Modular factorization of superconformal indices

• DOI: 10.1007/jhep10(2023)105
• Publication Date: 2023-10-18T12:02:19Z
• Authors: Vishnu Jejjala; Yang Lei; Sam van Leuven; Wei Li
• Keywords: Diffeomorphism

A bstract Superconformal indices of four-dimensional $$ \mathcal{N} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action an SL(3, ℤ ) and SL(2, ⋉ 2 transformation. The former corresponds to gluing transformation latter overall large diffeomorphism, both associated with Heegaard splitting underlying geometry. extension more general transformations leads us argue that given index can be factorized in terms family blocks parametrized by (congruence sub)groups. find precise agreement between proposal new properties elliptic Γ function. This our conjecture for “modular factorization” superconformal lens theories. provide evidence context free chiral multiplet SQED sketch arguments Assuming validity conjecture, we systematically prove normalized part defines non-trivial first cohomology class ). Finally, use framework propose formula space index.