Two-Term Dilogarithm Identities Related to Conformal Field Theory

@article{Bytsko1999TwoTermDI,
  title={Two-Term Dilogarithm Identities Related to Conformal Field Theory},
  author={Andrei Bytsko},
  journal={Letters in Mathematical Physics},
  year={1999},
  volume={50},
  pages={213-228}
}
  • A. Bytsko
  • Published 1 November 1999
  • Mathematics
  • Letters in Mathematical Physics
AbstractWe study 2 × 2 matrices A such that the corresponding thermodynamic Bethe ansatz (TBA) equations yield $$ c\left[ A \right] $$ in the form of the effective central charge of a minimal Virasoro model. Certain properties of such matrices and the corresponding solutions of the TBA equations are established. Several continuous families and a discrete set of admissible matrices A are found. The corresponding two-term dilogarithm identities (some of which appear to be new) are obtained… 

Special values of Legendre's chi-function and the inverse tangent integral

. In our recent publication in this Bulletin [88 Winter (2021), 31–37] a series transform proved via Fourier–Legendre theory and fractional operators in a 2022 article was applied to prove five

On the Accessibility of Khoi’s Dilogarithm Identity Involving the Golden Ratio

In this note, I make use of the Rogers five-term functional relation for the dilogarithm function with a suitable choice of arguments to show that a two-term dilogarithm identity involving the golden

Institute for Mathematical Physics

Collection of Abstracts of the Lectures which will be given at the International Workshop \Mathematical Physics { today, Priority Technologies { for tomorrow"

Some simple proofs of Lima's two-term dilogarithm identity

  • S. Stewart
  • Mathematics
    Irish Mathematical Society Bulletin
  • 2022
. Recently, Lima found a remarkable two-term dilogarithm identity whose proof was based on a hyperbolic form of a proof for the Basel problem given by Beukers, Kolk, and Calabi. A number of simple

On the Accessibility of Khoi’s Dilogarithm Identity Involving the Golden Ratio

  • F. Lima
  • Materials Science
    Vietnam Journal of Mathematics
  • 2016
In this note, I make use of the Rogers five-term functional relation for the dilogarithm function with a suitable choice of arguments to show that a two-term dilogarithm identity involving the golden

New definite integrals and a two-term dilogarithm identity from a hyperbolic version of Calabi's change of variables

Among the several proofs known for  ∞ n = 1 1 / n 2 = π 2 / 6, the one given by Beukers, Calabi, and Kolk involves the evaluation of  10  10 1 /( 1 − x 2 y 2 ) d x d y . It starts by showing that

References

SHOWING 1-10 OF 13 REFERENCES

The theory of partitions

1. The elementary theory of partitions 2. Infinite series generating functions 3. Restricted partitions and permutations 4. Compositions and Simon Newcomb's problem 5. The Hardy-Ramanujan-Rademacher

Phys

  • Lett. B304
  • 1993

J. Phys

  • J. Phys
  • 1999

Fermionic representations for characters of calM(3,t), calM(4,5), calM(5,6) and calM(6,7) minimal models and related dilogarithm and Rogers-Ramanujan-type identities

Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various

Ramanujan J

  • 1
  • 1997

Nucl. Phys

  • Nucl. Phys
  • 1990

Progr

  • Theor. Phys. Suppl. 118
  • 1995

JETP

  • JETP
  • 1985