A Compendium of Sphere Path Integrals

A Dirichlet-type integral on spheres, applied to the fluid/gravity correspondence

We evaluate an analogue of an integral of Dirichlet over the sphere S^D, but with an integrand that is independent of [(D + 1)/2] Killing coordinates. As an application, we evaluate an integral that arises when comparing a conformal fluid on S^D and black holes in (D + 2)-dimensional anti-de Sitter spacetime.

Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere

We study a perturbative expansion of the squashed 3-sphere ($S^3_b$) partition function of 3d $\mathcal{N}=2$ gauge theories around the squashing parameter $b= 1$. Our proposal gives the coefficients of the perturbative expansion as a finite sum over the saddle points of the supersymmetric-localization integral in the limit $b \rightarrow 0$ (the so-called Bethe vacua), and the contribution from each Bethe vacua can be systematically computed using saddle-point methods. Our expansion provides an efficient and practical method for computing basic CFT data ($F,C_T,C_{JJ}$ and higher-point correl…

The Casimir effect for a sphere and a cylinder in front of plane and corrections to the proximity force theorem

Using a path integral approach we rederive a recently found representation of the Casimir energy for a sphere and a cylinder in front of a plane and derive the first correction to the proximity force theorem.

同调3-球面上BF理论的三种定义

3 Definitions of BF Theory on Homology 3-Spheres

针对同调3-球面上的BF理论，通过规范选择将配分函数化为有限维矩阵积分，并提出留数、大k极限等三种定义，检验其对平坦联络求和/积分的捕捉程度。

Integration on quantum Euclidean space and sphere in $N$ dimensions

Invariant integrals of functions and forms over $q$ - deformed Euclidean space and spheres in $N$ dimensions are defined and shown to be positive definite, compatible with the star - structure and to satisfy a cyclic property involving the $D$ - matrix of $SO_q(N)$. The definition is more general than the Gaussian integral known so far. Stokes theorem is proved with and without spherical boundary terms, as well as on the sphere.

Poisson sigma model on the sphere

We evaluate the path integral of the Poisson sigma model on sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlato…

费米规范场的球面路径积分

Sphere path integrals for fermionic gauge fields

本文计算了四维球面上严格无质量费米规范场的单圈路径积分，用特征标表达并推广到任意自旋，证明对数发散由特征标编码且无虚相位，并确认无限塔费米子的体边抵消。

Casimir's energy of a conducting sphere and of a dilute dielectric ball

In this paper we sum over the spherical modes appearing in the expression for the Casimir energy of a conducting sphere and of a dielectric ball (assuming the same speed of light inside and outside), before doing the frequency integration. We derive closed integral expressions that allow the calculations to be done to all orders, without the use of regularization procedures. The technique of mode summation using a contour integral is critically examined.

Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model

U(n) Yang-Mills theory on the fuzzy sphere S^2_N is quantized using random matrix methods. The gauge theory is formulated as a matrix model for a single Hermitian matrix subject to a constraint, and a potential with two degenerate minima. This allows to reduce the path integral over the gauge fields to an integral over eigenvalues, which can be evaluated for large N. The partition function of U(n) Yang-Mills theory on the classical sphere is recovered in the large N limit, as a sum over instanton contributions. The monopole solutions are found explicitly.