Instanton-Monopole Correspondence from M-Branes on ${\mathbb{S}}^1$ and Little String Theory

Abstract

We study BPS excitations in M5-M2-brane configurations with a compact transverse direction, which are also relevant for type IIa and IIb little string theories. These configurations are dual to a class of toric elliptically fibered Calabi-Yau manifolds $X_N$ with manifest $SL(2,\mathbb{Z})\times SL(2,\mathbb{Z})$ modular symmetry. They admit two dual gauge theory descriptions. For both, the non-perturbative partition function can be written as an expansion of the topological string partition function of $X_N$ with respect to either of the two modular parameters. We analyze the resulting BPS counting functions in detail and find that they can be fully constructed as linear combinations of the BPS counting functions of M5-M2-brane configurations with non-compact transverse directions. For certain M2-brane configurations, we also find that the free energies in the two dual theories agree with each other, which points to a new correspondence between instanton and monopole configurations. These results are also a manifestation of T-duality between type IIa and IIb little string theories.

48 Pages; v2. a footnote is updated and a reference is added; v3. a misplaced file is replaced, v4. version to be published

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Cited by in corpus (28)

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• Triality in Little String Theories
• Self-Duality and Self-Similarity of Little String Orbifolds
• Dual Little Strings and their Partition Functions
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• From Little String Free Energies Towards Modular Graph Functions
• Green-Schwarz Automorphisms and 6D SCFTs
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• Bound States of Little Strings and Symmetric Orbifold CFTs
• Five-Brane Webs and Highest Weight Representations
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• Elliptic modular double and 4d partition functions
• The ABCDEFG of Little Strings
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• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Little String Defects and Bala-Carter Theory
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• $DE$-type little strings from glued brane webs
• A string realisation of $\Omega$-deformed Abelian $\mathcal{N}=2^{\ast }$ theory
• Symmetries in A-Type Little String Theories, Part I
• Compactified Webs and Domain Wall Partition Functions
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras
• Domain walls and M2-branes partition functions: M-theory and ABJM Theory