition 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 (respectively magnetic) confinement (respectively 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. Published by the American Physical Society 2024

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 compatibility 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. Published by the American Physical Society 2024

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 $$\mathscr{N}$$ = 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 noninvertible 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. Nontrivial 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 ∂X results in a 5D symmetry topological field theory. 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.

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 ∂X. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in ∂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.

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 determine 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 that extend to the boundary of the noncompact 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 five-dimensional (5D) superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as four-dimensional supersymmetric quantum chromodynamics-like theories engineered via M-theory on noncompact G₂ spaces.