In this paper we study the boundary effects for off-critical integrable field theories which have close analogues with integrable lattice models. Our models are the coset conformal field theories perturbed by an integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the thermodynamic Bethe ansatz (TBA) method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion restricted solid-on-solid (RSOS) lattice models. For super conformal field theories (CFTs) ( k = 2) we show that these flows are possible only for the Neveu-Schwarz sector and are consistent with the lattice results. The models we consider cover a wide class of integrable models. In particular, we show how the impurity spin is screened by electrons for the k -channel Kondo model by taking the limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.In this paper we study the boundary effects for off-critical integrable field theories which have close analogues with integrable lattice models. Our models are the coset conformal field theories perturbed by an integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the thermodynamic Bethe ansatz (TBA) method, we verify the flows of the conformal BCs by computing the boundary entropies. These flows of the BCs have direct interpretations for the fusion restricted solid-on-solid (RSOS) lattice models. For super conformal field theories (CFTs) ( k = 2) we show that these flows are possible only for the Neveu-Schwarz sector and are consistent with the lattice results. The models we consider cover a wide class of integrable models. In particular, we show how the impurity spin is screened by electrons for the k -channel Kondo model by taking the limit. We also study the problem using an independent method based on the boundary roaming TBA. Our numerical results are consistent with the boundary CFTs and RSOS TBA analysis.

arXiv:hep-th/9805101Journal of Physics A Mathematical and GeneralJan 1, 199959 citations

Universal spectrum of 2d conformal field theory in the large c limit

Thomas Hartman, Christoph A. Keller, Bogdan Stoica

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all $\Delta \ge \frac{c}{6}$ . The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much stronger form of universality holds in theories with a large central charge c and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all $$ \Delta \ge \frac{c}{6} $$ . The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.

arXiv:1405.5137Journal of High Energy PhysicsSep 1, 2014396 citations

Temperature corrections to conformal field theory

Fabian H. L. Eßler, V. E. Korepin, F. T. Latrémolière

arXiv:cond-mat/9801122The European Physical Journal BOct 1, 19984 citations

Physics of conformal field theories

Yevgeny Kats

Jan 1, 20100 citations

Topological and geometric universal thermodynamics in conformal field theory

Haoxin Wang, Lei Chen, Hai Lin +1 more

Universal thermal data in conformal field theory (CFT) offer a valuable means for characterizing and classifying criticality. With improved tensor network techniques, we investigate the universal thermodynamics on a nonorientable minimal surface, the crosscapped disk (or real projective plane, ${\mathbb{RP}}^{2}$ ). Through a cut-and-sew process, ${\mathbb{RP}}^{2}$ is topologically equivalent to a cylinder with rainbow and crosscap boundaries. We uncover that the crosscap contributes a fractional topological term $\frac{1}{2}lnk$ related to a nonorientable genus, with $k$ a universal constant in two-dimensional CFT, while the rainbow boundary gives rise to a geometric term $\frac{c}{4}ln\ensuremath{\beta}$, with $\ensuremath{\beta}$ the manifold size and $c$ the central charge. We have also obtained analytically the logarithmic rainbow term by CFT calculations, and discuss its connection to the renowned Cardy-Peschel conical singularity.Universal thermal data in conformal field theory (CFT) offer a valuable means for characterizing and classifying criticality. With improved tensor network techniques, we investigate the universal thermodynamics on a nonorientable minimal surface, the crosscapped disk (or real projective plane, ${\mathbb{RP}}^{2}$). Through a cut-and-sew process, ${\mathbb{RP}}^{2}$ is topologically equivalent to a cylinder with rainbow and crosscap boundaries. We uncover that the crosscap contributes a fractional topological term $\frac{1}{2}lnk$ related to a nonorientable genus, with $k$ a universal constant in two-dimensional CFT, while the rainbow boundary gives rise to a geometric term $\frac{c}{4}ln\ensuremath{\beta}$, with $\ensuremath{\beta}$ the manifold size and $c$ the central charge. We have also obtained analytically the logarithmic rainbow term by CFT calculations, and discuss its connection to the renowned Cardy-Peschel conical singularity.

arXiv:1801.07635Physical review. B./Physical review. BJun 28, 20187 citations

\Delta \ge \frac{c}{6}

. The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal ‘enigma’ saddlepoints in the thermodynamics of 3d gravity.

{\mathbb{RP}}^{2}

). Through a cut-and-sew process,

{\mathbb{RP}}^{2}

is topologically equivalent to a cylinder with rainbow and crosscap boundaries. We uncover that the crosscap contributes a fractional topological term

\frac{1}{2}lnk

related to a nonorientable genus, with

k

a universal constant in two-dimensional CFT, while the rainbow boundary gives rise to a geometric term $\frac{c}{4}ln\ensuremath{\beta}$, with $\ensuremath{\beta}$ the manifold size and

c

the central charge. We have also obtained analytically the logarithmic rainbow term by CFT calculations, and discuss its connection to the renowned Cardy-Peschel conical singularity.