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A<sc>bstract</sc> We study anO(N) invariant surface defect in the Wilson-Fisher conformal field theory (CFT) ind= 4 –ϵdimensions. This defect is defined by mass deformation on a two-dimensional surface that generates localized disorder and is conjectured to factorize into a pair of ordinary boundary conditions ind= 3. We determine defect CFT data associated with the lightestO(N) singlet and vector operators up to the third order in theϵ-expansion, find agreements with results from numerical methods and provide support for the factorization proposal ind= 3. Along the way, we observe surprising non-renormalization properties for surface anomalous dimensions and operator-product-expansion coefficients in theϵ-expansion. We also analyze the full conformal anomalies for the surface defect. 

We introduce an effective field theory (EFT) for conformal impurity by considering a pair of transversely displaced impurities and integrating out modes with mass inversely proportional to the separation distance. This EFT captures the universal signature of the impurity seen by a heavy local operator. We focus on the case of conformal boundaries and derive universal formulas from this EFT for the boundary structure constants at high energy. We point out that the more familiar thermal EFT for conformal field theory is a special case of this EFT with distinguished conformal boundaries. We also derive, for general conformal impurities, nonpositivity and convexitylike constraints on the Casimir energy which determines the leading EFT coefficient. Published by the American Physical Society2024 

A<sc>bstract</sc> We study the operator algebra of extended conformal defects in more than two spacetime dimensions. Such algebra structure encodes the combined effect of multiple impurities on physical observables at long distances as well as the interactions among the impurities. These features are formalized by a fusion product which we define for a pair of defects, after isolating divergences that capture the effective potential between the defects, which generalizes the usual Casimir energy. We discuss general properties of the corresponding fusion algebra and contrast with the more familiar cases that involve topological defects. We also describe the relation to a different defect setup in the shape of a wedge. We provide explicit examples to illustrate these properties using line defects and interfaces in the Wilson-Fisher CFT and the Gross-Neveu(-Yukawa) CFT and determine the defect fusion data thereof. 

A<sc>bstract</sc> We investigate finite-temperature observables in three-dimensional largeNcritical vector models taking into account the effects suppressed by$$ \frac{1}{N} $$ $\frac{1}{N}$. Such subleading contributions are captured by the fluctuations of the Hubbard-Stratonovich auxiliary field which need to be handled with care due to a subtle divergence structure which we clarify. The examples we consider include the scalarO(N) model, the Gross-Neveu model, the Nambu-Jona-Lasinio model and the massless Chern-Simons Quantum Electrodynamics. We present explicit results for the free energy density to the subleading order in$$ \frac{1}{N} $$ $\frac{1}{N}$, which captures the thermal one-point function of the stress-energy tensor to this order. We also include the dependence on a chemical potential. We determine the Wilson coefficient in the thermal effective action that is sensitive to global symmetry for the first time directly in interacting CFTs, which produces a symmetry-resolved asymptotic density of states. We further provide a formula from diagrammatics for the one-point functions of general single-trace higher-spin currents. We observe that in most cases considered, these subleading effects lift the apparent degeneracies between observables in different models at infiniteN, while in special cases the discrepancies only start to appear at the next-to-subleading order. 

A<sc>bstract</sc> Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized symmetries in two-dimensional QFT. Such symmetries are described by topological defect lines (TDLs) which obey fusion rules that are non-invertible in general. Despite this seemingly exotic feature, all well-known properties in gauging invertible symmetries carry over to this general setting, which greatly enhances both the scope and the power of gauging. This is established by formulating generalized gauging in terms of topological interfaces between QFTs, which explains the physical picture for the mathematical concept of algebra objects and associated module categories over fusion categories that encapsulate the algebraic properties of generalized symmetries and their gaugings. This perspective also provides simple physical derivations of well-known mathematical theorems in category theory from basic axiomatic properties of QFT in the presence of such interfaces. We discuss a bootstrap-type analysis to classify such topological interfaces and thus the possible generalized gaugings and demonstrate the procedure in concrete examples of fusion categories. Moreover we present a number of examples to illustrate generalized gauging and its properties in concrete conformal field theories (CFTs). In particular, we identify the generalized orbifold groupoid that captures the structure of fusion between topological interfaces (equivalently sequential gaugings) as well as a plethora of new self-dualities in CFTs under generalized gaugings.