7,493 research outputs found
Log-sine evaluations of Mahler measures, II
We continue the analysis of higher and multiple Mahler measures using
log-sine integrals as started in "Log-sine evaluations of Mahler measures" and
"Special values of generalized log-sine integrals" by two of the authors. This
motivates a detailed study of various multiple polylogarithms and worked
examples are given. Our techniques enable the reduction of several multiple
Mahler measures, and supply an easy proof of two conjectures by Boyd.Comment: 35 page
Log-sine evaluations of Mahler measures
We provide evaluations of several recently studied higher and multiple Mahler
measures using log-sine integrals. This is complemented with an analysis of
generating functions and identities for log-sine integrals which allows the
evaluations to be expressed in terms of zeta values or more general
polylogarithmic terms. The machinery developed is then applied to evaluation of
further families of multiple Mahler measures.Comment: 25 page
Integrable Quantum Field Theories in Finite Volume: Excited State Energies
We develop a method of computing the excited state energies in Integrable
Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate
compactified on a circle of circumference R. The IQFT ``commuting
transfer-matrices'' introduced by us (BLZ) for Conformal Field Theories (CFT)
are generalized to non-conformal IQFT obtained by perturbing CFT with the
operator . We study the models in which the fusion relations for
these ``transfer-matrices'' truncate and provide closed integral equations
which generalize the equations of Thermodynamic Bethe Ansatz to excited states.
The explicit calculations are done for the first excited state in the ``Scaling
Lee-Yang Model''.Comment: 54 pages, harvmac, epsf, TeX file and postscript figures packed in a
single selfextracting uufile. Compiles only in the `Big' mode with harvma
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