Abstract
We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional mathcal{N} = 2 U(2) gauge theories coupled to (A1, D2n) Argyres-Douglas theories. This is carried out by extending the generalized AGT correspondence to the case of U(2) gauge group, which requires us to define irregular states of the direct sum of Virasoro and Heisenberg algebras. Using our formula, one can evaluate the contribution of the (A1, D2n) theory at each fixed point on the U(2) instanton moduli space. As an application, we evaluate the instanton partition function of the (A3, A3) theory to find it in a peculiar relation to that of SU(2) gauge theory with four fundamental flavors. From this relation, we read off how the S-duality group acts on the UV gauge coupling of the (A3, A3) theory.
Highlights
Where b0 ≡ 4 − Nf, Λ is a dynamical scale, a is the vacuum expectation value (VEV) of a scalar, Yk are Young diagrams, and |Yk| is the number of boxes in Yk
We propose a Nekrasov-type formula for the instanton partition functions of four-dimensional N = 2 U(2) gauge theories coupled to (A1, D2n) Argyres-Douglas theories
We evaluate the instanton partition function of the (A3, A3) theory to find it in a peculiar relation to that of SU(2) gauge theory with four fundamental flavors
Summary
We briefly review the AGT correspondence [19, 20] and its generalization [17, 18]. The irregular state |I(n) generally depends on n extra parameters, β0, · · · , βn−1, corresponding to the “boundary condition” of a solution to the differential equations (2.6) These extra parameters correspond to inserting screening operators in the product (2.8). Note here that the above characterization of the irregular state does not fix the overall normalization, as in the case of the SU(2)-version of the generalized AGT correspondence. This means an ambiguity in the computation of the perturbative part of the partition function (3.6). We explicitly evaluate this decomposition to read off the factor ZY(A1,1Y,2D2n) in (1.2)
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