标题： $\mathcal{N}=4$超Yang-Mills 的特殊凯勒几何 显示英文标题

标题： Special Kähler geometries of $\mathcal{N}=4$ superYang-Mills

摘要： The low energy effective theory on the moduli space of vacua of 4d superYang-Mills (sYM) theory defines a special Kähler geometry. For simple sYM gauge algebras, $\mathfrak{g}$, we classify all compatible special Kähler structures by showing that they are in one-to-one correspondence with certain equivalence classes of integral symplectic representations of the Weyl group of $\mathfrak{g}$. We further demonstrate that, for principal Dirac pairing, these equivalence classes are in one-to-one correspondence with the S-duality orbits of the global structures of the corresponding $\mathfrak{g}$ sYM gauge theory, after a mistake in the field theory literature is corrected. This provides a low-energy test of S-duality. We also discuss twisted product geometries made from factors with special Kähler structures with non-principal Dirac pairings. 显示英文摘要

摘要： The low energy effective theory on the moduli space of vacua of 4d superYang-Mills (sYM) theory defines a special K\"ahler geometry. For simple sYM gauge algebras, $\mathfrak{g}$, we classify all compatible special K\"ahler structures by showing that they are in one-to-one correspondence with certain equivalence classes of integral symplectic representations of the Weyl group of $\mathfrak{g}$. We further demonstrate that, for principal Dirac pairing, these equivalence classes are in one-to-one correspondence with the S-duality orbits of the global structures of the corresponding $\mathfrak{g}$ sYM gauge theory, after a mistake in the field theory literature is corrected. This provides a low-energy test of S-duality. We also discuss twisted product geometries made from factors with special K\"ahler structures with non-principal Dirac pairings.