Twisted circle compactifications of 6d SCFTs

Abstract

We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.

Higher-form symmetries of 6d and 5d theories

“…Let us discuss the structure of (3.89) in more detail for different kinds of twists of 6d theories. So far these twists have been studied only in the context of 6d SCFTs [21,24] but similar structure is expected to extend to the case of 6d LSTs. From the study of twists of 6d SCFTs, we expect three different kinds of twists for 6d theories:…”

“…Much progress has been made on mapping out the theories in 6d, including a putative classification of SCFTs [2][3][4][5] and LSTs [5,6] from F-theory on elliptic Calabi-Yau three-folds -for a review of the 6d classification, see [7]. In 5d recent progress has been made in mapping out and furthering the classification of SCFTs using the M-theory realization on canonical singularities [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

“…The edge between i and l in the above graph is such an example. See [21] for more details on this notation in the context of 6d SCFTs.…”

“…(see [21] for more details). We let S 0,i be the surface corresponding to the affine node of the Dynkin diagram of g Now let us consider the nodes i for which g i is trivial.…”

Elliptic quantum curves of class $$ {\mathcal{S}}_k $$

“…Since their classification [1,2], 6d superconformal field theories (SCFTs) with 8 supercharges have played a prominent role in constructing lower dimensional quantum field theories. In particular, it appears that 5d SCFTs arise as compactifications of such 6d theories with Wilson line expectation values for background flavour fields turned on [3,4], while 5d theories of KK type admitting an affine quiver description can be understood as twisted compactifications of 6d SCFTs [5][6][7]. Moreover, 4d N = 1 SCFTs can be understood as compactifications on Riemann surfaces with fluxes [8][9][10][11][12][13][14].…”