Related papers: Spectral zeta function and non-perturbative effect…
The partition function on the three-sphere of ABJ theory can be rewritten into a partition function of a non-interacting Fermi gas, with an accompanying one-particle Hamiltonian. We study the spectral problem defined by this Hamiltonian. We…
The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this…
The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas…
We develop a method to obtain fermion spectral functions non-perturbatively in a non-Abelian gauge theory with high occupation numbers of gauge fields. After recovering the free field case, we extract the spectral function of fermions in a…
We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local P^1*P^1 Calabi-Yau geometry. In…
Formulas for the most general case of the zeta function associated to a quadratic+linear+constant form (in {\bf Z}) are given. As examples, the spectral zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to…
We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1,2,3,4,6 up to N=44,20,18,16,14 respectively, and extract…
We study various properties of a nonperturbative partition function which can be associated to any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix…
The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N…
We investigate the large $N$ instanton effects of partition functions in a class of $\mathcal{N}=4$ circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas…
We develop a general theory of Fermi polarons at nonzero temperature, including particle-hole excitations of the Fermi sea shake-up to arbitrarily high orders. The exact set of equations of the spectral function is derived by using both…
Noninteracting fermions, placed in a system with a continuous density of states, may have zeros in the $N$-fermion canonical partition function on the positive real $\beta$ axis (or very close to it), even for a small number of particles.…
Explicit formulas for the zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to fermionic ($\alpha =3$) quantum fields living on a noncommutative, partially toroidal spacetime are derived. Formulas for the most…
Using the AdS/CFT correspondence, we calculate a fermionic spectral function in a 2+1 dimensional non-relativistic quantum field theory which is dual to a gravitational theory in the $AdS_4$ background with a charged black hole. The…
We study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop the method to compute the grand partition function of the ABJM theory, and compute exactly the partition function Z(N) up to N=9 when the Chern-Simons…
We calculate non-perturbative self-consistent fermionic and bosonic spectral functions of ultra-cold Fermi gases with the spectral functional approach. This approach allows for a direct real-time computation of non-perturbative correlation…
We discuss a possible spectral realization of the Riemann zeros based on the Hamiltonian $H = xp$ perturbed by a term that depends on two potentials, which are related to the Berry-Keating semiclassical constraints. We find perturbatively…
Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a…
We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a hermitian…
We review recent progress in determining the partition function of the ABJM theory in the large N expansion, including all of the perturbative and non-perturbative corrections. Especially, we will focus on how these exact expansions are…