有限温度下一般维度的共形缺陷
Conformal defects of general dimensions at finite temperature
- The University of Osaka（大阪大学）
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AI总结：
本文研究有限温度下一般维度共形缺陷的热单点函数，通过对称性和守恒定律确定其一般形式，并在自由理论例子中验证，发现界面情形与Dirichlet边界条件一致。
AI中文摘要：
我们考虑有限温度下的缺陷共形场论（DCFTs），其中$p$维共形缺陷环绕热圆。将先前对线缺陷的研究推广到一般维度的缺陷，我们通过施加剩余对称性和守恒定律，确定了体标量、守恒流和应力张量的热单点函数的一般形式。热单点函数的低温展开被证明可由体-缺陷算符展开重现，从而允许我们读出缺陷算符的热单点系数。我们在四类具有自由体理论的例子中检验了这些一般结果：平凡缺陷、具有边界的自由标量和费米子理论、$d=2\\,p+2$维中具有局域$\phi$形变的自由标量理论，以及$d=p+2-\epsilon$维中具有局域$\phi^2$形变的自由$\mathrm{O}(N)$模型。在最后一个$\epsilon = 1$的例子中，缺陷变为界面，我们发现热单点函数与具有Dirichlet边界条件的自由标量理论的热单点函数一致，这与界面CFT分解为两个解耦边界CFT的猜想因式分解相符。
英文摘要：
We consider defect conformal field theories (DCFTs) at finite temperature, where a $p$-dimensional conformal defect wraps the thermal circle. Extending the previous study of line defects to defects of general dimensions, we determine the general forms of the thermal one-point functions of bulk scalars, conserved currents and the stress tensor by imposing the residual symmetry and the conservation laws. The low temperature expansion of the thermal one-point functions is shown to be reproduced by the bulk-defect operator expansion, allowing us to read off the thermal one-point coefficients of defect operators. We examine the general results in four classes of examples with free bulk theories: the trivial defect, free scalar and fermion theories with a boundary, the free scalar theory with a localized $ϕ$ deformation in $d=2\,p+2$ dimensions and the free $\mathrm{O}(N)$ model with a localized $ϕ^2$ deformation in $d=p+2-ε$ dimensions. In the last example with $ε= 1$, where the defect becomes an interface, we find that the thermal one-point functions coincide with those of the free scalar theory with the Dirichlet boundary condition, in accordance with the conjectured factorization of an interface CFT into two decoupled boundary CFTs.
