Abstract
We discuss Type IIB 5-brane configurations for 5d mathcal{N}=1 gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow from a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these SU(6) gauge theories.
Highlights
Sp(N ) [7, 8], or it can introduce different representations such as the symmetric or antisymmetric representation of SU(N ) or Sp(N ) [8,9,10,11]
In this paper we argue that 5-brane web diagrams may yield further new type of gauge theories which are SU(6) or Sp(3) gauge theories with half-hypermultiplets in the rank-3 antisymmetric representation
Since the decomposition of the conjugate spinor representation under SU(6) × U(1) includes the rank-3 antisymmetric representation of the SU(6) which is not charged under the U(1), decoupling the degrees of freedom associated to the U(1) should yield a 5-brane diagram of the SU(6) gauge theory with a half-hypermultiplet in the rank-3 antisymmetric representation
Summary
We obtained 5-brane diagrams for SU(6) gauge theories with rank-3 antisymmetric matter. We give further support for the claim by comparing the monopole string tension computed from the diagram in figure 3 with that calculated from the prepotential in the gauge theory. The tension of the monopole string is given by the area of the face on which the D3-brane is stretched. We can compare the area (2.9)–(2.13) with the monopole string tension computed from the effective prepotential. We rewrite the effective prepotential (2.15) in terms of the Coulomb branch moduli φi, (i = 1, · · · , 5) in (2.8), and the monopole string tension is given by taking the derivative of the effective prepotential with respect to the φi. The other comparison between the area and the monopole string tension may be interpreted as support for our claim that the diagram in figure 3 yields the SU(6).
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