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Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals

Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals,Niclas Wyllard

Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals   (Citations: 6)
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We write down an explicit conjecture for the instanton partition functions in 4d N=2 SU(N) gauge theories in the presence of a certain type of surface operator. These surface operators are classified by partitions of N, and for each partition there is an associated partition function. For the partition N=N we recover the Nekrasov formalism, and when N=1+...+1 we reproduce the result of Feigin et. al. For the case N=1+(N-1) our expression is consistent with an alternative formulation in terms of a restricted SU(N)xSU(N) instanton partition function. When N=1+...+1+2 the partition functions can also be obtained perturbatively from certain W-algebras known as quasi-superconformal algebras, in agreement with a recent general proposal.
Published in 2010.
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    • ...N [57], where these algebras can be constructed from SL(N) WZNW models via Drinfel’d-Sokolov reduction [58]...

    Thomas Creutziget al. Supergroup — extended super Liouville correspondence

    • ...With the quiver description at hand, it is straightforward to enumerate and calculate the contribution from the fixed points on the moduli space under the action of the spacetime rotation and the gauge rotation, confirming the formula proposed in [27]...
    • ...Since 1 ≤ I, J ≤ M, it gives either 0 for I ≥ J or −1 for I < J. Expansion of (2.38) reproduces the conjecture made by Wyllard in [27]...
    • ...Then it is natural to conjecture [26, 27] that for the pure gauge theory...
    • ...This condition is a natural generalization of the conditions proposed in [26, 27], and also takes into account the dependence of the Verma module and the instanton partition function on the composition (nI)...
    • ...The equality Z = h W |W i was checked for a few cases by Wyllard [26, 27] using the explicit commutation relations of the corresponding W-algebras worked out for the partition of the form [2,1, . . . ,1] in [69, 70]...
    • ...The salient points are that we always found the agreement, once the maps k = −N − ǫ2/ǫ1 and hi ∼ ai/ǫ1 are used, and that the formula giving the level k agrees with the previous papers [18, 20, 21, 26, 27]...

    Hiroaki Kannoet al. Instanton counting with a surface operator and the chain-saw quiver

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