Related papers: Grand Partition Functions of Little Matrix Models …

We study the dynamics of a BPS D3-brane wrapped on a three-sphere in AdS_5 x L, a so-called dual giant graviton, where L is a Sasakian five-manifold. The phase space of these configurations is the symplectic cone X over L, and geometric…

We study the low energy effective action of the $\Omega$-deformed $\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $\epsilon_{1},\epsilon_{2}$, the scalar field expectation value $a$, and the…

We perform two independent calculations of the two-loop partition function for the large N 't Hooft limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane.…

The nonabelian Berry phase is computed in the T dualized quantum mechanics obtained from the USp(2k) matrix model. Integrating the fermions, we find that each of the spacetime points X_{\nu}^{(i)} is equipped with a pair of su(2) Lie…

We continue our study on the partition function for 5D supersymmetric Yang-Mills theory on toric Sasaki-Einstein $Y^{p,q}$ manifolds. Previously, using the localisation technique we have computed the perturbative part of the partition…

For quantum field theories with global symmetry, we can study the behavior of the partition function with the background gauge field to diagnose different quantum phases. For the case of discrete symmetries, we find that the…

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related…

We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno's. In order to achieve the generalization we need to define a…

Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the…

We study BPS monopoles in 4 dimensional N=4 SO(N) and $Sp(N)$ super Yang-Mills theories realized as the low energy effective theory of $N$ (physical and its mirror) parallel D3 branes and an {\it Orientifold 3 plane} with D1 branes…

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix…

For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2x2 polynomial differential systems satisfied by the associated orthogonal polynomials is…

We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main…

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry…

We consider the computation of the topological string partition function for 5-brane web diagrams with an O7$^-$-plane. Since upon quantum resolution of the orientifold plane these diagrams become non-toric web diagrams without the…

Supersymmetric sectors of $\mathcal{N}=4$ super-Yang-Mills theory motivate the study of the partition function for the counting of gauge-invariant functions of $d=2,3$ matrices transforming under the adjoint action of $U(N)$. The partition…

Some matrix models admit, on top of the usual 't Hooft expansion, an M-theory-like expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N. These models, which we call M-theoretic…

We write down an explicit conjecture for the instanton partition functions in 4d N=2 SU(N) gauge theories in the presence of a certain type of surface operator. These surface operators are classified by partitions of N, and for each…

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less…

We propose a minimal SO(10) model in 5 space-time dimensions. The single extra spatial dimension is compactified on the orbifold S^1/(Z_2 x Z_2') reducing the gauge group to that of Pati-Salam. The breaking down to the standard model group…