Fiber-base duality from the algebraic perspective

Abstract

Quiver 5D $\mathcal{N}=1$ gauge theories describe the low-energy dynamics on webs of $(p,q)$-branes in type IIB string theory. S-duality exchanges NS5 and D5 branes, mapping $(p,q)$-branes to branes of charge $(-q,p)$, and, in this way, induces several dualities between 5D gauge theories. On the other hand, these theories can also be obtained from the compactification of topological strings on a Calabi-Yau manifold, for which the S-duality is realized as a fiber-base duality. Recently, a third point of view has emerged in which 5D gauge theories are engineered using algebraic objects from the Ding-Iohara-Miki (DIM) algebra. Specifically, the instanton partition function is obtained as the vacuum expectation value of an operator $\mathcal{T}$ constructed by gluing the algebra's intertwiners (the equivalent of topological vertices) following the rules of the toric diagram/brane web. Intertwiners and $\mathcal{T}$-operators are deeply connected to the co-algebraic structure of the DIM algebra. We show here that S-duality can be realized as the twist of this structure by Miki's automorphism.

49 pages, 7 figures (v3: statement on universal R-matrix corrected)

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Cited by in corpus (12)

• A slow review of the AGT correspondence
• Higgsed network calculus
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• Mixed network calculus
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Gauge origami and quiver W-algebras
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• A note on S-dual basis in free fermion system
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• Quantum $W_{1+\infty }$ subalgebras of BCD type and symmetric polynomials
• Intertwining operator and integrable hierarchies from topological strings