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… 
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References

SHOWING 1-10 OF 13 REFERENCES

Purely elastic scattering theories and their ultraviolet limits

Fermionic quasi-particle representations for characters of (G (1) ) 1 × (G (1) ) 1 /(G (1) ) 2

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