We define gauge theories whose gauge group includes charge conjugation as well as standard SU(N ) transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For N even, we show that there are exactly two possible such groups which we dub SU(N ) I,II . We construct the transformation rules for the fundamental and adjoint representations, allowing us to explicitly build fourdimensional N = 2 supersymmetric gauge theories based on SU(N ) I,II and understand from first principles their global symmetry. We compute the Haar measure on the groups, which allows us to quantitatively study the operator content in protected sectors by means of the superconformal index. In particular, we find that both types of SU(N ) I,II groups lead to non-freely generated Coulomb branches.
We study the sector of large charge operators φ n (φ being the complexified scalar field) in the O(2) Wilson-Fisher fixed point in 4 − ǫ dimensions that emerges when the coupling takes the critical value g ∼ ǫ. We show that, in the limit g → 0, when the theory naively approaches the gaussian fixed point, the sector of operators with n → ∞ at fixed g n 2 ≡ λ remains non-trivial. Surprisingly, one can compute the exact 2-point function and thereby the non-trivial anomalous dimension of the operator φ n by a full resummation of Feynman diagrams. The same result can be reproduced from a saddle point approximation to the path integral, which partly explains the existence of the limit. Finally, we extend these results to the three-dimensional O(2)-symmetric theory with (φ φ) 3 potential.
We compute general higher-point functions in the sector of large charge operators φ n ,φ n at large charge in O(2) (φφ) 2 theory. We find that there is a special class of "extremal" correlators having only one insertion ofφ n that have a remarkably simple form in the doublescaling limit n → ∞ at fixed g n 2 ≡ λ, where g ∼ ǫ is the coupling at the O(2) Wilson-Fisher fixed point in 4 − ǫ dimensions. In this limit, also non-extremal correlators can be computed. As an example, we give the complete formula for φ(x 1 ) n φ(x 2 ) nφ (x 3 ) nφ (x 4 ) n , which reveals an interesting structure.
We study large charge sectors in the O(N) model in 6 − ϵ dimensions. For 4 < d < 6, in perturbation theory, the quartic O(N) theory has a UV stable fixed point at large N . It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic O(N) model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2N) ⊃ U(1) × SU(N) theory, as a first step towards tests of (higher spin) AdS/CFT.
We study global 1-and (d − 2)-form symmetries for gauge theories based on disconnected gauge groups which include charge conjugation. For pure gauge theories, the 1-form symmetries are shown to be non-invertible. In addition, being the gauge groups disconnected, the theories automatically have a Z 2 global (d − 2)-form symmetry. We propose String Theory embeddings for gauge theories based on these groups. Remarkably, they all automatically come with twist vortices which break the (d − 2)-form global symmetry. This is consistent with the conjectured absence of global symmetries in Quantum Gravity.
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