Duality and enhancement of symmetry in 5d gauge theories

Abstract

Abstract:We study various cases of dualities between N = 1 5d supersymmetric gauge theories. We motivate the dualities using brane webs, and provide evidence for them by comparing the superconformal index. In many cases we find that the classical global symmetry is enhanced by instantons to a larger group including one where the enhancement is to the exceptional group G 2 .

Lifting 4d dualities to 5d

“…An x → 1/x invariant partition function is obtained by 19) JHEP04 (2015)141 where q 1 , q 2 are the SU(3) and SU(2) instanton fugacities, respectively. This apparently includes "U(1) remnant" states associated both with the SU(3) part, visible in the web of figure 11b in terms of a D1-brane between the external NS5-branes, as well as with the SU(2) part.…”

“…This apparently includes "U(1) remnant" states associated both with the SU(3) part, visible in the web of figure 11b in terms of a D1-brane between the external NS5-branes, as well as with the SU(2) part. The latter are not obvious in the given 5-brane web, but appear to be a necessary ingredient in computing the instanton partition function for USp(2) + 6 (see [18,19]). 3 With this, we find the instanton contributions (for conciseness we show to O(x 2 ), but we computed to O x 3 )…”

Brane webs, 5d gauge theories and 6d N = 1 , 0 $$ \mathcal{N}=\left(1,\;0\right) $$ SCFT’s

“…An example of this is SU 0 (3) + 2F gauge theory and SU π (2) × SU π (2) quiver theory [5,10]. 1 By now a great many examples of this are known, see [10][11][12][13][14][15].…”

Compactifications of 5d SCFTs with a twist

“…This phenomenon, where different mass deformations of the same 5d SCFT can lead to different low-energy gauge theory descriptions is called a 5d duality. For the SU 0 (2) case, this is a self-duality yet there are many other known examples where different gauge theories are related in this way [9,[12][13][14][15][16][17].…”