From SO/Sp instantons to W-algebra blocks

Abstract

We study instanton partition functions for N=2 superconformal Sp(1) and SO(4) gauge theories. We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge couplings, since the instanton counting involves different renormalization schemes. Geometrically, this mapping relates the Gaiotto curves of the different realizations as double coverings. We then formulate an AGT-type correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying W(2,2)-algebra symmetry. This form of the correspondence eliminates the need to divide out extra U(1) factors. Finally, to check this correspondence for linear quivers, we compute expressions for the Sp(1)-SO(4) half-bifundamental.Comment: 83 pages, 29 figures; minor change

5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory

“…The results for the (+, +) component can also be lifted from the result from the 4d expression in [24]. These are given by…”

Brane webs and O5-planes

“…These can materialize in the partition function as a breakdown of x → 1 x invariance, which must be obeyed as it is part of the superconformal algebra. Another way these can appear in the partition function is as an infinite tower with representations of increasing dimension The generalization to half-bifundamentals follows straightforwardly, similarly to the 4d case done in [37]. To avoid the need to add an half-fundamental, we specialize to the case χ 1 = 0.…”

“…We concentrate on the contributions of bifundamentals and half-bifundamentals. In 4d these were considered in [37]. The 5d results in the O + sector can be derived by lifting the 4d ones, but for the O − sector one has to derive these directly using the methods in [38].…”

On the Jeffrey–Kirwan residue ofBCD-instantons

“…We should split the two circles and determine an integration cycle. †4 The graphical algorithm concerns the "multiplicities" of poles in [20]. The notion of the multiplicity may arise from the choice of the integration cycle.…”