Yu Nakayama

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 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.

We present a systematic exploration of conformal field theories (CFTs) constrained by duality-inspired fusion rules using the conformal bootstrap. We classify the operator spectrum into three sectors: [ σ ], [ ε ], and [ 1 ] . The [ σ ] sector consists of all Z 2 -odd operators. The Z 2 -even operators are further divided into the [ ε ] sector, which contains only the operators that change sign under duality, and the [ 1 ] sector, which encompasses all remaining operators. We impose a selection rule motivated by Kramers-Wannier duality, specifically forbidding the appearance of the [ ε ] sector in the [ ε ] × [ ε ] operator product expansion. By applying this constraint to the lowest-lying relevant scalars, we derive bounds on their conformal dimensions ( Δ σ , Δ ε ) in dimensions d = 2 through d = 7 . Our bounds correctly allow the d = 2 Ising model while excluding the d = 3 Ising model, demonstrating the effectiveness of the imposed condition. Furthermore, we observe a distinct feature in d = 2 corresponding to the M ( 8 , 7 ) minimal model and find nontrivial constraints in d = 3 ( Δ σ ≳ 0.85 ), relevant for theories like QED 3 . This work opens a new avenue for nonperturbatively probing the landscape of CFTs constrained by fusion rules.

The factorization proposal claims that the codimension one “pinning defect,” on which a local relevant operator is integrated, factorizes the space into two halves in general conformal field theories in the infrared limit. In this paper, we study a two-dimensional long-range Ising model at criticality with a line defect or an interface, which physically corresponds to changing the local temperature on it. We show that in the perturbative regime, it is not factorizing even in the infrared limit. An intuitive explanation of the nonfactorization is that the long-range Ising model is equivalent to a local conformal field theory in higher dimensions. In this picture, the space is still connected through the “extra dimension” across the defect line.

A bstract: The fundamental theorem in renormalization group flows in two dimensions is the c -theorem, which dictates that the number of degrees of freedom must decrease monotonically along the renormalization group flow. The k -theorem claims that the number of charged degrees of freedom also decreases monotonically. Here, k is the current central charge defined by the two-point function of the current. A recent derivation of the c-theorem by Hartman and Mathys, which uses the three-point function sum rule and the positivity of the averaged null energy (ANE) operator, motivates us to seek a similar proof of the k -theorem. In the case of the k -theorem, the partial contact terms need to be taken into consideration. While ignoring the partial contact terms yields contradictory results, our careful analysis incorporating them leads to the correct sum rule and a complete proof based on the positivity of the ANE operator.

A bstract: It is long known that A-series minimal models and D-series minimal models are exchanged by gauging the invertible ℤ ₂ symmetry. More recently, it has been shown that A-series minimal models and E-series minimal models are exchanged by gauging a non-invertible symmetry. We complete the triality picture by showing that D-series minimal models and E-series minimal models are exchanged by gauging another non-invertible symmetry.

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: The extended Majorana Nicolai model is one of the simplest models of supersymmetry realized on a fermionic chain in 1 + 1 dimensions. Within a certain parameter region, the extended theory breaks the supersymmetry spontaneously, but it has a distinguished feature that the general counting rule of the Nambu-Goldstone mode does not apply: we observe twice as many low-energy degrees of freedom than the broken lattice symmetry. We argue that the extra degrees of freedom originate from the spontaneous breaking of the emergent chiral supersymmetry. This chiral supersymmetry becomes an emanant symmetry in the non-interacting limit.