Tadashi Okazaki

A bstract: We investigate holographic spectral functions for general Sasaki-Einstein 5-manifolds dual to four-dimensional superconformal field theories, including supersymmetric indices, supersymmetric zeta functions, and supersymmetric determinants. The analytic structure of the supersymmetric zeta function, particularly its residue and special value, allows for the computation of the curvature-squared integral of the Sasaki-Einstein manifold and the subleading holographic anomaly. The reach of this spectral framework is not restricted to toric geometries and accommodates non-toric Sasaki-Einstein manifolds. For toric Sasaki-Einstein manifolds, we develop a combinatorial method to compute the holographic spectral functions and the holographic geometric invariants directly from the toric data.

A bstract: We examine the giant graviton expansions of the Higgs indices for the 3d 𝒩 = 4 U ( N ) ADHM theories with l fundamental hypermultiplets. The indices for the M5-brane giant gravitons of wrapping number m appearing in the expansions consist of the contributions that generalize the characters of the W-algebra 𝒲(𝔤𝔩( m )) and those which realize the characters of the affine Kac-Moody algebras of type A _{l −1} . Also we confirm that the inverse giant graviton expansions of the resulting M5-brane indices consistently reproduce the Higgs indices.

A bstract: We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of the supersymmetric indices and the supersymmetric Casimir energies associated with the supersymmetric partition functions. We investigate a variety of examples of the supersymmetric zeta functions and determinants for two-, four-, and six-dimensional supersymmetric field theories.

A bstract: We propose SL(2, ℤ) dualities of supersymmetric boundary conditions in the three-dimensional supersymmetric field theories describing a semi-infinite M2-brane terminating on M5-branes. Specifically, we present dualities of boundary conditions for Abelian (quiver) ADHM theories and circular quiver Chern-Simons matter theories including the ABJM model. For the circular quiver Chern-Simons theories we take boundary conditions breaking a U(1) ₁ × U(1) ₋₁ gauge group to its diagonal subgroup which is decoupled. This can be generalized to break U(1) _k × U(1) _{− k} , leaving a ℤ _k gauge theory. We find matching of the ’t Hooft anomalies and supersymmetric half-indices for all the proposed dual boundary conditions.

We define supersymmetric zeta functions and supersymmetric determinants, which can reveal spectral properties complementary to those captured by the supersymmetric indices. They play a crucial role in analyzing the Cardy-like behaviors of the supersymmetric indices and the supersymmetric Casimir energies associated with the supersymmetric partition functions. We investigate a variety of examples of the supersymmetric zeta functions and determinants for two-, four-, and six-dimensional supersymmetric field theories.