6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications

Abstract

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6d gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zeroform symmetry, including possible non-trivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4d N = 2 SCFTs obtained by compactifying on a T 2 in the presence of a topologically non-trivial flat flavor bundle characterized by a 't Hooft magnetic flux. The resulting "Stiefel-Whitney twisted" compactifications realize several new infinite families of 4d N = 2 SCFTs, and also furnish a 6d origin for a number of recently discovered rank one and two 4d N = 2 SCFTs.

On the 6d Origin of Non-invertible Symmetries in 4d

“…Finally, a potentially interesting class of examples to which our methods also apply is provided by compactifications of 6d (1, 0) theories down to 4d (see e.g. [100][101][102][103][104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119] for a (partial) list of references on the subject). In this context the role of the Heisenberg algebra we discuss in this paper is played by the corresponding Heisenberg algebra arising from the 6d defect group of the 6d (1,0) SCFT [6,13].…”

The Branes Behind Generalized Symmetry Operators

“…This perspective has by now been generalized in a number of directions, and has reached the stage where there are explicit algorithms for reading off generalized symmetries for a large number of geometries. [6,20,23,25,26,29,34,42,46,53,63,70,72,[76][77][78]94,[128][129][130] One of the puzzling features of these analyses is that the topological operators of reference [1] are in some sense only implicitly referenced in such stringy constructions. The absence of an explicit brane realization of these symmetry topological operators makes it challenging to access some features of generalized symmetries in these systems.…”

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

“…The extensive appearance of higher-form symmetry in quantum field theory means that frequently one finds higher group global symetries, which have their own anomalies and dynamical implications. Highergroup global symmetry has also been extensively explored in five and six-dimensional quantum field theory and little string theories [329,32,61,30,330,71,331,75,76,79,332], where in the latter continuous higher symmetry is particularly natural due to the presence of a conserved string number [333,64]. In particular, these ideas have been applied to better understand certain supersymmetric dualities [334][335][336]65,[337][338][339], and to derive universal constraints on renormalization group flows [340][341][342].…”