Related papers: Affine Laumon spaces and integrable systems
We introduce a completely integrable system on the Grassmannian of 2-planes in an n-space associated with any triangulation of a polygon with n sides, and compute the potential function for its Lagrangian torus fiber. The moment polytopes…
We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism,…
We study the partition function of three-dimensional ${\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM…
In this paper we study the extension of Painlev\'e/gauge theory correspondence to circular quivers by focusing on the special case of $SU(2)$ $\mathcal{N}=2^*$ theory. We show that the Nekrasov-Okounkov partition function of this gauge…
We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained…
Motivated by possible applications to condensed matter systems, in this paper we construct U(N) noncommutative Chern-Simons (NCCS) action for a disc and for a double-layer geometry, respectively. In both cases, gauge invariance severely…
Using the Cartan-Kahler theory, and results on real algebraic structures, we prove two embedding theorems. First, the interior of a smooth, compact 3-manifold may be isometrically embedded into a G_2-manifold as an associative submanifold.…
We evaluate the Nekrasov partition function of 5d gauge theories engineered by webs of 5-branes, using the refined topological vertex on the dual Calabi-Yau threefolds. The theories include certain non-Lagrangian theories such as the T_N…
We explore the dynamics of three-dimensional Chern-Simons gauge theories with N=2 supersymmetry and matter in the fundamental and adjoint representations of the gauge group. Realizing the gauge theories of interest in a setup of threebranes…
It is proved that for $\alpha\in (0,1)$, $Q_\alpha(\rn)$, not only as an intermediate space of $W^{1,n}(\rn)$ and $BMO(\rn)$ but also as an affine variant of Sobolev space $\dot{L}^{2}_\alpha(\rn)$ which is sharply imbedded in…
In 2012, Nazarov used Bergman kernels and Hormander's $L^2$ estimates for the $\bar\partial$-equation to give a new proof of the Bourgain--Milman theorem for symmetric convex bodies and made some suggestions on how his proof should extend…
We study the mixed topological / holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold $(\Sigma\times{\mathbb C})/{\mathbb Z}_2$, obtaining a description of lattice integrable systems in the presence of a boundary.…
We conjecture, and show in a plethora of examples, that the sphere partition function of 3d $\mathcal{N}=4$ Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli…
We relate Nekrasov partition functions, with arbitrary values of $\epsilon_1,\epsilon_2$ parameters, to matrix models for $\beta$-ensembles. We find matrix models encoding the instanton part of Nekrasov partition functions, whose measure,…
The semiclassical approximation for the partition function in Chern-Simons gauge theory is derived using the invariant integration method. Volume and scale factors which were undetermined and had to be fixed by hand in previous derivations…
We started a program to study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane) several years ago. This paper is devoted to the case of resolved conifold with one out…
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a};\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant…
Starting from a $D=3$, $N=4$ supersymmetric theory for matter fields, a twist with a Grassmann parity change is defined which maps the theory into a gauge fixed, abelian $BF$ theory on curved 3-manifolds. After adding surface terms to this…
We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal $G$-bundle with connection and a class in $H^4(BG, \ZZ)$ for a compact semi-simple Lie group $G$. The Chern-Simons bundle…
We conjecture a new sequence of dualities between Chern-Simons gauge theories simultaneously coupled to fundamental bosons and fermions. These dualities reduce to those proposed by Aharony when the number of bosons or fermions is zero. Our…