Related papers: Three-manifold invariant from functional integrati…
In this paper, we apply ideas of Dijkgraaf and Witten on 2+1 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define…
In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The…
The refined Chern-Simons theory is a one-parameter deformation of the ordinary Chern-Simons theory on Seifert manifolds. It is defined via an index of the theory on N M5 branes, where the corresponding one-parameter deformation is a natural…
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 investigate the Reshetikhin--Turaev invariants associated to SU(2) for the 3-manifolds M obtained by doing any rational surgery along the figure 8 knot. In particular, we express these invariants in terms of certain complex double…
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…
Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…
We construct the (enhanced Rogers) dilogarithm function from the spin Chern-Simons invariant of C*-connections. This leads to geometric proofs of basic dilogarithm identities and a geometric context for other properties, such as the…
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae…
We observe a property of orthogonality of the Mellin-Barnes transformation of the triangle one-loop diagrams, which follows from our previous papers [JHEP {\bf 0808} (2008) 106, JHEP {\bf 1003} (2010) 051, JMP {\bf 51} (2010) 052304]. In…
We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar…
We introduce the notion of round surgery diagrams in $S^3$ for representing 3-manifolds similar to Dehn surgery diagrams. We give a correspondence between a certain class of round surgery diagrams and Dehn surgery diagrams for 3-manifolds.…
Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of…
We lay down a general framework for how to construct a Topological Quantum Field Theory $Z_A$ defined on shaped triangulations of orientable 3-manifolds from any Pontryagin self-dual locally compact abelian group $A$. The partition function…
We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four…
The logarithm of the Kontsevich-Kuperberg-Thurston invariant counts embeddings of connected trivalent graphs in an oriented rational homology sphere, using integrals on configuration spaces of points in the given manifold. It is a universal…
In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds…
For any complete hyperbolic three-manifold of finite volume, we construct a mixed Tate motive defined over the invariant trace field whose image under Beilinson regulator equals the PSL2(C)-Chern-Simons invariant, thus equals the complex…
We construct a topological Chern-Simons sigma model on a Riemannian three-manifold M with gauge group G whose hyperkahler target space X is equipped with a G-action. Via a perturbative computation of its partition function, we obtain new…
In this paper, we will analyse a three dimensional supersymmetric Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry, breaks half the supersymmetry of the Lorentz invariant…