Abstract
We discuss generalized partition function of 2d CFTs on thermal cylinder decorated by higher qKdV charges. We propose that in the large central charge limit qKdV charges factorize such that generalized partition function can be rewritten in terms of auxiliary non-interacting bosons. The explicit expression for the generalized free energy is readily available in terms of the boson spectrum, which can be deduced from the conventional thermal expectation values of qKdV charges. In other words, the picture of the auxiliary non-interacting bosons allows extending thermal one-point functions to the full non-perturbative generalized partition function. We verify this conjecture for the first seven qKdV charges using recently obtained pertrubative results and find corresponding contributions to the auxiliary boson masses. We further extend these results by conjecturing the full spectrum of bosons and find an exact expression for the generalized partition function as a function of infinite tower of chemical potentials in the limit of large central charge.
Highlights
We discuss generalized partition function of 2d CFTs on thermal cylinder decorated by higher qKdV charges
We propose that in the large central charge limit qKdV charges factorize such that generalized partition function can be rewritten in terms of auxiliary non-interacting bosons
The explicit expression for the generalized free energy is readily available in terms of the boson spectrum, which can be deduced from the conventional thermal expectation values of qKdV charges
Summary
In this paper we are concerned with the extensive part of free energy, i.e. we are taking thermodynamic limit by taking the size of the spatial circle to infinity → ∞, while c is. In this limit the only relevant contributions to (1.1) are those when Q2k−1 contribute extensively, i.e. scale linearly with. We assume that ∆ scales as 2 while the scaling of σr ∝ r+1 follows from its explicit form. This result agrees with the calculation of [15], which utilizes the explicit form of Q3 in terms of Virasoro algebra generators. Where the last term came from c2E6Dk−3χ, k = 3 This result is in full agreement with the explicit calculation of [15]. Calculation of the eigenvalues of Q11 and Q13 is completely analogous, but to rewrite the leading part of Tr∆(qL0Q2k−1) as a linear combination of Dk and terms of the form ck−1−pE2(k−p)Dp, p = 0, .
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