Abstract
Supersymmetric theories with the same bosonic content but different fermions, aka twins, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic mathcal{N} = 3 and mathcal{N} = 1 theories in D = 4 space-time dimensions, can also be twin. We provide evidence from three different perspectives: (i) a twin S-fold construction, (ii) a double-copy argument and (iii) by identifying candidate twin holographically dual gauged supergravity theories. Furthermore, twin W-supergravity theories then follow by applying the double-copy prescription to exotic super conformal field theories.
Highlights
For each twin supergravity pair in D = 5 there is a candidate twin pair of dual D = 4 W-SCFTs, that admit a twin S-fold construction and may be deduced through the double-copy of massive spin-1 multiplets following the procedure of [10], as we describe in section 3.1 and section 3.2
The analogous consistent truncation to the little N = 2 gauged supergravity should be effected by the same procedure used in [1] for N = 6, but with the little twin S-duality U(1) rotation, and should have a dual theory with superconformal group SU(2, 2|1) that corresponds to the little N = 1 W-SCFT
In Romans’ gauged N = 4 supergravity the vectors of N = 4 Poincare supergravity sitting in the 5 of Sp(2) are replaced by three vectors and two “self-dual” two-forms in the 30 and 12 + 1−2 of U(2) ⊂ Sp(2), as required by the preservation of supersymmetry, which is precisely reflected by the multiplet structure of the candidate dual N = 2 W-SCFT, cf. appendix A
Summary
The singularities are isolated if and only if the weights (a, b, c, d) are all relatively prime to k This action is embedded in the R-symmetry and S-duality groups, Zk ⊂ Ua(1) × Ub(1) × Uc(1) × Ud(1) ⊂ Spin(6) × SL(2, Z),. The R-symmetry is broken to SU(3) × U(1)R, but for k > 2 the remnant SU(3) is a flavour symmetry rather than an R-symmetry, since only four supercharges are left invariant, reducing the N = 4 algebra to the N = 1 algebra Note, this is the unique (up to trivial automorphisms) N = 1 projection preserving an SU(3). In term of the on-shell superfields of [22, 23] we obtain a single spin-2 and 14 spin-1 supercurrents This can be deduced directly from the Sl{3,1}-invariant truncation of the N = 4 supercurrent, JAB,CD. The actual string/F-theory embedding is rather more subtle; we shall return to this question in future work
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