Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new user3D Topological Models and Heegaard Splitting I: Partition Function
217
0
0.0
(
0
)
Authors
Frank Thuillier
Ask ChatGPT about the research
No Arabic abstract
The aim of this article is twofold: firstly, we show how to recover the smooth Deligne-Beilinson cohomology groups from a Heegaard splitting of a closed oriented smooth 3-manifold by extending the usual tch-de Rham construction; secondly, thanks to the above and still relying on a Heegaard splitting, we explain how to compute the partition functions of the $U(1)$ Chern-Simons and BF theories.
rate research
Read More
In a previous article, a construction of the smooth Deligne-Beilinson cohomology groups $H^p_D(M)$ on a closed $3$-manifold $M$ represented by a Heegaard splitting $X_L cup_f X_R$ was presented. Then, a determination of the partition functions of the $U(1)$ Chern-Simons and BF Quantum Field theories was deduced from this construction. In this second and concluding article we stay in the context of a Heegaard spitting of $M$ to define Deligne-Beilinson $1$-currents whose equivalent classes form the elements of $H^1_D(M)^star$, the Pontryagin dual of $H^1_D(M)$. Finally, we use singular fields to first recover the partition functions of the $U(1)$ Chern-Simons and BF quantum field theories, and next to determine the link invariants defined by these theories. The difference between the use of smooth and singular fields is also discussed.
An algebraic structure, Quotient Algebra Partition or QAP, is introduced in a serial of articles. The structure QAP is universal to Lie Algebras and enables algorithmic and exhaustive Cartan decompositions. The first episode draws the simplest form of the structure in terms of the spinor representation.
We use techniques in the shuffle algebra to present a formula for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charges at certain inverse temperature $beta$ in terms of the Berezin integral of an associated non-homogeneous alternating tensor. This generalizes previously known results by removing the restriction on the number of species of odd charge. Our methods provide a unified framework extending the de Bruijn integral identities from classical $beta$-ensembles ($beta$ = 1, 2, 4) to multicomponent ensembles, as well as to iterated integrals of more general determinantal integrands.
This paper develops a method to carry out the large-$N$ asymptotic analysis of a class of $N$-dimensional integrals arising in the context of the so-called quantum separation of variables method. We push further ideas developed in the context of random matrices of size $N$, but in the present problem, two scales $1/N^{alpha}$ and $1/N$ naturally occur. In our case, the equilibrium measure is $N^{alpha}$-dependent and characterised by means of the solution to a $2times 2$ Riemann--Hilbert problem, whose large-$N$ behavior is analysed in detail. Combining these results with techniques of concentration of measures and an asymptotic analysis of the Schwinger-Dyson equations at the distributional level, we obtain the large-$N$ behavior of the free energy explicitly up to $o(1)$. The use of distributional Schwinger-Dyson is a novelty that allows us treating sufficiently differentiable interactions and the mixing of scales $1/N^{alpha}$ and $1/N$, thus waiving the analyticity assumptions often used in random matrix theory.
In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the models partition function.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
