Conformal defects of general dimensions at finite temperature
Abstract
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 O(N) model with a localized ϕ2 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.
Related
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BibTeX
@misc{li2026conformal,
title = {{Conformal defects of general dimensions at finite temperature}},
author = {Yucheng Li and Haruki Nakayama and Tatsuma Nishioka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.12720},
eprint = {2609.12720},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12720},
}
RIS
TY - UNPB
TI - Conformal defects of general dimensions at finite temperature
AU - Yucheng Li
AU - Haruki Nakayama
AU - Tatsuma Nishioka
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.12720
UR - https://arxiv.org/abs/2609.12720
AB - 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 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.
ER -