dinger Equation and Q-Operators of Conformal Field Theory
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dinger Equation and Q-Operators of Conformal Field Theory
3Ð4, 2001. Spectral Determinants for Schrodinger Equation and. Q-Operators of Conformal Field Theory. Vladimir V. Bazhanov,1 Sergei L. Lukyanov,2 and.
Journal of Statistical Physics, Vol. 102, Nos. 34, 2001
Spectral Determinants for Schrodinger Equation and Q-Operators of Conformal Field Theory Vladimir V. Bazhanov, 1 Sergei L. Lukyanov, 2 and Alexander B. Zamolodchikov 2 Received April 10, 2000 Relation between the vacuum eigenvalues of CFT Q-operators and spectral determinants of one-dimensional Schrodinger operator with homogeneous potential, recently conjectured by Dorey and Tateo for special value of Virasoro vacuum parameter p, is proven to hold, with suitable modification of the Schrodinger operator, for all values of p. KEY WORDS:
In recent remarkable paper (1) a novel relation was observed between the vacuum eigenvalues of so-called Q-operators introduced in ref. 2 and the spectral characteristics of the Schrodinger equation [ & 2x + |x| 2: ] 9(x)=E9(x)
(1)
Namely, for special value of the vacuum parameter p (see below) the vacuum eigenvalues of the operators Q + and Q & essentially coincide with the spectral determinants associated with the odd and even sectors of (1), respectively. In this note we show that a similar relation, with an appropriately generalized spectral problem (1), holds for all values of the vacuum parameter p. The Q operators were constructed in ref. 2 in our attempt to understand c
